Method that models multiphase signals in the same graph

Abstract

A method for modeling and analysing single-phase or multiphase digital signals in an angular coordinate axis defined depending on the signal's arguments and phase angles in a device having information processing capability is disclosed, a system comprising instructions operating on a device having a processor for applying the method of the invention to various signals and various angular axes, and a novel method for estimating signal vectors for multiphase signals at angular phases not provided as input signals. In the inventive method, single-phase or multi-phase digital signals received from a data source are displayed on an angular coordinate axis defined depending on the independent variables and phase angles of the signal. Depending on signal variables such as resolution amounts of the parameters desired to be displayed on the angular coordinate axis in the signal, linear or non-linear increase amounts, lower and upper limit values, a graphic pattern is created that is divided into sections called segments and layers (grids) on the angular coordinate axis. The signal is then expressed in segments and layers of the graph on the angular coordinate axis with numerical values, colours, symbols, signs or other visual elements. The method of the present invention can be used in devices with information processing capacity and can be used in modeling all kinds of signals. The method was implemented in a signal modeling system designed using the method, and various single-phase and multi-phase signals were tested on this system.

Description

[0001] DESCRIPTION

[0002] METHOD THAT MODELS MULTIPHASE SIGNALS IN THE SAME GRAPH

[0003] FIELD OF THE INVENTION

[0004] This invention, in general terms, relates to a digital signal processing method that can model all single-phase or multi-phase time series (digital) signals in the same graph, a signal vector estimation method that provides benefits in realizing the method, and a signal modeling system that is realized by applying the method of invention. More specifically, it relates to a method for modeling single-phase or multi-phase digital signals on a graph on an angular axis and a system implemented to implement the method.

[0005] BRIEF DESCRIPTION OF THE INVENTION

[0006] Within the scope of the present invention, a method as defined in claim-1 and detailed herein, and a signal modeling system as defined in claim-3, which is formed for the purpose of performing the method of claim-1 on various signals, are described by way of non-limiting examples which are intended only for a better understanding of the subject matter.

[0007] In the signal modeling system running on a device with information processing capacity, the number of segments and layers are first determined according to the resolution, linear or non-linear enhancement and limit values of the digital signal to be modelled on the angular axis. An angular coordinate axis is defined depending on the phase angles of the signal and its independent variables. On this angular axis, a graph pattern is defined to model the signal. The graphical pattern is divided into sections depending on the number of segments and layers, and the methods for calculating each of these sections are determined. The inventive method models and analyses the change in phase angles of a digital signal on an angular coordinate axis defined according to the independent variable components of the signal (time, frequency, etc.) or, if desired, the change against other signal parameters using the same independent variable. Furthermore, a new method is explained that estimates other vector signals between two vector signals, starting from two vector signals of the same length with a certain phase angle between them, with a linear interpolation-based method developed within the scope of the invention.

[0008] Instead of graphically modeling the change in the dependent variables of a signal with respect to an independent variable on any coordinate axis in the state of the art, the invention allows the dependent variables of the signal to be expressed on an angular coordinate axis defined by the independent variables and phase angles of the signal, which simplifies many signal processing methods on a digital signal and makes it possible to express multiphase signals in a single graph. Moreover, with the method of invention, different signal parameters using the same independent variable have the opportunity to be expressed on the same angular graph.

[0009] DESCRIPTION OF THE REFERENCE NUMBERS IN THE FIGURES

[0010] S01 : Input signal receiving unit

[0011] S02 : Signal analysis window identifier

[0012] S03 : Layer and segment identifier

[0013] S04 : Angular axis and graphic identifier

[0014] S05 : Signal analysis loop unit

[0015] S06 : Signal vector estimation unit

[0016] S07 : Signal parameters identifier

[0017] S08 : Signal representation format identifier

[0018] S09 : Graphic display continuity provider

[0019] S10 : Loop initial values unit

[0020] S11 : Layer and segment loops unit

[0021] S12 : Layer and segment boundary identifier

[0022] S13 : Signal to be displayed identifier

[0023] S14 : Signal visualization unit

[0024] S15 : Layer and segment loop continuation unit

[0025] S16 : Graphic display continuity disabler

[0026] S17 : Signal analysis window progressor

[0027] S18 : Program terminator

[0028] 301: Input signal receiving unit

[0029] 302: Signal analysis window identifier

[0030] 303: Layer and segment identifier

[0031] 304: Angular axis and graphic identifier

[0032] 305: Signal analysis loop unit

[0033] 306: Signal vector estimation unit

[0034] 306b: New array calculator from input array

[0035] 306a: Input array copier to new array

[0036] 307: Signal parameters identifier

[0037] 308: Signal representation format identifier

[0038] 309: Graphic display continuity provider

[0039] 310: Loop initial values unit

[0040] 311: Layer and segment loop unit 311a: Layer loop unit

[0041] 311b: Segment loop unit

[0042] 312: Layer and segment boundary identifier

[0043] 313: Signal to be displayed identifier

[0044] 314: Signal visualization unit

[0045] 315a: Segment loop continuation unit

[0046] 315b: Layer loop continuation unit

[0047] 315c: Graphic display labels unit

[0048] 316: Graphic display continuity disabler

[0049] 317: Signal analysis window stepper

[0050] 318: Program terminator

[0051] EXPLANATIONS OF ABBREVIATIONS

[0052] Angular coordinate axis: A defined coordinate axis dependent on phase angles and independent variables

[0053] Signall: Single-phase signals, where a signal emitted from a source exhibits the same behaviour in all angular directions for any instant of time, and / or signals where the signal is analysed by sampling in a single angular direction.

[0054] Signal2: Multiphase signals in which a signal emitted from a source exhibits different characteristics in different angular directions and / or signals in which the signal is sampled and analysed in more than one angular direction.

[0055] Segment: A representation of the signal to be displayed in a graphic pattern on an angular coordinate axis, divided into sections (grids) depending on variations such as the resolution of the signal, linear or nonlinear enhancement, lower and upper limit values, etc., with any of the sections seeing any phase angle of the angular axis.

[0056] Layer: The representative expression of the set formed by all segments of the graph when a full tour is made along the phase angles in the graph starting from the first element of any segment row, by dividing the signal to be displayed in a graphic pattern on the angular coordinate axis into sections (grids) depending on changes such as the resolution of the signal, linear or non-linear increase, lower and upper limit values.

[0057] Array: the general definition of a data array, which is a one-dimensional (vector), 2-dimensional (matrix) or higher dimensional data set. EEG: Electroencephalogram

[0058] EKG: Electrocardiogram

[0059] EMG: Electromyogram

[0060] FFT : Fast Fourier Transform

[0061] DESCRIPTION OF THE FIGURES

[0062] In order to more clearly describe the solutions embodied in the embodiments of the present invention or in the prior art, reference is briefly made to the necessary drawings defined for the following embodiments or prior art. Significantly, the following figures and drawings illustrate only some embodiments of the present invention, and a person of ordinary skill in the art will be able to obtain further drawings from these associated drawings using the method of the invention without creative effort. The drawings are not necessarily to scale and may omit details that are not necessary to understand the present Invention. Furthermore, elements that are at least substantially identical or have at least substantially identical functions are indicated by the same number.

[0063] FIGURE 1, is a schematic flow diagram of the signal modeling method;

[0064] FIGURE 2, is a schematic flow diagram of an implementation of the end-to-end operation of the Signal modeling method in Figure 1;

[0065] FIGURE 3.1, is a schematic flow diagram of a signal modeling system created using the inventive method;

[0066] FIGURE 3.2 is a schematic flow diagram of a signal modeling system created using the Inventive method, as a continuation of the schematic diagram in FIGURE 2.1;

[0067] FIGURE 4, is a flow diagram of the processes illustrating an embodiment of estimating unknown signal vectors in angular directions from known signal vectors at step (S06) in the inventive method and step (306) in the inventive system;

[0068] FIGURE 5, is a representation of the plane fields xy, xz, yz when the spherical axis is defined in 3D in terms of the x, y, z axes;

[0069] FIGURE 6, is the notation for dividing the angle between vectors x1 and x2 of any length L into n equal parts to obtain n-1 vectors;

[0070] FIGURE 7, is a representation of the description of a point (x,y) in two-dimensional space in terms of a function F(x,y) in Cartesian coordinates and a function F(r,θ) in polar coordinates; FIGURE 8, is a graph representing the representation of a segment represented by an area A between a curve r1 and a curve r2 passing through the lines θ=α and θ=β on the polar axis;

[0071] FIGURE 9, represents a representation of the coordinate points of a segment on the polar axis using the trapezoidal area approximation;

[0072] FIGURE 10, is a representative representation of two-dimensional coordinate axes in Cartesian coordinates, segmented and layered by the method of the invention, and the boundaries of any segment thereof;

[0073] FIGURE 11, is a representative representation of the positions and segment numbers of the 12 segments in each layer with respect to their angular phase intervals when a layer is divided into 12 segments in polar coordinates;

[0074] FIGURE 12, is a view of segments and layers in a polar coordinate definition with Kf=8 layers and Sf=24 segments;

[0075] FIGURE, 13 is an illustration of an example of modeling the angular axis when more than one independent variable is to be expressed on the angular axis with the inventive system;

[0076] FIGURE 14, is a representation of an angular graph where the polar coordinates are layered in the form of rings and the segments are plotted according to the graph in FIGURE 7;

[0077] FIGURE, 15 is a representation of the location of the octave frequency bands on a graph showing the spectrum amplitudes and phase angles in Cartesian coordinates, in the state of the art, as a result of FFT analysis of a signal sampled at Fs=44100Hz;

[0078] FIGURE 16, is a graph of the spectrum amplitudes and phase angles of the signal in Cartesian coordinates, where the amplitude values and phase angles corresponding to the resonant frequencies are marked;

[0079] FIGURE 17, is a representation of the graph of a signal sampled at Fs=44100Hz using the system designed with the Discovery method, where the maximum FFT spectrum amplitudes of the signal are expressed in colour tones and the frequency values at these amplitudes are expressed in numerical values in segments;

[0080] FIGURE 18, is a plot of the variation of signal amplitudes with respect to time for a segment of audio signal amplitudes sampled at 1Khz in a 100ms analysis window, as a result of the experiment using the system designed with the Discovery method; FIGURE 19, is a plot of the variation of signal amplitudes with respect to time for the section of an audio signal amplitudes sampled at 1 kHz in the 250ms analysis window, as a result of the experiment using the system designed with the Discovery method;

[0081] FIGURE 20, is a graphical representation of the system developed using the method of the invention in which the polar coordinates are described in 14 layers and 24 segments, the maximum spectrum amplitudes in each segment in any analysis window (window length 300ms) of an audio signal sampled at 44kHz are described by colour tones and the frequency values for the corresponding spectrum amplitudes are shown as numerical values;

[0082] FIGURE 21, is a drawing showing the graph of a music track sampled at 44Khz in the 300ms analysis window of a music track sampled at 44Khz in the system developed using the method of the invention, which is defined as 128 segments and 14 layers according to the increasing frequency according to the logarithm-2 base along the segments polar axis, by showing the spectrum parameters in colour tones;

[0083] FIGURE 22, is a drawing of a music track in mp3 format sampled at 44kHz, divided into analysis windows, showing the spectrum amplitudes of 12 consecutive analysis windows in polar coordinates described by the method of the invention in colour tones, and showing the FFT amplitudes of 12 analysis windows in Cartesian coordinates;

[0084] FIGURE 23, is the representation of seismic (earthquake) waves and their subgroups;

[0085] FIGURE 24, is a plot of a 100ms portion of the Acceleration signal samples versus time in channels CH1 and CH2 of the earthquake P-wave in Cartesian coordinates in the state of the art;

[0086] FIGURE 25, is a plot of the 100ms portion of the Acceleration signal samples of the earthquake P wave versus time in the CH1 and CH2 channels as a result of the experiment using the system designed by the Discovery method;

[0087] FIGURE 26, is a plot of a 1s portion of the Acceleration signal samples versus time in channels CH1 and CH2 containing surface waves (Rayleigh waves and Love waves) in Cartesian coordinates in the state of the art;

[0088] FIGURE 27 is a plot of the 1s portion of the Acceleration signal samples versus time in channels CH1 and CH2, which include surface waves (Rayleigh waves and Love waves), is a plot of the result of the experiment using the system designed by the method of the invention; FIGURE 28, is a plot of the 1 s portion of the Acceleration data of the earthquake surface waves in the directions (east-west, north-south, and up-down) in Cartesian coordinates in the known state of the art;

[0089] FIGURE 29, is the plot of the 1 s portion of the Acceleration data of the earthquake surface waves in the directions (east-west, north-south, and up-down) on the 3-dimensional cylindrical axis as a result of the experiment using the system designed by the Discovery method;

[0090] FIGURE 30, is an illustration of the positions of the 12 lead channels for a 12-channel ECG;

[0091] FIGURE 31 is the representation of the amplitude distributions of the 1 -second portion of the 6 channels (CH1, CH2, CH3, AVR, AVR, AVF) of an ECG signal in Cartesian coordinates using the state-of-the-art;

[0092] FIGURE 32, is the drawing that gives the graph of the 1-sec portion of 6 channels (CH1, CH2, CH3, AVR, AVR, AVF) of an ECG signal on the angular axis as a result of the experiment using the system designed by the Discovery method;

[0093] FIGURE 33, is a plot of a 1 s portion of 12 channels (CH1, CH2, CH3, AVR, AVR, AVF channels and channels V1 to V6) of an ECG signal in Cartesian coordinates graph in the state of the art;

[0094] FIGURE 34 is the drawing showing the graph of the 1 -second portion of the CH1, CH2, CH3, AVR, AVR, AVF channels and V1-V6 channels of an ECG signal on a 3-dimensional cylindrical axis as a result of the experiment conducted using the system designed with the method of the invention;

[0095] FIGURE 35, is the International 10 / 20 placement system of EEG electrodes;

[0096] FIGURE 36, is a representation of the amplitude distributions in Cartesian coordinates of the 8 electrode signals in the inner square area of the EEG electrodes in FIGURE 35, using the known state of the art;

[0097] FIGURE 37, is a drawing showing the angular axis graph of the 8 electrode signals remaining in the inner square area of the EEG electrodes in FIGURE 35, as a result of the experiment using the system designed by the method of the invention; FIGURE, 38 is a representation of the amplitude distributions in Cartesian coordinates of 10 electrode signals in the outer square area of the EEG electrodes in FIGURE 35, using state of the art;

[0098] FIGURE 39, is a drawing showing the angular axis graph of the 10 electrode signals in the outer square area of the EEG electrodes in FIGURE 35, as a result of the experiment using the system designed by the method of the invention;

[0099] FIGURE 40, is a drawing showing the graph of the 10 electrode signals in the outer square area of the EEG electrodes in FIGURE 35 on the spherical axis (defined between the spherical vertical axis (0-pi / 2)) as a result of the experiment using the system designed by the method of the invention;

[0100] FIGURE 41, shows the amplitude distributions of the earthquake R waves in the CH1 and CH2 directions in the time and frequency domains in Cartesian coordinates as a result of the experiment using the method of the invention;

[0101] FIGURE 42 is the representation of the amplitude distributions of the Earthquake R waves in the CH1 and CH2 directions in Cartesian coordinates as a result of the experiment carried out using the method of invention;

[0102] FIGURE 43, shows the reproduction of the ECG signal with CH1, CH2, CH3 channel inputs to 48 channels with the system of the invention and the spectrum distribution in the angular axis in the system of the invention with colour shades; each layer shows the distribution of the FFT acquired signal in angular phases for frequency values between [0-125Hz];

[0103] FIGURE 44, is a drawing showing the graph of the spectrum amplitudes on the angular axis of the 8 electrode signals remaining in the inner square area of the EEG electrodes in FIGURE 35, as a result of the experiment using the system designed by the method of the invention;

[0104] FIGURE 45, Colour representation of the ECG spectrum distribution of the ECG signal by determining the angle between (0-pi / 2) in the vertical direction of the 3-dimensional spherical axis formed by the system of the invention. Each layer shows the distribution of the FFT of the received signal in angular phases for frequency values between [0-125Hz], PRIOR ART AND TECHNICAL PROBLEMS

[0105] In general, a signal can be described as a function that carries information about the state of a physical change, showing the mathematical relationship between at least one independent variable and a time-varying dependent variable. The signal is divided into two groups as analogue signals and digital signals. Digital signals consist of data representing timedependent changes, either converted from analogue measurements to digital values, or obtained or generated from various data sources and recorded at certain time intervals, or generated by various mathematical functions or computer simulations. The feature parameters of digital signals include measures such as amplitude, frequency, wavelength and phase obtained from the signal by various mathematical operations, and these features are used to describe the characteristics of a signal. As a result, digital signals consist of sets of numbers representing signal samples, and these numbers can be stored in a vector array, a matrix array, higher dimensional arrays or other structured digital data formats.

[0106] In reality, the physical changes collected as signals are independent of coordinate systems. However, expressing the result of a physical change using at least one of the axes in a coordinate system creates a dependent relationship between the physical change and the coordinate system, and both the appearance of the physical phenomenon changes according to the coordinate system used and the actual change of the physical phenomenon becomes difficult to visualize as the number of complexity increases. The method of the invention removes the organic dependence between the coordinate system and the physical change and allows the physical change to be expressed in a desired form in a graph on a coordinate axis.

[0107] There is no system in the literature that models the change of a digital signal according to its independent variables and phase angles by dividing a graph on a coordinate axis determined depending on these variables into layers and segments. In addition, there is no system in the literature that presents a sinusoidal signal on a single graph by associating it with the fundamental frequencies, phase angle, and all the components of the signal on an axis modelled as above. On the other hand, observing the relationships between the fundamental frequencies and the components of a signal is very important for further analyses of the signal.

[0108] In the known state of the art, the analysis of a signal in the spectrum plane is described by converting the signal to the frequency plane and plotting the spectrum parameters versus frequencies and the phase angles versus frequencies of the signal on separate graphs, with all frequencies lined up side by side on the coordinate axis. It is very difficult to observe the relationship between the fundamental frequencies and the natural frequencies of such a signal. The greater the number of frequency components in a sinusoidal signal, the more difficult it is to evaluate the analysis of these frequencies and phase angles.

[0109] In the known state of the art, in order to analyze a multiphase signal, the behavior of each -signal vector collected at different phase angles is analyzed separately in Cartesian or polar coordinates, and an estimate of the original signal is made from all the analysis results. On the other hand, there is no method in the literature for modeling the behavior of a multiphase signal emitted from a source in different angular directions by using various input signal vectors collected in different angular directions, estimating the signal vectors in other angular directions, and modeling the behavior of the signal emitted from a source in different angular directions with the derived signal vectors in a single graph similar to the method of the invention. Thanks to the inventive method, energy, frequency, and harmonics can be modelled in the same graph by associating them with each other, which was the dream of the famous scientist Nikola Tesla.

[0110] In the known state of the art, the analysis of the input signals in the time domain is carried out in Cartesian coordinates by means of graphs plotting the property parameters of the signal content against time, and the analysis in the frequency domain is carried out by means of graphs plotting the spectrum property parameters against the frequency components, e.g. Bode diagrams. Bode diagrams are a standardized method that has been used for many years. In this method, the distribution of the spectrum amplitudes of the signal according to frequency is presented on one graph and the distribution of the phase angle values of the signal according to frequency is presented on another graph. The Bode diagram shows the variation of the angular phase values of a signal measured in a single vectorial direction in vector space with respect to the frequency variable. However, due to the need for a separate graphical analysis for phase changes in two different vectorial directions for the same signal and also due to the fact that the relationship between the fundamental frequencies and the components of a signal cannot be easily established on the graph, signal analysis becomes difficult and these graphs cannot solve some specific problems.

[0111] In the known state of the art, since the signal is not modelled with its components in the frequency domain, it is very difficult to distinguish between noise and signal and to monitor the effect of components on the signal, for example when there is background noise in the signal. Therefore, methods such as noise analysis based on a threshold value have been applied to detect the negative effects of noise signal and its artefacts on the original signal. All this makes noise analysis difficult. In the known state of the art, the problems in signal spectrum analysis caused by the display of the signal spectrum amplitudes and phase angles with respect to frequency in separate graphs, as well as the lack of inter-harmonic relationships, increase as the number of sine harmonics in the signal increases. As a result, difficulties arise in producing and implementing the necessary solutions for the signal. In addition, in these graphs, which are usually drawn in Cartesian coordinates, signal parameters in all frequency bands are presented on the graph as if they are of equal importance and not related to each other. On the other hand, the frequencies that give a signal its wave form are the dominant frequencies called resonant frequencies, and generally the contribution of high-frequency frequency amplitudes to the overall shape of the signal decreases inversely.

[0112] Even if the plots of multiphase signals in polar coordinates are encountered in various programming languages with the ‘polar’ command or in graphics such as antenna radiation diagrams, such plots are generally limited to linearly expressed graphics, either by scaling and plotting a phase-dependent signal function in polar coordinates in the range [0-2*pi] or by experimentally measuring signal samples collected at different phases from a fixed distance from the source signal, marking certain points in polar coordinates and connecting the points. In other words, in the known state of the art, the segments and layers in polar coordinates represent the signal parameters themselves.

[0113] In the known state of the art, to construct a two-dimensional antenna power radiation diagram of an antenna, the power values of the signal emitted by the transmitting antenna in various angular directions in the range [0, 2π] are measured by a receiving antenna at a given distance These values are then normalized and calculated in dB (decibels) On the polar axis, the outermost ring represents the maximum normalized power value (0 dB), while the center of the assumed polar coordinate where the antenna is positioned represents the minimum normalized power value in dB. Each ring of the polar axis represents a value in negative dB towards the center, with the power value decreasing towards the center. The measured antenna power values in the range [0, 2π] are then plotted on the graph according to the phase angle and in dB. The line graph formed by connecting these points shows the antenna power pattern at the measured distance. For different distances, it will be necessary to make different power measurements and create different pattern diagrams. [1]

[0114] In the known state of the art, for input signals propagating in various angular directions from a source such as biomedical signals (such as EEG (electroencephalogram), EMG (electromyogram), ECG (electrocardiogram) signals), earthquake signals or multiphase systems, the variations of various feature parameters of vectorial input signal samples collected in multiple directions with respect to an independent variable are examined in Cartesian coordinates and separately. In this way, an attempt is made to estimate the original source signal from the separate analyses of multiple signals. In addition, since the analysed signals are tried to be evaluated together on a graphic screen, as seen in EEG signals, more than one signal is drawn on the same screen and expressed in very small amplitudes. A signal modeling of the entire signal behaviour in the region where the signal is measured cannot be done by using only the measured values, and the signal is processed with various machine learning methods and modeling is tried to be done. These situations make the imaging and analysis of multiphase signals very difficult. [2]

[0115] Another point is that in the case of multiphase signals, only the angular directions in which the signals are collected are evaluated and conclusions are drawn based on these signals. No estimation is made of the signal behaviour in other angular directions where no signal was collected. Therefore, the behaviour of the original signal in all angular directions cannot be comprehensively modelled.

[0116] As a result, due to the above-mentioned negativities and the inadequacy of the existing solutions on the subject, it has become necessary to make a development in the relevant technical fields. With the method developed within the scope of the method of the invention, based on the input signals of a multiphase signal in the measured phases, signal vectors are derived in the angular directions of a specified number of other segments, and all signal vectors are collected in a signal matrix, making it possible to perform an estimated modeling of the source signal in all angular directions in polar coordinates. Again, with the current method, in the spectrum analysis of single-phase signals, graphs can be created in which the relationships between fundamental frequencies and their originators can be easily observed.

[0117] As a result of the preliminary research on the state of the art, the patent file numbered ‘TR200906882 (EP1723638B1 )’ was examined. The abstract of the invention subject to the application states that ‘for analysis and synthesis filter sets, such as those used in audio and video coding systems, the primary transformations function as analysis-synthesis systems in which time-domain overlap structures are cancelled. Secondary transformations linked to the primary transformations are applied to the transformation coefficient blocks, which are modified to adapt to the time resolution of the analysis and synthesis filter sets’.

[0118] The patent application numbered ‘TR20181911006T4’ in the known state of the art was examined. The invention relates to an audio signal processing method. In practice, the process steps include the calculation of gain parameters on the signal after receiving the audio signal, correction of high-frequency signal parameters over these gain values, and synthesis of the corrected signal.

[0119] The patent application numbered ‘TR201808257T4’ in the known state of the art was examined. The summary of the invention subject to the application relates to a signal processing apparatus and a signal processing method, an encoder and an encoding method, a decoder, a decoding method, and a program for reproducing a music signal having a better sound quality by widening the frequency band.

[0120] The patent application numbered ‘US20150332667A1 in the known state of the art was examined. The summary of the invention as applied comprises systems and processes for analyzing an audio or music signal for use in audio signal recognition. Firstly, the audio or music classification of the input signal is made, and if it is a music signal, the process steps of extracting the fingerprint information related to the music signal from this signal are performed. For the speech signal, the extraction of speech regions takes place.

[0121] The patent application numbered ‘ARC2008P00166’, which is in the known state of the art, was examined. The invention subject to the application relates to a device that utilizes the phenomenon of lost fundamental frequency when processing an audio signal. Said audio device converts an audio signal from analog to digital and is operated by a processor. As a result of these processes, an audio signal with the missing fundamental frequency effect and the mismatch between the packets is obtained.

[0122] In the studies subject to the above-mentioned patents, a signal processing method and a system based on modeling and analyzing the feature parameters of one-dimensional or multi-dimensional digital signals against independent variables, angles, and signal axis size on an angular axis and a system realized with it were not encountered.

[0123] ADVANTAGEOUS EFFECTS OF THE INVENTION

[0124] The present invention relates to a method for modeling signals as segments and layers in a graph on an angular axis, as described in Claim-1, in order to eliminate the disadvantages mentioned above in the state of the art and to bring new advantages to the relevant technical field. The method of the invention provides a detailed monitoring of the change in the signal of digitally sampled digital (discrete-time) signals in different segments and layers on a graph on a coordinate axis dependent on the independent variables and phase angles of the signal. In the method of the invention, the independent variables and phase angles of the signal and the coordinate axis are determined, and the variation of the signal (e.g. spectrum signal) versus the phase angles and independent variables can be expressed on a single graph with variables such as numerical values, symbols, signs or colour tones in layers and segments on the coordinate axis.

[0125] With the modeling in the method of the invention, the modeling of the independent variables of all digital signals and their variations against phase angles in the angular coordinate axis can be performed by dividing the signal into segments and layers. In this way, for example, when modeling a two-dimensional signal, three different parameters of the signal, such as the signal variables, the phase angle of the signal, and the independent variable with which the signal is associated, can be modelled on a single two-dimensional graph. Similarly, depending on the angles and independent variables, a graphical area on a three-dimensional axis can be divided into segments and layers, and the signal variables at all phase angles of the signal in 3 different dimensions can be modelled on a single graph on the angular axis.

[0126] In the method of the invention, the fact that the angular axis does not depend on the dependent variables of the signal allows the graphic pattern on the angular axis to be designed as desired depending on the independent variables and phase angles of the signal to be modelled, and the signal can be placed on this graphic pattern like a ‘puzzle’ pieces. Another convenience of attenuating the relationship between the signal and the axis is the possibility to select a different graphic pattern at each phase angle on the angular axis. In this way, any multi-phase multi-dimensional digital signal can be modelled and placed on a pattern in any coordinate axis designed to match the size and phase angles of the signal. Thus, a signal can be expressed in a desired graphic pattern in the graphic pattern on the axis determined depending on the phase angles and independent variables, as long as the boundaries of each layer and segments of the graphic pattern to represent the signal can be calculated. The angular axis can be designed in a desired shape, appearance and size, and the signal parameters can be easily expressed on angular axes designed in different shapes.

[0127] Unlike the polar coordinate system or other coordinate systems in the known state of the art, the axis parameters in the angular coordinate axis in the signal modeling system using the inventive method depend only on phase angles and independent variables. In this context, the segments and layers of the graph on the angular axis are modelled to represent signal parameters that vary linearly or non-linearly in all angular directions defined on the coordinate axis against the values of an independent variable. When the graphic pattern is divided into segments and layers by the method of the invention, it is up to the user whether the boundaries of the segments and layers are indicated by clear lines in the graphic pattern. In the method of the invention, the variation of the angular phase values of the signal emitted from a source in all vectorial directions in the vector space with respect to the frequency variable can be seen in the same graph and the signal behaviour in all angular directions for any time instant can be monitored.

[0128] When time is taken as the independent variable in the system of the invention, the real-time behaviour and appearance of multiphase signals in real life can be easily modelled on the computer screen, and the traceability of the angular direction and time-dependent changes of multiphase systems such as ECG, EEG, earthquake signals becomes very easy. The method of the invention of Claim-1, wherein the multiphase input signals are modelled, monitored and analysed in an angular graph in real time, enabling biomedical signals such as EEG, ECG, EMG, etc. to be monitored and evaluated at the time of collection from the patient and continuously, and recorded when necessary.

[0129] Another invention developed within the scope of the method of the invention is the method developed for multiphase systems, which estimates the signal parameters in the unmeasured phases from the measured values on both sides. In this way, the values of the multiphase signals in the unmeasured angular directions can be estimated from the measured values on both sides.

[0130] The method of the invention facilitates the visibility of the dominant resonant frequencies in the signal and the visualization and analysis of the signal with all its harmonics through the signal amplitudes at these dominant frequencies. The method of the invention can be expressed in segments and layers on a graphic display, allowing the signal to be expressed at a desired level of resolution. In addition, the signal graphs modelled by the inventive method can be converted into an image format and saved, even for graphical modeling obtained in a single signal analysis window, making them very suitable for use in applications such as deep learning and machine learning.

[0131] In the method of the invention, the negative contribution of a noise signal and its artifacts to the original signal can be analyzed independently for all frequency components in angular coordinates, in segments and layers defined in angular coordinates. Furthermore, in the system designed by the method of the invention, all angular frequency components of an input signal are divided into N frequency layers ([0-2*f*pi, f=1,2,4,8,...2^N]) to form octave layers in the spectrum analysis of signals, so that the fundamental frequency components of the signal spectrum are modelled by associating them with all harmonics. In the inventive system created using the inventive method, sound and music signals are modelled by associating them with their harmonics.

[0132] In the method of the invention, if it is desired to construct a power diagram of an antenna by modeling the coordinate axis so that the segments and layers define the measured distance, the power values measured in all directions between the transmitting and receiving antenna and at all distances towards the center can be recorded independently within the segments and layers on the polar axis, and the resulting graph will be a graph in which the power values at all distances and directions between the transmitting and receiving antenna are recorded in different segments and layers on the same graph. In this graph, the independent variable will be the distance between the transmitting and receiving antenna. Thus, a much more realistic antenna radiation pattern with all distances and directions on the same graph will be obtained than in the known state of the art, where the power values measured at a certain distance on the transmitting antenna side are transferred to the graph where different rings on the polar axis represent different power values. In addition, an antenna power radiation pattern can be plotted as a complete antenna power radiation pattern in terms of individual power values in each layer and segment, where the varying power values in all polar directions and distances are represented by colours that vary between power limit values.

[0133] Since the method of the invention defines the connection between the signal and the coordinate axis only in terms of the angles and independent variables of the signal, the method of the invention is able to provide a view of a signal with all its angular behavior on a desired ground by modeling the signal in a desired graphical pattern on a desired coordinate axis, instead of a view of a signal on a coordinate axis associated with its amplitudes in any angular direction in the state of the art. Due to this flexibility, signals with high complexity in terms of size, frequency and angular values can be defined in different angular coordinate axis grounds. Expressing only the signal data by placing them in appropriate segments on any coordinate axis designed in accordance with the number of dimensions in a signal and expressing more than one signal on the same angular coordinate axis will provide great convenience for multidimensional modeling of signals in digital signal processing. With its advantages, the method allows the integration of new visualization tools and analysis techniques.

[0134] For the first time in the literature, for signals such as heart, brain, earthquake, earthquake, sound / music spectrum signals, signals at different phase angles have been combined and imaged in a single signal form. In this context, it can be said that in all of the test results of multiphase signals, for the first time in the literature, multiphase signals have been modelled in the form of a single signal on the same graph, and the original test results are presented in this description. PURPOSE OF THE INVENTION AND ITS APPLICATION IN VARIOUS DIGITAL SIGNALS

[0135] In order to model any input signal on the angular axis with the invention model, the input signal was evaluated by dividing it into two groups. Single-phase signals, where a signal emitted from a source exhibits the same behavior in all angular directions for any instant of time, and / or signals where the signal is analyzed by sampling in a single angular direction. Signal samples of this type are recorded as vectors (for example, audio signals). The signal types that can be included in this group will be referred to as Signall in the following sections.

[0136] In the second group, multiphase signals in which a signal emitted from a source exhibits different characteristic properties in different angular directions and / or signals in which the signal is sampled in more than one angular direction are considered. The signal types that can be included in this group (biomedical signals, earthquake signals or multiphase signals such as antenna propagation signals) will be referred to as Signal2 in the following sections. The signal modeling system implemented using the method of invention can analyse both Signall and Signal2 type signals within short-term analysis windows and model and analyze them in angular coordinates in both the time axis and the frequency axis. For signals recorded as Signal2, the signal vectors in each angular direction can be treated as vector signals as Signall on their own.

[0137] The main purpose of the inventive method is to provide a general system model for modeling all digital signals of type Signal1 or Signal2 on a coordinate axis created depending on the phase angles and independent variable (time axis, frequency axis, etc.) components. With the invention, more than one signal can be modelled in different segments on the same coordinate axis, and the same signal can be modelled against more than one independent variable.

[0138] In the method of the invention, all signals of type Signall and Signal2 can be modelled. The signals themselves, the feature parameters obtained from the signal by various calculations, and the axis parameters to which the feature parameters are connected (such as the time or frequency axis) can be scaled linearly or, if desired, non-linearly, such as logarithmic scaling, and their analyses can be displayed graphically on the angular axis. In this way, the modeling of the signals and their feature parameters on the angular axis can be subjected to different evaluations.

[0139] In order to model an input signal of type Signall and Signal2 in the time domain in the time domain or in the frequency domain in angular coordinates, first of all, after determining the short time interval ([tmin-tmax]) in which the signal is divided into short time periods will be analyzed with a windowing method, it is determined at what resolution the angular coordinates will be divided into time intervals (layers) horizontally and at what resolution the angular intervals (segments) vertically. Then, for the analysis in the time domain, the angle of the time domain feature parameters related to the signal, such as the amplitudes, power values, angular values, and the independent variable on the angular axis are expressed on the modelled graph in terms of layers and segments.

[0140] In order to model an input signal in the time domain of Signal1 and Signal2 types in the frequency domain in angular coordinates, the signal is first transformed into the frequency domain with any signal spectrum analysis method known in the literature, such as the Fourier Transform method, power spectrum analysis methods or wavelets, and the feature parameters in the frequency axis are obtained. Subsequently, the layers and segments of the signal are modelled to express the frequency variable, and the feature parameters of the signal are modelled on the graph by expressing them in each segment in the layers defined on the angular axis.

[0141] While signals of type Signall and Signal2 are separated into layers in the time domain or frequency domain, the axis components in the time domain or the axis components in the frequency domain that will cover each layer can be increased linearly or non-linearly in each layer. In this way, for example, the frequency plane of a signal can be increased according to the logarithm-2 base in each layer, and an octave-based axis can be created in each layer. Thus, a signal is modelled on an octave basis on the frequency axis by associating it with the fundamental frequencies (F0) and harmonics in its content on the graph on the angular axis. In the known technique, according to Fourier's theorem, signals are expressed as a sum of fundamental sine signals and their derivatives at different frequencies, amplitudes, and phase angles. The method of the invention enables the analysis of an input signal by correlating the fundamental frequency components in the signal content with their determinants on the angular axis, and thus, for example, in music signal analysis, it enables the spectrum amplitudes and angular values of the fundamental frequencies and determinants in the signal content to be easily monitored on the same graph. In this way, it is possible to visualize sound and music signals by associating them with their harmonic components.

[0142] Another purpose of the invention is to define the frequency band range by dividing it into frequency octave band layers and segments on the angular axis by advancing the frequency components of the signal to be located in each layer on the angular axis according to the logarithm-2 base. In this way, it is possible to create octave frequency band ranges and to create a structure in which the fundamental frequencies and their derivatives in the signal are grouped together and associated. Especially for voice and music signals, it is important to describe the input signal by dividing it into octave frequency band layers on the frequency axis, in order to describe the signal by relating it to its genesis.

[0143] When the signal modeling system designed using the method of invention is defined according to the octave frequency band layers (Kf), the fundamental frequencies and the genesis frequencies in the frequencies in the signal content are associated together and revealed quite clearly. In this context, with the signal modeling system within the scope of the method of invention, a signal divided into short-term analysis windows can be displayed on a graph in angular coordinates with all its amplitudes and frequencies, as well as the phase angle differences of the sinus components in the signal content relative to each other, and the relationships between the fundamental harmonics in the signal and their genesis can be easily monitored. For this purpose, the system designed with the method of invention divides the frequency region [fmin-fmax] in the signal into equal intervals at a desired positive integer (n) value with a factor of 2^(1 / n) (2 to the (1 / n)th power, where n=1: Kf) in order to separate the frequency ranges to be included in each layer in angular coordinates on an octave basis.

[0144] The invention relates to a method that allows the spectrum parameters of the signal to be given as numerical quantities or colours by associating the fundamental frequencies of the signal with their genesis in the determined frequency band intervals and angular coordinates of the input signals at different signal / noise (SNR) levels and thus enables the amplitude values and angular values of the frequencies that can be effective in separating the signal and noise from each other to be easily monitored. It is considered that the method of the invention will greatly facilitate the analysis of the effects of noise frequency components on the main signal in noise signal analysis.

[0145] There are many common steps in the system implemented with the method of invention for modeling signals of type Signall and Signal2. In the signal modeling system in question, the processor first asks whether the input signal is of type Signal1 or Signal2. In order to model an input signal of type Signal1 or Signal2 in the system in the time domain or in the frequency domain in angular coordinates, after determining the short time interval ([tmin-tmax]) in which the signal divided into short time periods will be analysed with a windowing method, the angular coordinates are divided horizontally into independent variable layers with the desired resolution and vertically into segment intervals according to the desired resolution level in the signal to be modelled. Then, unlike the signal of type Signall, in order to model the input signals in the time domain of type Signal2 by dividing them into a specified number of layers and segments in angular coordinates, a signal matrix containing signal vector samples in angular directions related to other segments in the angular axis is derived, firstly starting from the input signal samples collected in different angular directions related to the signal. In the interpolation method developed within the scope of the invention, using input signal vector samples collected in different angular directions related to a signal of the Signal2 type, signal vectors in other angular directions related to Signal2 are estimated at the determined segment resolution level, and signal vectors related to Signal2 in the angular directions of each of the segments determined in the range of [0-2*pi] on the angular axis are derived. Thus, a signal matrix is derived to represent Signal2 (Equation-3). The subsequent process is similar to the process described in Signall.

[0146] In this context, in the signal modeling system created using the method of the invention, in order to model an input signal in the time plane of the Signal2 type in angular coordinates, firstly the short time interval ([tmin-tmax]) in which the signal divided into short time periods will be analyzed with a windowing method is determined, and then the resolution layers and segment intervals of the graphic display in angular coordinates are determined. Then, a signal matrix array containing signal vector samples in angular directions related to all segments determined on the angular axis is derived from the input signal samples of Signal2. Using the signal sequence in question, the feature parameters of the signal are calculated and modelled on the graph by expressing them in each segment in the layers defined on the angular axis. In this context, the biggest difference in modeling signals of Signal1 and Signal2 type in the method of invention is the step of creating a signal matrix by deriving the signal vectors in angular directions not given as input signal data from the input signal vectors for a signal of Signal2 type. In subsequent processing steps, the similarities are high for both types of signals.

[0147] As an alternative way to model an input signal of type Signal2 in the time domain in angular coordinates in the frequency domain, each signal vector in the Signal2 matrix, which is created using signal vectors derived in all angular directions in angular coordinates in the time domain, is considered as a signal of type Signall on its own, and the methods followed in angular coordinates of type Signall in the inventive method can also be applied.

[0148] With the invention, monitoring of the frequencies, frequency amplitudes, power values, and phase angle values of the signals in the frequency domain has become quite easy. In addition, the invention relates to a method that enables multiphase input signals, such as biomedical signals or earthquake signals, in which there are multiple input signals in different angular directions related to the same source of the Signal2 type, to be remodeled in all angular phases and displayed at the desired resolution in angular coordinates.

[0149] Another purpose of the invention is to monitor the changes of all time series signals according to independent variables and phase angles by seeing the signal itself, its phase and independent variable in a single graph on the coordinate axis. In the system developed using the method of invention, behavior graphs of the signals on two and three-dimensional axes were created. With the invention, the behavior graph of the signals on the three-dimensional cylindrical axis and the spherical axis has been realized by using the transformation formulas between the two and three-dimensional axes in the state of the art. Other three-dimensional modeling can be easily done using the method of invention, using the transformation formulas between two and three-dimensional axes in the state of the art.

[0150] Another purpose of the invention is to model the frequency, amplitude, and phase angle values of the spectrum parameters such as frequencies, spectrum amplitudes, spectrum power values, and phase angles of the sinusoidal signal obtained as a result of any spectrum transformation method applied to the signal, on a single graph in angular coordinates in order to model an input signal of Signal1 or Signal2 type in the frequency plane. In this way, the spectrum parameters, frequency, and phase changes of a signal can be monitored in a single graph on the angular axis and in separate segments. In the state of the art, the spectrum parameters and phase changes in question are usually shown in Cartesian coordinates and in separate graphs.

[0151] With the method developed within the scope of the invention, the vector signal samples in the angular directions of other determined segments between two input signal vectors can be estimated by starting from the input vector signal samples collected in different angular directions of a signal of the Signal2 type. Subsequently, after determining the short time interval in which the signal will be analyzed, the purpose of the invention is to model the feature parameters related to the signal on the graph in all angular directions in the axis plane to which it is connected, for example, in the time plane or in the frequency plane in angular coordinates.

[0152] Another object of the invention is to associate a sinusoidal signal and its feature parameters with a colour palette (colour chart) between the minimum and maximum values in its content and thus to show the numerical magnitude of the parameters by colouring them with the corresponding colours in the colour palette for the relevant parameter. In this way, in addition to the numerical values of the parameters in each segment, the different sizes of the parameters are displayed with colour variables determined between the limit values of the relevant parameters.

[0153] Another purpose of the invention is to provide the display of the spectrum parameters related to the note frequencies of any musical scale system defined as an n-scale between two-octave frequency intervals, where n is an integer, on the angular axis by dividing the interval between two octaves into n segments with a factor of (2^(1 / n)) for the octave frequency layered display on the angular axis. In this way, it is aimed to provide the visualization of musical works composed with different musical scales in the world in octave bands and to determine a system in which different musical systems can be compared with each other and the mutual relationships between note frequencies and phase angles can be revealed. In this way, for example, by selecting n=12 in the 2^(1 / n) scale, the Western music chromatic scale system can be displayed on the angular axis, and by selecting n=53, the Turkish music scale system can be displayed on the angular axis.

[0154] Another object of the invention is to monitor and analyse all audio and musical signals and their spectrum components in the frequency plane on the angular axis. In this way, the correct determination and analysis of the locations of resonance frequencies (formants) in audio signal analysis and resonance frequencies (note frequencies (pitches)) in music signal analysis, the traceability of frequencies with each other in terms of spectrum amplitude, phase angle and octave bands, and the ability to carry out analyses to the desired frequency resolution level.

[0155] Another purpose of the invention is to facilitate the monitoring of harmonic changes that occur when multiple sounds are brought together for mixer operations of sound and music signals on the angular axis. Another purpose of the invention is to facilitate the monitoring of harmonic changes that occur when multiple sounds are brought together for mixer operations of sound and music signals on the angular axis.

[0156] Another purpose of the invention is to display, monitor and analyse biomedical signals such as heart (ECG), brain (EEG), and nervous system (EMG) signals of the Signal2 type or multiphase signals collected from multiple points of a source such as earthquake signals of the Signal2 type, on the angular axis.

[0157] Another purpose of the invention is to enable market data analysis to be performed on an angular coordinate axis defined using the inventive method in order to reveal the effect of multi-directional changes in market data.

[0158] Another purpose of the invention is to facilitate the monitoring of the noise analysis of signals and the effects of noise on the signal in the spectrum band ranges in each octave and to facilitate the visual monitoring of possible changes in the spectrum shape of the signal in terms of all frequency components when the signal is cleared of noise.

[0159] Another object of the invention is to enable the antenna radiation diagram to be drawn in a way that includes the power values at all distances in a single graph. In the state-of the-art, antenna radiation diagrams are created by plotting the power values measured from a fixed distance on a graph.

[0160] In the state of the art, the spectrogram method defines a graph that presents the change of the frequency spectrum of signals with respect to time in a picture format with different colour tones and in Cartesian coordinates. In the spectrogram method, the spectrum parameters of a signal in any analysis window are expressed in different colour tones. Subsequently, the information in multiple analysis windows is placed side by side and combined into a single image format, and these images are used as input data in machine learning or deep learning. On the other hand, the spectrogram graph presents data for the change of the signal over time, within a ‘specific time interval’. However, there is no spectrogram plotted for signals within a single analysis window.

[0161] Another purpose of the invention is to create a graph in image format for each analysis window regarding the feature parameters of the signals so that they can be used as data in machine learning and deep learning algorithms. In this respect, within the scope of the method of invention, the use of graphic models in image format obtained for each signal analysis window in deep learning algorithms will enable more detailed analysis results regarding the signals to be obtained.

[0162] The method of invention provides great advantages over the graphs expressing the signal spectrum amplitudes and phase angles obtained as a result of methods such as Fourier Transform and wavelet method, which are among the spectrum analysis techniques of signals up to now, in separate graphs and Cartesian coordinates. When the method is used, after the spectrum amplitudes and phase angles of the input signal within the analysis window are found, it is possible to display and analyze the spectrum parameters of the signals in terms of fundamental harmonics and their derivatives by expressing these values in angular coordinates in the layers described by the invention and in the intervals in each layer. In this way, great improvements have been observed in determining the peak and valley values of the sinusoidal components in the signal content, which gives the signal its shape, and in determining the phase angle position of the relevant sinusoidal components in angular coordinates. For this reason, the method of the invention meets all the performance expectations listed above regarding modeling a sinusoidal signal.

[0163] Modeling the coordinate axis depending on the angular values and the independent variables of the signal offers some advantages other than modeling the signal in a desired graphic pattern. Multiple signals on the same angular axis can be modelled in different segments and layers against the same independent variable. In modeling the signals on the angular coordinate axis with the method of invention, the following arrangements can be made without increasing the coordinate axis size:

[0164] (i) If the behavior of a signal against other independent variables is desired to be expressed in the same graph (for example, if the change of a signal with respect to time and distance is desired to be seen in the same graph),

[0165] (ii) If other signal feature parameters of the same signal using the same independent variables are desired to be expressed in the same graph (for example, if the power and amplitude changes in the frequency plane of a signal are desired to be monitored in the same graph),

[0166] (iii) If different signals using the same independent variable are to be expressed on the same angular graph,

[0167] By developing the graph on the angular axis with alternative solutions as follows, the desired parameters can be expressed in this graph as follows;

[0168] • The new parameter to be expressed is written into the existing segment with expressions such as numerical value, symbol, sign, etc.

[0169] • by dividing the segment into sub-segments and expressing it in these segments,

[0170] • expressed in new segments created by dividing layers into sub-layers,

[0171] In the graph on the angular axis, areas for new signal variables can be defined in sub-layers connected to layers or sub-segments connected to segments and modelled in the same graph.

[0172] Another purpose of the invention is that it is considered to contribute to the increase in efficiency in Tensor models, which currently form the basis of multi-dimensional data models in structures such as artificial intelligence, machine learning, and deep learning. In the state of the art, tensors are mathematical structures that describe the relationship between objects associated with a coordinate system in terms of unit vectors. Tensors are based on unit vectors and define a vector from the sums of unit vectors. Not every vector is a tensor, but all tensors of rank-1 are vectors. In this sense, the most fundamental difference between tensors and vectors is that while tensors are a representation of abstract variables that indirectly describe a physical situation with mathematical expressions, vectors can be expressed as a representation of concrete variables that show the magnitude and direction of a physical situation. While vectors are often used in fields such as physics, engineering, and computer graphics to represent specific quantities or forces, tensors address the components of forces or deformations acting on an object's geometry rather than its geometry. Tensors have shortcomings such as high dimensionality and computational difficulties. Working with tensors on high-dimensional datasets increases the complexity of computations and required storage space, and storing sparse tensor data on the computer becomes difficult. To effectively optimize tensors, other algorithms (e.g. PCA (Principal Component Analysis)) and high-speed and parallel processors such as GPU (Graphics Processing Unit) are usually required.

[0173] The method of invention differs significantly from the state-of-the-art solutions, thanks to its original technique in modeling the signals and the solutions it provides to the technical issues listed above and similar ones. In order to best understand the embodiment of the present invention and its advantages together with the additional elements, it should be evaluated together with the figures and models explained below.

[0174] In the state of the art, the appearance of the xy, xz, yz plane areas is shown in Figure 5, on the axis defined as 3D in terms of x, y, z axes. In order to describe a signal on the 3D coordinate axis in Figure 5, the relationship between the axis parameters and the signal must be established. All these operations become increasingly complex as the dimensions of the signal and the axis on which it will be expressed increase. Since the inventive method defines the coordinate axes depending only on the phase angles and the independent variable, it becomes easier to increase the coordinate axis dimensions and subsequently express the signal in segments and layers in these coordinates. The structural and characteristic features of the invention and all its advantages will be understood more clearly thanks to the figures provided in this document and the detailed explanations written by referring to these figures. Therefore, the evaluation should be made by taking these figures and detailed explanations into consideration.

[0175] INDUSTRIAL APPLICABILITY OF THE INVENTION

[0176] The method of invention, which serves the above-mentioned purposes, can be used in modeling analog or digital signals in any branch of industry and is applicable in many branches of industry (medicine, engineering, health, measurement / evaluation, industry, communication, electronics, etc.). Some advantageous effects of the method of the invention in digital signal processing are briefly as follows; EEG, ECG, EMG, earthquake, radar, sonar, sound / music spectrum, etc. all multiphase signals:

[0177] It can be analysed in all angular aspects in the same graph, in a realistic image, and in width and length; A multiphase signal in the short-term analysis window can be viewed as an instantaneous graphic image on a screen, and by converting these images to different formats, a picture or video image of the multiphase signals can be created;

[0178] • With modeling of a signal at different resolution levels, it will be easier to extract important information in multi-phase & multi-dimensional signals;

[0179] • The information given as input for "object recognition" in artificial intelligence can be reduced to a much more precise level by including graphic images in each signal analysis window;

[0180] • The signal may be described in a graph pattern on a desired angular axis basis. For example, by measuring an ECG signal with multiple electrodes, similar to an EEG signal measurement in Figure 35, all electrical activities in the heart can be monitored simultaneously and in detail with much more sensitive and much higher resolution measurements, and when the heart signal is displayed on a graphic pattern in a heart image, changes in 360° angles in the heart can be m onitored instantly, very close to reality and much more precisely;

[0181] • By simulating earthquake signals multi-dimensionally on the geographical ground where they propagate, analyses of their realistic effects will be easier, and new technologies against possible earthquakes can be developed based on the findings at hand;

[0182] • Radar and sonar signals will be simulated multi-dimensionally on the current ground environment, and the movements of more than one target will be monitored simultaneously, and more detailed data on the targets will be collected and analyzed;

[0183] • The antenna radiation pattern of a transmitting / receiving antenna signal in the global environment where it propagates can be displayed and analyzed more comprehensively;

[0184] • It is evaluated that the method of the invention will contribute to the increase in efficiency by providing effective solutions to the problems experienced in tensor models where multi-dimensional signals are modelled with mathematical values created in terms of unit vectors; All the above signal data can be measured instantly and displayed on graphs, and realistic simulation / video images of the signals can be created and recorded. The possible effects of the invention are not limited to those listed here but will affect all areas of industry, medicine, and engineering with the results of multiphase signal modeling and analysis.

[0185] The behavior of all multiphase signals in [0-360] angular directions can be continuously displayed, analysed and recorded for subsequent processing in digital environments. The invention provides the possibility of modeling, monitoring, and analysing multiphase input signals in real-time in an angular graph; and the possibility of monitoring and evaluating biomedical signals such as EEG, ECG, and EMG in real-time while they are collected from the patient, and recording them when necessary. The ability to display multiphase signals in a single graph will enable the number of sensors used in the collection of biomedical signals to be easily increased and, in this context, all biomedical signal analyses to be performed more precisely and in real-time. With the invented system, in the very near future, biological signal analysis in the whole body will be able to be monitored simultaneously on graphic screens with a wearable sensor set like a dress. The new advantages and opportunities it provides will enable the production of many systems, devices, and sensors with different designs and new solutions in areas affected by signal processing.

[0186] It is considered that one of the important contributions of the invention will be in quantum physics. The quantum uncertainty principle, which assumes that it is not possible to measure the position and speed of an electron particle simultaneously with exact values, can be reevaluated by examining the behavior of an electron particle in orbit around the atom simultaneously in all angular phases. It is evaluated that the method of invention will make very important contributions to the studies of quantum space, which is one of the areas of interest of quantum physics, and to the investigation of space-time theorems in more advanced dimensions.

[0187] As a result, the method of invention will create a "game-changing" effect in all software and hardware products within the scope of digital signal processing; it will lead to great opportunities for the rapid development of technology in health, industrial, and commercial areas and the realization of products with more sensitive, more reliable, more flexible and multi-dimensional designs.

[0188] THE INVENTION METHOD AND THE SYSTEM REALIZED USING THE METHOD

[0189] 1. Introduction In this detailed description, the invention method and the signal modeling system, which is related to at least one independent variable connected to the signal, phase angles, and the axis dimension of the signal, are explained with examples provided solely to enhance understanding of the subject and without any limiting effect. This system models signals on an angular graph by dividing a coordinate axis, which depends on the signal's independent variables, phase angles, and axis dimension, into segments and layers at the resolution of the signal to be modeled.

[0190] The capabilities and possible effects of the inventive method in digital signal processing are not limited to the system described herein, and the signal modeling system described herein and the tests of which are presented has been implemented to present a prototype model of how the inventive method can be implemented on a signal processing system.

[0191] Since this invention defines a method for graphically modeling and analyzing all digital signals, those who wish to can apply the process steps given to model various signals of the method of the invention in hardware systems with digital signal processing circuits, such as computers or devices capable of processing information, in various ways and by changing the order of some processes without disrupting the general flow of the method.

[0192] 2. Method of Invention

[0193] The invention is a method that enables modeling and analysis of digital signals within analysis windows in a graph defined on an angular coordinate axis depending on their independent variables and phase angles, on a device with information processing capacity. In this way, in addition to the analysis of pre-recorded signals, it enables the signals to be taken into analysis windows in real-time and displayed on the angular axis, and the obtained results to be analyzed, transmitted to other sources or saved. With the systems realized with the inventive method, multi-phase signals such as heart, brain, nervous system, earthquake signals, and signal spectrum can be described in a single graph and monitored in analysis windows, and when desired, the graphs obtained in the analysis windows with the inventive model can be saved in a desired format.

[0194] The process steps in the method of invention, which is a method of modeling single-phase or multi-phase signals in a graph on an angular coordinate axis depending on phase angles and independent variables, included in Claim-1 and also given as a schematic flow diagram in Figure 1, are as follows, together with the relevant process numbers: S01: Input signal receiving unit: receives digital input signals from a data source, pre-processes them, and takes the signal vectors into a series of variables in accordance with the phase angle directions in which they will be modelled on the angular axis.

[0195] S02: Signal analysis window identifier: In order to model and analyze input signals in analysis windows, a signal window analysis method determines parameters such as the window analysis period.

[0196] S03: Layer and Segment Identifier: It determines the number of segments and layers that will form the graphic pattern, depending on the changing parameters such as the desired signal resolution amounts, linear or non-linear increase amounts of the signal, lower and upper limit values, to be displayed on a graph on an angular coordinate axis of the signal within the analysis period.

[0197] S04: Angular axis and graphic identifier: Depending on the independent variables and phase angles of the signals to be displayed on the angular axis, it determines an angular coordinate axis and the geometric shape and pattern of the graphic on which the signal is desired to be displayed on this axis, in accordance with the layer and segment numbers determined in step (S03). It also determines the parameters related to the calculation methods of the boundary areas of each of the segments and layers to which the signals will be added in the graph.

[0198] S05: Signal analysis loop unit: Starts a loop to display the signal data during the analysis period in the graph defined in step (S04)

[0199] S06: Signal vector estimation unit: In order for the signal to be displayed in all layers and segments of the graph in step (S04), it must be taken into an array variable, and in this context, if it is necessary to calculate signal vectors at phase angles not given as input signals, the unknown signal vectors must be calculated using a vectorial signal estimation method;

[0200] S07: Signal parameters identifier: If it is desired to continue with the signal in the array variable in step (S06) or to display the signal feature parameters obtained from the signal by some calculations instead of the signal in question in the graph, the feature parameters in question are determined;

[0201] S08: Signal representation format identifier: It determines the display format of the signal to be displayed in the graph defined in step (S04). In this context, the variables required to represent the signal with numerical values, colour tones, symbols, special signs, or other visual elements in the relevant segments and layers of the graph on the angular coordinate axis are determined.

[0202] S09: Graphic display continuity provider: In order to add the signal values to be displayed in the graph in step (S04) to all segments and layers in the graph, the hold on feature of the graph image is provided throughout the loops in step (S11 ).

[0203] S10: Loop initial values unit determines the initial parameters needed during layer and segment loops.

[0204] S11: Layer and segment loops Unit: It starts loops for layers and segments to display the signal in each layer and segment of the graph.

[0205] S12: Layer and segment boundary identifier: During the loop in step (S11), in order to display the signal variables in the relevant layers and segments of the graph determined in step (S04) on the angular axis, the calculation of the variables defining the boundary regions of the relevant layer and segment of the graph is carried out according to the graphic calculations defined in step (S04).

[0206] S13: Signal to be displayed identifier: The signal parameters to be displayed in the relevant layer and segment of the graph in Step (S12) are determined.

[0207] S14: Signal visualization unit: The signal parameters in step (S13) are displayed on the graph according to the location of the graph determined in step (S12) and the signal display style in step (S08).

[0208] S15: Layer and segment loops continuation unit: In order to process the signal variables in each layer and segment of the graph, the segment and layer loops are continued and the relevant index variables are updated.

[0209] S16: Graphic display continuity disabler: After completing the graphical representation of the signal parameters within the analysis window, the continuity feature of the graphical display is turned off (hold off).

[0210] S17: Signal analysis window progressor: The signal analysis loop in step (S05) continues to repeat the operations for the graphical display of the signal variables in the next analysis window.

[0211] S18: Program terminator: When the loop in step (S05) is completed or terminated by the user, the operations are terminated. Method according to claim-1, characterized by comprising the following process steps: determining the digital signals that are desired to be displayed on an angular coordinate axis; arraying the signals in accordance with the angular directions in which they will be modelled on the angular coordinate axis; determining an angular coordinate axis depending on the independent variables and phase angles of the signals to be displayed on the angular axis and defining a graphic pattern with the number of segments and layers determined according to the variables such as the resolution amount of the signal, the amount of linear or nonlinear increase, and the lower and upper limit values; determining the calculation methods of the boundary areas of the segments and layers in this graph; if there are unknown signal variables at the phase angles desired to be displayed on the angular axis, calculating the relevant parameters with a signal estimation method; expressing signal variables in the relevant segments and layers of the graph defined on the angular coordinate axis, with numerical values, colour tone, sign, symbols or other visual elements.

[0212] An implementation of a signal modeling method according to Claim-1 for operation on various devices comprises the following mechanisms and process steps: Obtaining digital samples of an input signal from an input terminal (501); transmitting the input signal to an output terminal connected to the processor after an application of the inventive method according to Claim-1 or Claim-2 or Claim-3 is run on a processor connected to the input and output terminals (for example, displaying it on a graphic screen (502a); or recording the obtained information in the memory (502b); or transmitting it to another device via the I / O interface (502c)); the process includes the steps.

[0213] A signal spectrum modeling method according to Claim-1 or Claim-2 or Claim-3 may include the following steps: In the analysis of the spectrum analysis of an input signal in angular coordinates using the methods in Claim-1 or Claim-2 and Claim-3, it comprises the following process steps; dividing all angular frequency components of an input signal into frequency segments and layers by increasing them according to the logarithm base between the minimum and maximum frequencies of the signal in order to create logarithmic-based frequency layers; thus, modeling the signal spectrum on the angular axis by associating it with all harmonics of the fundamental frequency components.

[0214] 3. Signal Modeling System Implemented by Inventive Method

[0215] The signal modeling system, developed using the inventive method and running on a device with a processor, implements a number of processing steps to display and analyze signals. These processing steps are performed by the processor in any device with a processor. The signal modeling system in Claim-2, which is implemented to apply the inventive method described in Claim-1 to various single-phase or multi-phase signal examples, is a computer-based digital signal modeling system consisting of instructions to run on a computer with standard input and output devices. The capabilities and possible effects of the inventive method in digital signal processing are not limited to the system described herein, and the system described herein and the tests of that are presented have been implemented to help better understand the inventive method. The signal modeling system, which was developed using the inventive method and runs on a device with a processor, implements a number of processing steps to display and analyze signals. These processing steps are performed by any device with a processor and the processor of the device.

[0216] The inventive signal modeling system (Figure-3) has been implemented to apply the inventive method described in Claim-1 to various signal examples of Signal1 and Signal2 types. The invention signal modeling system is a computer-based digital signal modeling system consisting of instructions to run on a computer with standard input and output devices and is included in Claim-2.

[0217] The method in question is used to model the input signal in a single graph on the angular axis with a system created by applying the method in question. In the tests performed with the system in question, very successful results were obtained in the tests of 2-dimensional or 3-dimensional multiphase signals. A signal modeling system implemented in accordance with the inventive method includes the following process steps. The inventive system is explained in relation to the process steps in the inventive method in order to easily establish mutual connections and to avoid repetition. The process steps in the inventive system, together with the relevant process numbers associated with them for the system and method, are as follows:

[0218] 301: Input signal receiving unit (S01): In the signal modeling system implemented using the inventive method, an input signal receiver unit that receives the input signal in real time with a sampling rate of Fs from an input device managed by a processor or reads a digital input signal from a file and pre-processes the signal determines whether the input signal type is single-phase or multi-phase and the independent axis variables to which the signal to be analysed on the angular axis is connected. If the input signal is single-phase, it transfers the input signal to a one-dimensional array (AA), and for multi-phase signals, it transfers the vectors of the signal to be analysed to a multi-dimensional array (AA) in accordance with the angular direction of the signal on the angular axis. For example, if it is desired to obtain an angular graph by starting from 4 input vector arrays in the range [0-2*pi] of a two-dimensional angular axis, the vectors in the angular directions of the input signal [0°, 90°, 180°, 270°] are taken and placed in the AA matrix array in the order appropriate to their angular directions. Then, various processing steps are performed on this data in the system.

[0219] 302: Signal Analysis Window Identifier (S02): In the inventive system realized with the inventive method, parameters such as signal windowing analysis method, overlap amount in adjacent windows and signal windowing period (Twndw) are determined in order to separate each vector in an AA array variable of input signals into Nf element analysis windows. In this context, the window type, length and vector lengths of the signal to be analysed in each window are determined in order to divide the input signal into sections according to the analysis window intervals. It determines the number of elements of the signal vectors within the analysis window (Nf = Twndw*Fs) according to the signal analysis window period and the sampling rate (Fs) of the digital input signal.

[0220] 303: Layer and segment identifier (S03): In the inventive system realized with the inventive method, the number of layers (Kf) representing the independent variable and its non-linear increase are determined with the phase angle value range in which the input signal will be analysed in angular coordinates. Determination of the Kf value is as explained in the following examples;

[0221] • If the independent variable is the time variable (t), the Kf value that will represent time on the angular axis will be determined according to the linear / non-linear increase in time in the analysis window time range ([tmin-tmax]) of the signal to be represented on the angular axis and the time resolution (At) value between time limits,

[0222] • If the independent variable is the frequency variable (f), the Kf value to be represented on the angular axis will be determined according to the linear / non-linear increase of the frequencies [fmin-fmax] in the frequency band range of the signal and the frequency resolution (Af) value.

[0223] It determines the number of segments (Sf) that will represent the resolution of the phase angles in each layer on the angular coordinate axis and determines the linear or non-linear increase of the intervals. When the inventive system is used to model the spectrum amplitudes of signals on the octave-based frequency axis, for example, the frequency (fi) intervals (fi->(2^fi)Hz, i=1→Kf) between any two octave bands in the [0-2TT] angular direction are divided into Sf segments (sfi, i=1: Sf) in each layer. Layer (Kf) and Segment (Sf) values are determined depending on variables such as the resolution amounts of the signal variables to be displayed during the analysis period, linear or non-linear increase amounts, lower and upper limit values. 304: Angular axis and graphic identifier (S04): The method of invention enables the design of a graphic shape on the angular axis in the form of segments (grids) in the desired geometric shapes determined by the user, and the modeling of the signal in the desired shapes in each segment in each layer by proceeding in the coordinate axis directions during the modeling of the signals in the graphic during the analysis loop.

[0224] In the system realized with the method of invention, in the angular axis and graphic determinant section, it determines on which angular axis type the vectors in the AA array variable of the input signal will be displayed. The angular axis type is determined depending on the independent variables and phase angles of the signal variables desired to be displayed on the angular coordinate axis. In the inventive system, in order to model various 2-dimensional or 3-dimensional 7 angular coordinate axes (Cartesian, 2D-polar1, 2D-polar2, 2D-polar3, 2D-polar4, 3D-cylinder, 3D-spherical), functions including axis calculations under the title of " Definition of Various Angular Coordinate Types and Layer and Segment Regions for Use in the Inventive Method" have been determined in Article-6 of this document. If additional axes are desired, new angular axis types can be added to the system by the user using the option and signals can be modelled on these axes. In addition, in this section, the maximum & minimum values of the signal parameters subject to analysis, the angles seen by the Sf segments in the layers on the angular axis and other initial values and default values related to the system are determined. In the region between the axis parameter limits of the signal between any two layers, the angular value (0i) and the radius value (ri) from the center point are calculated for each segment in the relevant layer. For the axis parameters located between the boundaries of each segment (sfi), the feature parameters corresponding to the relevant parameters are determined as parametric values that can be located in the relevant segment region.

[0225] 305: Signal analysis loop unit (S05): In the system implemented with the method of invention, a loop is started to perform the analysis of the elements of the signal within the analysis windows (for ii=1 ->length(window)-> length(signal)). In this context, the input signal is divided into sections according to parameters such as window analysis method, overlap amount between windows and analysis time, and the signal vector lengths in each window are determined.

[0226] 306: Signal vector estimation unit (S06): If the signal to be displayed in the graph defined in step (304) is multiphase and the signal vectors at phase angles not given as the input signal need to be calculated, the calculation of the unknown signal vectors using a vectorial signal estimation method provides the creation of an array whose size is determined depending on the number of segments and layers in step (304) by combining the known and calculated signal vectors in accordance with the angular directions in the graph (calculator of the new array from the input array, 306b). In the signal modeling system created with the method of invention, a new method expressed with the calculations in Equation-3 in this document, included in Claim-5 and an application of which is described in Claim-7, is used as the vector estimation method in Step (306b). The method in question calculates signal vectors that are not given as input signals by a vector interpolation method. In the signal modeling system created by the method of invention, it calculates a BA array variable that will include other signal vectors in the angular directions of the specified number of segments between any two vectors, using each signal vector in the AA array variable, to estimate a total of Sf vectors in angular coordinates. It calculates all elements of the BA array variable, which has a total of (Sf) vectors from the AA array, by performing the process steps of Claim-7 (Figure-4) with the method developed in accordance with Equation-3.

[0227] If the signal to be displayed in the graph defined in step (304) is single-phase, in order to model the parts of the signal remaining within the analysis window in the graph in step (304), it ensures that all vectors of an array whose size is determined depending on the number of segments and layers in step (304) are created with the signal vector in question (Copier of the input array to the new array, 306a). Thus, for one-dimensional vectors in step (306a), the invention ensures that all vectors of the BA array variable are represented by the AA vector in the system.

[0228] 307: Signal parameters identifier (S07): In the inventive system, for the signal desired to be displayed on the angular axis, either the signal in the BA array variable in (306) is continued or, if the feature parameters are desired to be displayed on the graph by calculating the feature parameters from the BA array signal, the relevant feature parameters are calculated using the signal in the BA array variable. In this case, the process steps are continued with the calculated signal feature parameters instead of the signal parameters in the BA matrix. Signal feature parameters are parameters such as amplitude, spectrum, power, etc. obtained from the signal by various calculations.

[0229] In the inventive system, the feature parameters related to the signal for the part of the signal in the BA sequence variable within the analysis window are calculated as linear values or non-linear values. For example, to calculate the feature parameters in the spectrum plane, the processor converts the part of an input signal in the time plane in the BA sequence within any mth analysis window to the frequency plane by means of a spectrum transformation method known in the literature, and calculates the frequencies (F(m)), spectrum amplitude and power values (G(m), P(m)) and phase angle values (Q(m)) within the same analysis window of the signal in the frequency plane within the spectrum band. 308: Signal representation format identifier (S08): The invention determines the way the signals are displayed on the graphic screen in the system. It determines the colour palette for displaying signals, for example, with colour tones, and determines the minimum and maximum limit value ranges of the tones in the colour palette according to the signal lower and upper limit ranges. The variables required to display the signal with symbols and signs when desired are also determined in this process step. It determines the calculation methods of the elements of a BB matrix that will include the coordinate points in the graphic pattern on the axis of each part to be defined according to the selected angular coordinate axis and the determined (Kf, Sf) values of the coordinate axis. The 7 different angular axes and graphic patterns used in the inventive system are explained in Article-6 of this document under " Definition of various angular coordinate types and layer and segment regions for use in the inventive method". The stage of determining the display format of signal parameters on the graphic display includes the following steps:

[0230] • The representation format to be used for visualization of the signal is defined. In this context, the signal is represented on the graph with numerical values, colour tones, symbols, special signs or other visual elements.

[0231] • If the signal is to be displayed with colour tones, a colour palette is selected; the lower and upper limit values of the palette and the resolution amount are determined.

[0232] • If the signal is to be represented by symbols, signs or other visual elements, the symbols, signs or elements corresponding to each signal parameter are defined.

[0233] • More than one representation can be used together when visualizing the signal. For example, colour codes can be assigned for specific frequency ranges, while symbols can be used for specific amplitude levels.

[0234] • Variables related to the display format can be dynamically adjusted by the user, allowing the visualization to be customized to suit needs.

[0235] 309: Graphic display continuity provider (S09): In the system of the present invention, with the graphic display continuity provider, the 'hold on' feature of the graphic display is activated, ensuring that the graphic remains on the screen until the signal parts in all segments and layers are completed, because the new graphic in the next analysis window will be drawn on the existing graphic. In this context, in the graph on the angular axis consisting of Kf layers and Sf segments in each layer, the "hold on" feature is opened on the graphic screen so that the feature parameters related to the signal can be added to each segment on the graph in angular coordinates.

[0236] 310: Loop initial values unit (S10): determines the start parameters needed during the layer and segment loops.

[0237] 311: Layer and segment loop unit (S11): Segment and layer loops are continued to process signal variables in each layer and segment of the graph. In this context, in the inventive system, a nested layer and segment loop is initiated to display the signal parameters in the part of the input signal within the analysis window on the graph in each of the segments on the angular axis (Kf x Sf). 311a; Layer loop unit, 311b; Starts the segment loop unit.

[0238] 312: Layer and Segment boundary identifier (S12): In the invention system, in the process step of determining the Layer and Segment boundaries, according to the calculation method determined in Process step (S04), the boundary values on the coordinate axis are calculated for the signal data to be added to the graph in the Kf(j)th layer Sf(i)th segment on the angular axis. (For two-dimensional angular coordinates, the (x1,y1 ) values of the angular coordinates, for three-dimensional angular coordinates, the coordinate information of the layers and segments (x1,y1,z1 ) are calculated).

[0239] 313: Signal to be displayed identifier (S13): In this context, in the inventive system, the parameter to be displayed in the relevant segment, especially the signal variables to be displayed in the graphs on the 3-dimensional angular axes, are calculated from the signal parameters on each axis and the processes of finding the signal value to be displayed are carried out.

[0240] 314: Signal visualization Unit (S14): In the invention system, the signal visualization unit determines the colour tone corresponding to the relevant feature parameter in the section with the specified coordinate boundaries if the signal is to be displayed with colour tone on the coordinate system and fills the relevant segment with this colour. In each analysis window, the feature parameters of the signal are plotted in the relevant segment and layer on the graph on the defined angular axis or printed symbolically as numerical. If the feature parameters of the signal in the layer and segment with the specified coordinates are to be displayed with a colour code, the colour code corresponding to the parameter is found within a colour palette scaled at a desired resolution level between the minimum and maximum values of the relevant parameter, and the relevant segment is painted with this colour. If the signal to be displayed within the angular coordinate limits of the segments calculated in step (312) on the angular axis is to be displayed with a numerical value, this value is written to the relevant segment.

[0241] 315: Layer and Segment loops continuation unit (S15): In order to process the signal variables in each layer and segment of the graph, the segment and layer loops are continued and the relevant index variables are updated (311). Segment loop continuation unit (315a), Layer loop continuation unit (315b), Graphic display labels unit (315c) are parts of this unit. The loop ends when all segments and layers are completed and some explanatory signal definitions are displayed on the graph.

[0242] 316: Graphic display continuity disabler (S16): When the display of the signal in the analysis window in each segment and layer on the graphic display in angular coordinates is completed, it enables the 'hold on' feature of the graphic display to be turned off (Hold off).

[0243] 317: Signal analysis window stepper (S17): For angular coordinates, it moves to the beginning of the loop (305) for analysis of the signal in the next analysis window.

[0244] 318: Program terminator (S18): The program terminator ensures that the program is terminated when the signals to be processed are exhausted. The program terminator ensures that the program is terminated when the signals to be processed are exhausted.

[0245] 4. The Method for Estimating Signal Vectors in the Angular Axis Developed Within the Scope of the method of invention

[0246] In order to model multiphase signals of Signal2 type on the angular axis using the method of invention, the following method has been developed to obtain signal vector samples in other angular directions determined on the angular axis, based on the input signal vectors collected in various angular directions.

[0247] In the state of the art, the components of a y vector (Equality-1) representing the arithmetic average of any vectors x1 and x2 with an angle (0) between them and both of which have vector lengths L are calculated by taking the arithmetic averages of the corresponding components of the vectors x1 and x2 on an element basis (Equality-2). The angle between the y vector in Equation-1 and the x1 and x2 vectors is (6 / 2).

[0248] y = [ x2 + x1] / 2 (1)

[0249] y = [(x1(1)+x2(1)) / 2, (x1(2)+x2(2)) / 2, ………..,(x1(L)+x2(L)) / 2] (2) The invention vector calculation method (Equation-3) is iteratively derived from the connection in Equation-1, which gives the arithmetic mean of two vectors, and is transformed into a general vector calculation to find (n-1) vector components between vectors x1 and x2. In this context, as seen in (Figure 6), the distance between any two vectors x1 and x2 with an angle 0 between them is divided into n equal segments in order to obtain (n-1) number of vectors between the two vectors, in order to represent an integer value (n=2,3,4,..) where n is greater than 1. In order to find (n-1) the number of vectors y(i) between the vectors x1 and x2 (y(i), i=1,2,3,..., n-1), each vector component is derived using the calculations in Equation-3 below. Here, the angular value between any two adjacent y(i) vectors is (0 / n). In Equation-3, as in Equation-1 and Equation-2, the elements of a matrix Bx (j, i) of size (L x (n-1)), each column of which contains vector elements y(i) of length L, must be calculated from vectors x1 and x2. Equation-3 is included in Claim-5, the algorithmic processing steps of Equation-3 are described in Claim-6, and an application of Equation-3 within the scope of the signal vector estimation method in Claim-2 is described in detail in Claim-7 and Figure-4.

[0250] B

[0251]

[0252] x (j, i)= [ (n-i) * x1(j) + (i) * x2(j) ] / n, j=1 and i = 1,...,n -1) (3)

[0253] Similarly, as seen in Figure 6, if it is assumed that the signal shows similar behavior in negative polarity, the vectors in the 180°opposite direction for the vectors passing through the center of the coordinate point (0 coordinate point) can be taken as vector samples in negative polarity of the said vectors. In this way, for example, by using 3 input vectors with an angle of 180 between them, it is possible to derive (n-1) vectors in the angular directions related to n segments between two adjacent input vectors in angular coordinates. For example, when n = 8 is chosen for 3 signal vectors with an angle of 120° between them on the two-dimensional axis, an input signal matrix consisting of 3 x 8 = 24 vectors can be formed and thus, starting from only 3 input signal vectors, a total of 24 input signal vectors can be derived with angular directions of 360 / 24 = 15°. In this way, the algorithm developed to use the method in Equation-3 to create a signal matrix from more than 2 input vectors is described in Claim-7.

[0254] With this method, which was developed for the purpose of modeling Signal2 type signals using the method of invention, the input signal vector samples given in different angular directions for a signal of Signal2 type are used and the signal vector samples in other angular directions between these vectors are derived with the arithmetic mean formula in Equation-3. Thus, a signal matrix can be derived to represent Signal2, covering all segments in angular coordinates. The subsequent process is similar to the process described in Signal1. In this developed method, in order to estimate signal vectors in non-given angular directions using input signal vectors, it is assumed that there are no changes in the input signal vectors in the estimated angular directions of the signal that are too large to be removed by arithmetic average. In this respect, it is important that the input signal vectors in the angular directions between [0-2*pi] are given as input vectors in such quantities and angular directions that vectors in unknown phases can be estimated from known vectors. If there are large changes in the directions for which information about the signal has not been collected, the signal vectors found by the arithmetic average will not reveal the true behaviour of the signal.

[0255] In order to model an input signal of the Signal2 type in the time plane in angular coordinates in the ‘time plane’ with the invention, firstly the short time interval ([tmin-tmax]) in which the signal will be analysed is determined with a windowing method and then the graphic display in angular coordinates is divided horizontally into time layers with the desired resolution and vertically into segment intervals determined according to the desired resolution level. Subsequently, the time domain feature parameters related to the signal, such as the amplitudes, power values, and angular values of the signal, are modelled on the graph on the angular axis. In this context, the biggest difference in modeling signals of Signal1 and Signal2 type in the method of invention is the step of creating a signal matrix by deriving the signal vectors in angular directions not given as input signal data from the input signal vectors for a signal of Signal2 type. Thus, the behaviour of the signal in all angular directions for any time instant can be expressed in angular coordinates.

[0256] In order to model an input signal of type Signal2 in the frequency domain in angular coordinates, firstly, the vector signal parameters related to Signal2, which are derived in the angular directions of the segments determined in the angular coordinates in the time domain mentioned in the previous step, are derived and an input signal matrix representing Signal2 needs to be created. Subsequently, similar steps are followed to model the signal of type Signall in angular coordinates in the frequency plane. After the frequency components of the signal elements in the relevant segment in the derived input signal matrix are transformed to the frequency plane with any signal spectrum analysis method known in the literature, such as the Fourier Transform method, power spectrum analysis methods or wavelets, and the spectrum parameters such as the frequencies, frequency amplitudes, power values, and angular values of the signal are modelled on the graph on the angular axis in the relevant segment in the [O-Fs / 2] frequency region.

[0257] An application of the signal vector estimation algorithm in Equation-3, which is used to obtain Nj-1 new vectors between each of the Ni vector sequences ([x1,x2,...,x(Ni]), is carried out with the following process steps. An AA matrix array of size (Ni x L) containing Ni vectors of length L each with an angle 0 between them (AA = [x1,x2,...,x(Ni]) is taken from the AA matrix array to form a BA matrix array of size (Sf x L) (401). Here, (Nj-1 ) new vectors are added between every two adjacent vectors in the AA matrix and corresponds to Nj*Ni = Sf. The BA matrix is initialized as empty and starts with a value of k = 1 (402). A loop is started for Ni input vectors in the AA matrix (i=1: Ni) (403). The ithvector of the AA matrix array is transferred to an A2 array (A2(:)=AA(:,i)) (404). i is checked whether the index value is less than Ni (405). If i< Ni, it is taken as B2(:)=AA(:,i+1) (405a). If i>=Ni, it is taken as B2(:)=AA(:,1) (405b). A loop is initialized for Nj prediction vectors (j=1: Nj) (406). With the formula BA(:,k)=(Nj-j+1 ) / Nj)*A2+((j-1 ) / Nj)*B2, the kthvector of the BA matrix is calculated and the k value increases with k=k+1 (407). It is checked whether the j index value is smaller than Nj (408). If i< Ni, return to step (406). If i >= Ni, it is checked whether the index value i is less than Ni (409). If j< Nj, return to step (403). If j>=Ni, the loop operations are completed and the BA matrix of size (SfxL) is formed (410).

[0258] 5. A method of generating a signal from a graphic image by operating the method of invention from the end to the beginning

[0259] One application of the inventive method is the process of creating a signal from any graphic image or picture by operating the inventive method in Claim-1 from the end to the beginning, as described in Figure 2 and included in Claim-4. In this context, a graphic image is divided into segments and layers, and the parts in these segments and layers are combined into a series of variables to represent a signal, in order to obtain a signal form from any graphic shape. On the other hand, this form of modeling has only been modelled theoretically at this stage and its practical application is being worked on. The method of generating a signal from a graphic image may include the following steps:

[0260] Taking a picture or graphic image as input data (201), defining an angular coordinate system for the portion of a picture or graphic image to be converted into a signal, according to the arguments and phase angles of the signal to be converted in a loop within a signal analysis window (202), dividing the graph on the angular coordinate axis into segments and layers according to variables such as the amount of resolution, limit values, amount of linear or nonlinear variation and phase angles of the signal to be converted (203), Starting a loop for segments and layers of the chart (204), Converting the colour tones in the relevant segments into numerical values to represent the signal variables, according to a colour palette defined in the resolution and limit range to represent the signal, and transferring the same to an array, if each segment of the graphic and each remaining part of its layers are defined in terms of colour tones (205), converting the symbols, signs and numerical values into numerical values to represent the signal variables according to a defined range of variables with the resolution and limit range to represent the signal, if each segment of the graph and each part of the graph in its layers has symbols, signs and numerical values that can be associated with numerical values (206), Providing a loop continuation unit for segments and layers of the graph and conversion of all segments and layers into signal variables (207), storing the signal fragment in memory in accordance with the layer and segment in the larger signal and its angular orientation on the coordinate axis, and returning to the beginning of the analysis window loop (step 202) if the graphic image, as part of a larger graphic, is converted into a signal during the analysis time (208), Combining the signal data and storing the same in a multidimensional signal array according to their angular orientation, and completing the signal extraction from the graphic image, once the analysis is complete (209).

[0261] 6. Defining Various Types of Angular Coordinates and Layer and Segment Regions for Use in the Inventive Method

[0262] This section includes details on determining different types of angular axes and graphic patterns to be used in various signal modeling systems designed using the method of invention. In this context, the calculation of various types of angular coordinates and segments and layers is explained. On the other hand, the angular cutting models presented here are presented to help better understand the technique and are not critical models for applying the Inventive method. Any other angular axis coordinate defined by the technique specified in the inventive method can serve the same function as the angular coordinate types herein.

[0263] For the angular axis coordinate calculations in this section, the theories used for similar angular axes in the state of the art are mostly applied. In this context, in order to test the modeling of signals with the method of invention, a total of 7 different angular axes were designed in the 2-dimensional axis and 3-dimensional axis, and how to describe the segments and layers in these 7 different angular axes is explained in detail in this section.

[0264] In the state of the art, the parameters of the Cartesian or polar coordinate system used to define a point in a two-dimensional space can be converted to each other. In the two-dimensional Cartesian coordinate representation of any function F(x,y), the x-coordinate indicates how much to go right / left and the y-coordinate indicates how much to go up / down. In the polar representation of a function F(x,y), the same function is expressed in terms of F(r,0), where r indicates the distance to be travelled to reach the relevant point and 0 indicates in which direction the path should be travelled. Here, for the function F(r,0), we move within a circle of radius r (r:0-> oo) (2.ir.r) and on a circle segment at a certain polar angle 0 from the center (0: 0->2. IT). For the description of a point in Cartesian coordinates, the F(x,y) function representation is used, and for the description of the same point in polar coordinates, the F(r,0) function representation is used, and in the state of the art, Cartesian / polar coordinate point transformations are provided with the help of the formulas between Equations (4-6). Here, i and j values are the unit vector parameters of the x and y axes, respectively (Figure 7).

[0265] x = r.cos(0), y = r.sin(0) (4)

[0266] F(x,y) = r.cos(0).i + r.sin(0).j (5)

[0267] F(r,0) = r.ejO (6)

[0268] In the signal modeling system designed with the method of invention, when the angular coordinate axis in the two-dimensional axis is defined in terms of polar coordinates, 4 options are presented to the user and for the angular axis, the user is asked for the following for the layers;

[0269] • SELECTION 1: Spiral curvilinear area (Figure 8)

[0270] • SELECTION 2: annular curvilinear field (Figure 8)

[0271] • SELECTION 3: Spiral trapezoid area (Figure 9)

[0272] • SELECTION 4: Spiral trapezoid area (Figure 9)

[0273] Options are asked.

[0274] 6.1. Selection 1-2: The figure in Figure 8 shows an area A between the horizontal curves (r1-r3), (r2-r4) passing through the lines 0=a and 0= in polar coordinates, whose quadrant is depicted in the figure. If the graph in Figure 8 is composed of spiral curvilinear areas, the curve values in the notes r1,r2,r3,r4 are different from each other, since the curves r1 and r2 expand along the spiral. In Figure 8, the calculation of the hatched area A in polar coordinates in numerical systems is performed by integral approximation calculations. In integral approximation calculations, the relevant segment is divided into sub-segments of length N and calculated by forming a sequence. In this context, in order to draw or colour in the segment enclosed by area A, the segment denoted by area A is defined as a vector array of N elements between the curves (between r1 and r3), (between r2 and r4) defining the segment, and the lines 0=a and 0=0.

[0275] By using the Selection-1 option, when the segments are defined as the area A in Figure 8 and it is desired to draw the angular axis as circular areas in a full circular view but in a spiral shape as in the visual in Figure 14, the following path is followed to draw the segment surrounded by the area A in polar coordinates. The calculation of the (x1,y1,x2,y2) Cartesian coordinates for the drawing or painting of the segment between the alpha and beta angles of an area A as shown in Figure 8 on a spiral-shaped angular axis initiated by a radius RO with a degree of precision N can be performed by the following steps. Here, the values of r1 and r2 multiplied by the ‘ones’ command generate vector arrays rho1 and rho2 of length N. By means of these commands, the curves (r1-r3) and (r2-r4) in the segment in area A determined by the vectors (x1,y1,x2,y2) are drawn in a circular pattern as shown in Figure 8. All the following process steps are represented by Equation-7;

[0276] Theta=alpha:pi / N:beta;

[0277] R0=(1 / segment)*(r2-r1) / (length(Theta)-1);

[0278] rho1 (1 )=r1;

[0279] rho2(1 )=r2;

[0280] for i=2:length(Theta)

[0281] rho1 (i)=rho1 (i-1 )+R0;

[0282] rho2(i)=rho2(i-1)+R0;

[0283] end

[0284] for i=1: N, rho22(i)=rho2(N-i+1),end

[0285] x1= rho1*cos(Theta); y1= rhoTsin (Theta);

[0286] x2= rho22*cos(Theta); y2= rho22*sin (Theta); (7)

[0287] By using the Selection-2 option in the algorithm, if the area A in Figure 8 is defined and the angular axis is to be drawn as circular areas as in Figure 14, r3=r1, r2=r4 are taken. The calculation of the (x1,y1,x2,y2) Cartesian coordinates for the drawing and colouring of any segment between the alpha and beta angles of the area A in Figure 8 on the curvilinear annular angular axis initiated by a radius RO with a degree of precision N can be performed by the following steps. All the following process steps are represented by Equation 8;

[0288] Theta=alpha:pi / N:beta;

[0289] rho1 =r1 *ones(size(theta));

[0290] rho2=r2*ones(size(theta)); for i=1: N, rho22(i)=rho2(N-i+1),end

[0291] x1= rho1*cos(Theta); y1= rhoTsin (Theta);

[0292] x2= rho22*cos(Theta); y2= rho22*sin (Theta); (8)

[0293] 6.2. SELECTION 3-4: The determination of each segment defined by the area A in the graph in Figure 8 by integral approximation area calculations requires the calculation of a set of variables for the upper and lower boundaries of each segment, as described above. This increases the processing complexity in the program. On the other hand, the number of segments and layers in the graphs drawn in the method of the invention can reach hundreds in high-resolution operations, and the need for determining the segment area with array variables decreases as the segment intervals in polar coordinates become denser. In this respect, in addition to the above-mentioned method for determining the segment boundaries and colouring or drawing the segment at these boundaries, an alternative method of defining the angular coordinate axis, as shown in Figure 9, has been used in the method of the invention as an alternative option. In this context, if the number of segments determined in angular coordinates is high and the resolution level is increased, the area A in Figure 8 and its perimeter can be calculated by approximating a trapezoidal area represented by the points (a, b, c, d) as shown in Figure 9 in order to speed up the operations and reduce the computational complexity. Figure 9 shows the trapezoidal equivalent modeling of a segment in Figure 8 on the polar axis. Here, the vertices (a, b, c, d) indicate the boundaries of the segment. The segment region F(X, Y) enclosed by the points [a, b, c, d] in Figure 9, when the x and y axis parameters are defined in terms of polar parameters, will consist of the union of coordinate points (a, b, c, d) as follows, where each corner of the segment is described by a 2-variable array as angular distance and angular value, and each segment region will be represented by a 2x4 dimensional function F(X, Y).

[0294] The angle 01 at the points in the function F(X, Y) is the angle between the horizontal axis of the intersection point of the line 0= 01 and the curve r1 or r2, and the angle 02 is the angle between the horizontal axis of the intersection point of the line 0= 02 and the curve r3 or r4. In the function that describes the relevant segment as a segment region F(X, Y) in polar coordinates, the variables X and Y will consist of 4-element arrays as above. If the annular drawing of each layer in the graph in polar coordinates is chosen, the values of r3 and r4 are the same as r1 and r2. All the following process steps are represented by Equation-9.

[0295] a=[a(1 ), a(2)] = (r1,cos(01 ), r1,sin(01 )), where r1: (0->a) is the distance between points.

[0296] b=[b(1), b(2)] = (r2.cos(01), r2.sin(01 )), where r2: (0->b) is the distance between points. c=[c(1), c(2)] = (r3.cos(02), r3.sin(02)), where r3: (0->c) is the distance between points.

[0297] d=[d(1), d(2)] = (r4.cos(02), r4.sin(02)), where r4: (0->d) is the distance between points.

[0298] X=[a(1 ) b(1 ) c(1 ) d(1 )],

[0299] Y=[a(2) b(2) c(2) d(2)] ->

[0300] F(X, Y)=[a(1) b(1) c(1) d(1); a(2) b(2) c(2) d(2)] (9)

[0301] When it is desired to draw the segments as segments of an angular axis moving in a spiral as shown in Figure 3-c using Selection-3, the r curves will not remain constant since the rings along the segments in the spiral are expanding. With the increase of the segments with equal distances and a rinc value determined as the distance increment value between the two layers, the segment angular distance values will need to be calculated in the formulas above as r3= r1+rinc / Sf and r4= r2+rinc / Sf. In general, all segments in any spiral-shaped layer can be generated by the formula (ri=r(i-1)+(rinc / Sf), i=1,2,3,,,, Sf) if the segment spacing is equal. When the layers are increased in circular rings, the ri values of all segments are the same for the same layer, and the radius of all segments of the new layer is determined as (r=r+rinc) before the next layer is created.

[0302] 6.3. SELECTION-5: In the system of the invention, in order to define the angular axis in terms of segments and layers in the angular region between [0-2TT] and to construct it in Cartesian coordinates, a function (G(X, Y)) can be defined for the Cartesian coordinate region (a, b, c, d) of each segment (a, b, c, d) as shown in Figure 10, and in this way, the drawing of digital signals in Cartesian coordinates can be done by following a similar process steps in the method of the invention. In this case, the coordinates of the points (a, b, c, d) of the G(X, Y) segment will consist of a set of projections of the relevant points on the x and y axis. In addition, all segments can be created from a starting point a:(a(1),a(2)) by traveling ‘v’ units in the horizontal direction and ‘u’ units in the vertical direction representing the layer spacing. In the graph in Figure 6, the axes of the variables representing the angle and the independent variable can be switched when desired. All the following process steps are represented by Equation 10;

[0303] a=[a(1), a(2)]

[0304] b=[b(1), b(2)] =[a(1)+v, a(2)]

[0305] c=[c(1), c(2)] =[a(1)+v, a(2)+u] d=[d(1), d(2)] =[a(1), a(2)+u]

[0306] X=[a(1), (a(1)+ u), (a(1)+u), a(1)],

[0307] Y=[a(2), a(2), a(2)+u, a(2)+u ]

[0308]

[0309] G(X, Y)=[a(1 ), (a(1 )+ u), (a(1 )+u), a(1 ); a(2), a(2), a(2)+u, a(2)+u] (10)

[0310] 6.4. SELECTION-6: In the system of the invention, cylinder coordinate calculations in the known state of the art are utilised to define the angular axis in terms of segments and layers in the angular region between [0-2TT] and to generate it in 3D cylinder coordinates. The definition of a function P(X, Y, Z)) that will represent the parameters (a, b, c, d) in the cylinder coordinate region (P(X, Y, Z): a(x1,y1,z1), b(x2,y2,z2), c(x3,y3,z3), d(x4,y4,z4)) and its parameters in coordinates can be calculated as follows. In this case, the coordinates of the points (a, b, c, d) of the segment P(X, Y, Z) will consist of a set of projections of the corresponding points on the x and y axis. If we design the angular axis so that the z-axis represents the independent variable itself and the base of the cylinder represents the angles, for example, the signal behaviour on a time axis can be monitored in real time on the time axis. In this respect, the system of the invention is considered to be very effective in monitoring the continuous signal behaviour of the cylindrical angular axis. All the following process steps are represented by Equation-11;

[0311] zz=linspace(Kf,0, Kf+1);%Z coordinate in terms of Kf independent variable layers

[0312] angles = linspace(0, 2*pi, Sf+1); % angles of segment slices

[0313] for j=1: Kf+1

[0314] for i=1: Sf

[0315] X = rs*[cos(angles(i)), cos(angles(i+1)), cos(angles(i+1)), cos(angles(i))];

[0316] Y = rs*[sin(angles(i)), sin(angles(i+1 )), sin(angles(i+1 )), sin(angles(i))];

[0317] Y= [ zz(j), zz(j), zz(j+1), zz(j+1)];

[0318] end

[0319] end (11) 6.5. SELECTION-7: In the system of the invention, spherical coordinate calculations in the known state of the art are utilised to define the angular axis in terms of segments and layers in an angular region between [0-2TT] and to construct it in 3D spherical coordinates. The definition of a function Q(X, Y, Z)) to represent the axis parameters (a, b, c, d) in the spherical coordinate region (Q(X, Y, Z): a(x1,y1,z1), b(x2,y2,z2), c(x3,y3,z3), d(x4,y4,z4)) and its parameters in coordinates can be calculated as follows. In this case, the coordinates of the points (a, b, c, d) of the segment Q(X, Y, Z) will consist of a set of axis parameter calculations in the x y and z axis on a spherical axis with radius rs. All the following process steps are represented by Equation-12;

[0320] dangles = linspace(0, pi, Kf+1); % spherical axis angle in vertical direction

[0321] yangles = linspace(0, 2*pi, Sf+1); % spherical axis angle in horizontal direction

[0322] for j=1: Kf+1

[0323] for i=1: Sf

[0324] X= rs*[sin(dangles(layer))*cos(yangles(i)), sin(dangles(layer))*cos(yangles(i+1 )),...

[0325] sin(dangles(layer+1 ))*cos(yangles(i+1 )), sin(dangles(layer+1 ))*cos(yangles(i))];

[0326] Y= rs*[sin(dangles(layer))*sin(yangles(i)), sin(dangles(layer))*sin(yangles(i+1 )),...

[0327] sin(dangles(layer+1 ))*sin(yangles(i+1 )), sin(dangles(layer+1 ))*sin(yangles(i))];

[0328] Z=rs*[cos(dangles(layer)), cos(dangles(layer)), cos(dangles(layer+1 )),...

[0329] cos(dangles(layer+1 ))];

[0330] end

[0331] end (12)

[0332] The method of the invention is essentially based on the construction of a coordinate axis based on angular values, at least one independent variable and the signal axis dimensions, and the expression of the signals in these regions by dividing the axis variables into segments and layers in proportion to the resolution of the signal to be imaged. There are, of course, many ways in which the angular coordinate axis, which may be 2-dimensional or higher, can be modelled in many different shapes, views, and dimensions than the 7 angular coordinate axis models described here. On the other hand, the shape of the coordinate axis, the pattern, is not a fundamental factor for the application of the method of the invention. In this respect, coordinate axes to be designed or defined in different views and shapes do not affect the method of the invention. Angular coordinate axes modelled by defining angular coordinate axes dependent on angular values, the size of which depends at least as a minimum on the axis size of the signal and at least one independent variable, as long as at least one signal parameter is expressed in segments and layers in said angular coordinate axis, or methods for expressing a numerical data in said segments and layers, such as colouring segments pixel by pixel instead of colouring any segment completely, should not be considered as different from the inventive method.

[0333] Similarly, with components such as standard input devices that can be incorporated into a general-purpose computer system, the data of the modeling system of the invention can be retrieved therefrom or the model results can be displayed on output devices, transferred to another device via a network system or radio transmission system, and saved and stored as desired. Since the method of the invention is applicable to all digital signals, the field of application is very wide. Therefore, such embodiments that modify various embodiments of the inventive method for their application in specific signal modeling should not be considered separately from the inventive method, as they do not affect the basic structure of the inventive method.

[0334] The basic information of the above 7 different coordinate axes, which are optionally included in the signal modeling system realized by the inventive method, is given here. In this context, Figure 11 shows the angular phase values seen by the segments in the range [0-> 2TT] in radians when a layer interval is divided into 12 segments on the polar axis. When the segments are equally divided, the angle 0 seen by the extreme corner of any i-th segment is (2n*i / (Sf)) from the center. Figure 12 shows the view of the segments and layers in a polar coordinate with the number of layers Kf=8 and the number of segments Sf=24 and spiraling along the layers.

[0335] An example of an alternative model that can be produced by dividing the layers into sublayers for the expression of two separate variables of a signal in segments in a polar axis designed by the inventive method is presented in Figure 13. In Figure 13, which consists of two layers, variables are added as numerical values in the sub-layers and segments in each layer to express the second variable on the angular axis.

[0336] In the signal modeling system developed to realize the models in the system of the invention, the following path was followed; Firstly, the number of layers in the graphic display in angular coordinates between the lower and upper limits of the axis parameter, which is the independent variable in the analysis window of the input signal, and how many segments each layer will be divided into are determined. It is also determined whether the independent variable components related to the feature parameters of the signal to be displayed on the coordinate axis will increase linearly or non-linearly in each layer. Signal feature parameters at this layer and segment resolution are calculated linearly or non-linearly. In the region between the limits of the axis parameter between any two layers of the signal, the angular value (0i) is calculated for each segment in the relevant layer, and the radius value (ri) from the center point if the angular axis is polar. For the axis parameters between the boundaries of each segment (sfi), the signal feature parameters corresponding to the relevant parameters are determined as parametric values that can be included in the relevant segment region.

[0337] In Figure 15, when the polar coordinates are modelled according to octave frequency bands with the method of the invention, the corresponding frequency components of the 15-octave frequency layer regions in Cartesian coordinates are shown as blocks on the horizontal axis on a graph where the FFT amplitudes and phase angles in Cartesian coordinates are plotted. Figure 16 shows a graph of the signal FFT amplitudes and phase angle values on the vertical axis corresponding to the frequency values on the logarithmically scaled horizontal axis after applying the Fourier transform of a signal sampled at Fs=44100Hz. In Figure 16, FFT amplitude values corresponding to some resonance frequencies of a signal in Cartesian coordinates are marked.

[0338] In Figure 17, the structure is modeled in which the frequencies are modeled as independent variables in the layers and show an octave-based increase in each layer, with the layers increasing in a spiral from the inside to the outside. Here, when the total number of layers (Kfj, j=1:8) is selected as Kf=8 and the total number of segments (Sfi, i=1:24) is selected as Sf=24, the graphical display in polar coordinates in Figure 17 is obtained. The regions between each ring of the spiral circle represent the layers (Kfj) and the compartments in each layer represent the segments (Sfi).

[0339] In the graph in Figure 15, the distribution of all frequencies in Cartesian coordinates is located side by side on the horizontal axis and the relationship between the resonant frequencies and their congeners is not easily distinguishable. In Figure 17, which is designed in polar coordinates with the inventive method, the fundamental frequencies are located in each octave frequency layer in relation to their natures. In this way, it is possible to analyze the changes in the spectrum parameters against the frequency components of the signal by correlating the fundamental frequencies with the originals and dividing them into different layers. In addition, changing signal amplitude values can be easily evaluated by monitoring the tonal changes in colours. In Figure 16, the resonant frequencies or the frequencies corresponding to the sparks, which cannot be easily seen when the frequencies are increased to high frequencies, can be easily monitored simultaneously in Figure 17 in terms of both the colour tones corresponding to the amplitudes and the numerical values of the frequencies in each segment box. In the known state of the art, the relationship between the spectrum parameters of a signal and its frequency values can be seen comparatively in Figure 16, which presents the relationship between the spectrum parameters of a signal and its frequency values in a graphical display drawn in Cartesian coordinates, and in Figure 17, which is drawn in polar coordinates in the inventive method. As can be seen in Figure 17, the relationships between the frequencies and the nature of the octave layers can be seen quite easily. In Figure 17, the frequency value for the innermost ring (the first spiral ring) starts with 0Hz on the horizontal axis at the centre of the circle and reaches 1 Hz when one round is completed. Starting from 1 Hz in a circle with radius 1 and n being an integer, the frequencies of a signal can be described in the corresponding segments when travelling on a circle of equal scale with 2^(1 / n) frequency intervals. According to Nyquist theorem, since the maximum frequency value (Fmax) in a signal is equal to half of the sampling frequency (Fs) of the signal, the Fmax value for Fs=44100Hz is 22050Hz. In this respect, the frequency range in polar coordinates in the method of the invention is described by 15 octave layers between [(1^(2A15)Hz],

[0340] In the method of the invention, a digital signal is modelled in the angular segment and when the independent variable is taken as frequency and the frequencies are increased on an octave basis, starting from a minimum frequency value, the frequencies within the studied frequency limits are separated according to a (2An) (nth power of 2) value in each layer and octave frequency bandwidths are found. Here, the octave frequency bands to be located in each layer region (Kfj, j=O:n), where n is any integer, starting from the center of the graph and moving in the order of (0, 1, 2, 2A2, 2A3, 2A4, > )Hz at the beginning of the layers respectively ([0-1], [1-2], [2-4], [2-4], [4-8], [8-16], [16-32],...) Hz octave frequency bands are formed in each layer. In this way, the signal frequencies can be described in separate layers in the frequency bandwidths of the ‘octave’, a term often used in music. With the invention, the phase angles of the sine components in the signal are made visible in polar coordinates and the signal is divided into layers in the octave band, and all the components of any fundamental frequency (F0) in the signal are made visible by associating them with the spectrum amplitudes and phase angles. Since the frequency distribution in the signal is defined as octave intervals in each ring of the layers, in reality all frequencies and their dependent parameters are related to the logarithm-2 base. TESTS PERFORMED ON THE SIGNAL MODELING SYSTEM USING THE METHOD OF INVENTION

[0341] During the tests of the signal modeling system using the method of the invention, tests were carried out with various signals of the type Signal 1 and Signal2 by specifying the independent variable as time or frequency. As can be seen from the test results in the graphs between Figure 18 and Figure 45, many signal types such as sound, ECG, EEG, earthquake signals can be modelled in different angular axes with the inventive method. These tests are described below under the headings of time domain and frequency domain analyses for signals of type Signall and Signal2.

[0342] The figures and drawings obtained as a result of the tests carried out on the inventive signal modeling system are only examples for a better understanding of the method and do not constitute any limiting effect, and the signals such as sound, music, earthquake, biomedical signals, which are most commonly analysed in signal processing of the inventive method. On the other hand, the capabilities and possible effects of the method of the invention in digital signal processing are not limited to the system described herein, and the system described herein and tested and the test results presented herein may be used by a person skilled in the art to develop other systems and obtain other coordinate axes and signals modelled on these axes without creative effort and by using known techniques of signal processing to implement the method of the invention of Claim-1.

[0343] A. Testing and Analyses for Signals of Signall Type by the Inventive Method

[0344] A1. Testing and analysis of signals of type Signall in the time domain by means of a signal modeling system using the inventive method: With the system developed by the method of the invention, signal plots of audio signals of the type Signall were made in the time domain and in the polar axis. With the aforementioned analyses, various audio signals with different sampling frequencies were taken as input signals and the invention signal modeling system was implemented, tested, and analysed. For the audio data used in the tests, audio and music signals obtained from open sources on the Internet were used as input.

[0345] Figure 18 is a plot of the propagation graph of the sound signal amplitudes in all angular directions as a result of the experiment using the system designed by the method of the invention for the variation of the signal amplitudes with respect to time for the 100ms analysis window of a sound signal amplitude sampled at 1Khz. Each circular ring (layer) in Figure 18 represents the signal amplitudes in all angular directions at a time instant and the slices between two circular rings represent segments (48). Since Fs=1000Hz, there are Kf=100 layers for 100ms analysis window. In Figure 19, the analysis window time for the same signal is increased to 250ms. In this context, Figure 19 is the plot of the time variation of the signal amplitudes for the 250ms analysis window of an audio signal amplitude sampled at 1 Khz, as a result of the experiment using the system designed by the method of the invention.

[0346] A2. Testing and analysis of signals of type Signal1 in the frequency domain by means of a signal modeling system using the inventive method Using the system of the invention, various audio signals, including music signals of the type Signal 1, have been analysed in the frequency domain. With the aforementioned analyses, various audio signals with different sampling frequencies are taken as input signals, the invention system is implemented and the effects of different sampling frequencies and different windowing times on the signal are tested and analysed. One of the test results obtained as a result of the tests of the audio signals in the form of Signall with the invention system is shown in Figure 20. Figure 20 shows the graph of an audio signal sampled at 44kHz in polar coordinates in the inventive system, in any analysis window (window length 300ms), in which the coordinate axis is described in 14 layers and 24 segments, the maximum spectrum amplitudes in each segment are described by the corresponding colour tones in a colour palette ranging between the limits of the spectrum amplitude values, and the frequency values for the relevant spectrum amplitudes are shown as numerical values. For the signal, an octavebased modeling was performed, with each layer incremented according to the logarithm-2 base. It can be seen from the graphs herein that modeling the audio and music signals with the inventive system provides more detailed information than modeling in Cartesian coordinates in the state of the art and facilitates visual evaluation.

[0347] Figure 20 is the drawing where the maximum spectrum amplitudes in each segment are described with colour tones in any analysis window (window length 300ms) of an audio signal sampled at 44kHz on the polar axis where the polar coordinates are described in 14 layers according to the increasing frequency according to the logarithm-2 base in the system developed using the method of invention, and the frequency values for the relevant spectrum amplitudes are shown as numerical values. As can be seen in Figure 20, if the analysis window period is short, the frequency resolution remains low, so there are no frequencies in the layers corresponding to the low frequency region and the relevant segments appear empty. When the frequency resolution is increased by extending the signal analysis window period and when the signal spectrum resolution is increased by increasing the number of segments (Figure 21), results that allow more precise analysis of the signal are obtained. FIGURE 21, is a drawing showing the graph of a music track sampled at 44Khz in the 300ms analysis window of a music track sampled at 44Khz in the system developed using the method of the invention, which is defined as 128 segments and 14 layers according to the increasing frequency according to the logarithm-2 base along the segments polar axis, by showing the spectrum parameters in colour tones; Figure 22 is the drawing showing the colour tones of the spectrum amplitudes of 12 consecutive analysis windows in polar coordinates described by the method of the invention, divided into analysis windows of a music track in mp3 format sampled at 44 kHz, and the representation of the FFT amplitudes in 12 analysis windows in Cartesian coordinates.

[0348] B. Testing and Analysis for Signals of Signal2 Type with Inventive Method

[0349] B1. Tests and analyses in time and frequency domains for Earthquake signals of Signal2 type with the signal modeling system performed using the method of invention: In testing and analysing earthquake signals of the Signal2 type with the invention system, the structure of earthquake signals is first addressed. As can be seen in Figure 23, earthquake signals are divided into two groups: body waves and surface waves. Body waves that occur before the earthquake reaches the surface are divided into P-waves and S-waves, and surface waves, which are the most powerful and destructive effects after the earthquake waves reach the surface, are divided into Rayleigh (R) and Love (L) waves.

[0350] Using the method of invention, earthquake data for the analysis of Signal2 type earthquake signals in the time domain were taken from the internet address of Afad referenced [3] The earthquake data here includes earthquake signals from various regions of Turkey, and the earthquake data used during the tests is for March 29, 2023 and id: 15628 code: 3120 is the ‘Acceleration’ data of the earthquake with a magnitude of 4.1 that occurred 7km below ground in Kahramanmara§ province, recorded with a sampling rate of Fs=100Hz. The earthquake data in question consist of data series collected on three separate axes in the south-north, east-west and up-down directions. The axis direction in which these directions were evaluated during the tests is shown in Figure 23. The directions shown with dashed lines are accepted as completely opposite waves. If we accept the south-north direction as the y-axis and the east-west direction as the x-axis in a 3-dimensional axis, the up-down direction will be in the z-axis direction. In this respect, while accepting the earthquake data in a 2-dimensional axis with the inventive method, only the earthquake data in the x (CH1) and y (CH2) directions were used and with the linear interpolation method developed within the scope of the inventive method, other earthquake vectors in the angular directions as many as the number of Sf segments in the [x,y] plane in the coordinate axis were produced.

[0351] During the tests, body signals such as P-wave and S-wave of the earthquake signal and surface waves such as L-wave and R-wave were evaluated separately from each other due to the large differences in amplitude differences and different behaviour patterns. The waveforms in question were analysed by normalizing between the minimum and maximum values in the signal content.

[0352] In this context, for the two-dimensional analysis in the time plane of the earthquake acceleration data collected in all three coordinate axis directions in the inventive system, 4 different vector sequences of the form AXY = [CH1, CH2, -CH1, -CH2] are collected in an AXY matrix. Then, using the signal vectors in the AXY matrix, a BXY matrix containing a total of Sf earthquake vectors in the angular range [0-2*pi] was generated by the linear interpolation method described in the invention. The vector signal amplitude data in the BXY matrix are shown with colour shades on the angular axes designed by the method of the invention in accordance with their angular directions.

[0353] The results of the P wave analysis in the two-dimensional transect can be seen in Figure 16. Figure 24 is the plot of a 100ms section of the Acceleration signal samples of the Earthquake P wave against time in CH1 and CH2 channels in Cartesian coordinates in the state of the art. FIGURE 25, is a plot of the 100ms portion of the Acceleration signal samples of the earthquake P wave versus time in the CH1 and CH2 channels as a result of the experiment using the system designed by the Discovery method; In Figure 25, each circular ring (layer) represents the P wave signal amplitudes in all angular directions at a time instant, and the slices between two circular rings represent segments (24 pieces). Since the sampling rate is Fs=100Hz, there are Kf=100 layers for the analysis window in the 1 s time plane.

[0354] The analyses show that although the P-wave, which appears at the beginning of the earthquake signals, appears to be in a random noise behaviour, there are findings related to the direction of arrival of the wave within the wave. If this is supported by further tests on the earthquake signal, it is evaluated that the time to determine the direction of the signal regarding the possible target area and to take action in advance will be extended with the information provided at the very beginning of the earthquake signals. It is seen that it has become more possible to see earthquake surface waves (L and R waves) in all angular directions in the time plane and frequency plane and to evaluate the possible damages they will create in these directions.

[0355] Figure 26 is the plot of a 1s portion of the Acceleration signal samples against time in CH1 and CH2 channels containing surface waves (Rayleigh waves and Love waves) in Cartesian coordinates in the state of the art. Figure 27 is the graph showing the 1s part of the Acceleration signal samples against time in the CH1 and CH2 channels, which include surface waves (Rayleigh waves and Love waves), as a result of the experiment conducted using the system designed with the method of invention. In the figure, each circular ring (layer) represents the surface wave signal amplitudes in all angular directions at a time instant, and the slices between two circular rings represent segments (24 pieces). Since Fs=100Hz, there are Kf= 100 layers for the 1 s analysis window.

[0356] Earthquake surface waves are modelled on a 3-dimensional cylindrical axis in Figure 29. Figure 28 is the plot showing the 1 -second portion of the Acceleration data of the Earthquake surface waves (east-west, north-south and up-down) in Cartesian coordinates in the state of the art. FIGURE 29, is the plot of the 1 s portion of the Acceleration data of the earthquake surface waves in the directions (east-west, north-south and up-down) on the 3-dimensional cylindrical axis as a result of the experiment using the system designed by the Discovery method; In Figure 29, each circular ring (layer) represents the earthquake surface wave signal amplitudes in angular directions in three dimensions at a time instant, and the slices between two circular rings represent segments (24 pieces). Since Fs=100Hz, there are a total of Kf=100 layers representing each ring of the cylinder for the 1s analysis window and the CH3 data are in the z direction where the cylinder layers continue.

[0357] It is considered that frequency plane analyses of earthquake waves will make it easier to measure possible damage to the environment in all angular directions in each analysis window. Tests related to these were conducted using real earthquake signals obtained from open sources. Here, in the invention system, two ‘Accelaration’ data input signals collected in the ‘north-south’ and ‘east-west’ directions were used as input data, signal vectors were derived to represent all segments and signal matrix was created and analyses were performed on the polar axis. Figure 41 is the representation of the amplitude distributions of the Earthquake R waves in the CH1 and CH2 directions in the time and frequency domains in Cartesian coordinates as a result of the experiment carried out using the method of invention. Figure 42 is the representation of the spectrum amplitude distributions of the Earthquake R waves in the CH1 and CH2 directions in Cartesian coordinates as a result of the experiment carried out using the method of invention.

[0358] B2. Testing and analysis of Heart (ECG) signals in time and frequency domains with the signal modeling system performed using the method of invention: For the ECG data in the test and analysis of Signal2 type ECG signals with the invention system, the open source 12-channel ECG data at [4] was used [5]. The ECG data here are the data of (CH1, CH2, CH3, AVL, AVR, AVF) channels and (V1-V6) channels recorded with a length of 10 seconds and a sampling frequency of 500 Hz, an example of which and its angular directions are shown in Figure 26. In the figure, the derivations between CH1-CH3 channels are ‘bipolar’ derivations obtained by comparing the electrical potentials recorded by a reference electrode and the (+) electrode; AVF, AVR, AVL channels are ‘unipolar’ derivations that can be obtained from CH1-CH3. Channels V1-V6 measured perpendicular to the (CH1, CH2, CH3, AVL, AVR, AVF) channels are unipolar derivations.

[0359] While ECG data were defined on a 2-dimensional axis with the method of invention, CH1, CH2, CH3 channel data were used as input signal data. AVF, AVR, AVL derivations. In the method of invention, while Sf angular axis vectors are calculated from CH1-Ch3 derivations with the linear interpolation method developed for Signal2 type signals, they are automatically calculated in the algorithm. While modeling the ECG data on a 3-dimensional axis, (CH1, CH2, CH3, AVL, AVR, AVF) channels were accepted as representing the (xy) plane on the coordinate axis and (V1-V6) channels were accepted as representing the xz plane, and the data of all 12 channels were used together. During the experiments with the method of invention, since the angular directions of the V1-V6 vectors used as input signals in 3-dimensional angular axes were not written in the data at address [XX] and only the ECG data here were used for the purpose of testing the method of invention, based on the information regarding the V1-V6 vectors in the literature, the V6 vector was assumed to be in the same direction as Leadl and its angular axis was assumed to be 0°, and the electrodes measuring the vectors between V1-V6 from the V1 direction were assumed to be aligned at 30° angles counter clockwise.

[0360] In the tests performed in this context, Figure 30 is a representation of the locations of the 12 lead channels for a 12-lead ECG. Here, there are 30° angles between 12 channels, including 6 negative derivation channels generated from 6 positive derivation channels on the level axis. Although the exact angles for V1-V6 channels on the horizontal axis are not given in the literature, their layouts are as seen in the Figure. (The xy plane in the figure shows the plane where CH1, CH2, CH3, AVL, AVR, AVF channels are measured, and the xz plane shows the measurement direction of V1-V6 channels).

[0361] Figure 31 is the representation of the amplitude distributions of the 1 -second portion of the 6 channels (CH1, CH2, CH3, AVR, AVR, AVF) of an ECG signal in Cartesian coordinates using the state of the art. Figure 32 is the plot showing the polar axis graph of the 1 -second portion of the 6 channels (CH1, CH2, CH3, AVR, AVR, AVF) of an ECG signal, as a result of the experiment conducted using the algorithm designed with the method of invention. In the figure, each circular ring (layer) represents the ECG signal amplitudes in all angular directions on the two-dimensional axis at a time instant, and the slices between two circular rings represent segments (48 pieces). Since Fs=250Hz, there are Kf=250 layers for the 1s analysis window. Figure 33 is the drawing that shows the graph of the 1 -second portion of 12 channels of an ECG signal (CH1, CH2, CH3, AVR, AVR, AVF channels and channels V1-V6) in Cartesian coordinates with the state of the art. Figure 34 is the drawing showing the 1- second portion of an ECG signal, CH1, CH2, CH3, AVR, AVR, AVF channels and V1-V6 channels, on a 3-dimensional cylindrical axis as a result of the experiment performed using the algorithm designed with the method of invention. In the figure, each circular ring (layer) represents the ECG signal amplitudes in all angular directions in the three-dimensional axis at a time instant, and the slices between two circular rings represent segments (48 pieces). Since Fs=250Hz, there are Kf=250 layers for the 1s analysis window.

[0362] In the experiments carried out on the frequency axis, Figure 43, the reproduction of the ECG signal with CH1, CH2, CH3 channel inputs to 48 channels with the Invention system and the representation of the spectrum distribution on the polar axis in the Invention system with colour tones. Each layer shows the spectrum distribution in angular phases for the frequency values between [0-125Hz] of the FFT received signal.

[0363] B3. Each layer shows the spectrum distribution in angular phases for the frequency values between [0-125Hz1 of the FFT received signal. The EEG signal data used in the testing and analysis of EEG signals of the Signal2 type with the system within the scope of the invention were taken from the database of Physionet [6] [7], The database consists of EEG recordings of 14 patients, each 3600 seconds long, recorded in EDF format (European Data Format), obtained during a regional research project called PANACEE [XX], which aims to develop low-cost non-invasive patient-specific monitoring / control devices for the prediction of epileptic seizures at the Neurology and Neurophysiology Unit of the University of Siena in Italy, and has been approved for use in scientific studies. The EEG recording of the subjects was collected at a sampling rate of 512 Hz with electrodes arranged based on the international 10-20 System. Figure 35 shows the International EEG 10 / 20 placement system [8].

[0364] In this context, as a result of the experiments carried out with the invention system on the time axis of EEG signals, Figure 36 is the representation of the signal amplitude distributions in Cartesian coordinates of the 8 electrode signals remaining in the inner square area of the EEG electrodes in Figure 35, using the known state of the art. Figure 37 is the drawing showing the polar axis graph of the 8 electrode signals remaining in the inner square area of the EEG electrodes in Figure 35, as a result of the experiment conducted using the algorithm designed with the method of invention. In the figure, each circular ring (layer) represents the EEG signal amplitudes in all angular directions on the two-dimensional axis at a time instant, and the slices between two circular rings represent segments (64 pieces). Since Fs=128Hz, there are Kf=128 layers for the 1s analysis window. Figure 38 is the representation of the amplitude distributions of the 10 electrode signals located in the outer square area of the EEG electrodes in Figure 35, in Cartesian coordinates, using the state of the art. Figure 39 is the drawing showing the polar axis graph of the 10 electrode signals located in the outer square area of the EEG electrodes in Figure 35, as a result of the experiment conducted using the algorithm designed with the method of invention. In the figure, each circular ring (layer) represents the EEG signal amplitudes in all angular directions on the two-dimensional axis at a time instant, and the slices between two circular rings represent segments (64 pieces). Since Fs=128Hz, there are Kf=128 layers for the 1s analysis window. Figure 40 is the drawing showing the graph of the 10 electrode signals located in the outer square area of the EEG electrodes in Figure 35, on the spherical axis (defined between the spherical vertical axis (0-pi / 2)) as a result of the experiment conducted using the algorithm designed with the method of invention.

[0365] In the experiments conducted on the frequency axis, Figure 44 is the drawing showing the spectrum amplitude graph on the polar axis of the 8 electrode signals remaining in the inner square area of the EEG electrodes in Figure 35, as a result of the experiment conducted using the algorithm designed with the method of invention. Figure 45, Representation of the ECG spectrum distribution in colour tones by determining the vertical angle (0-pi / 2) of the 3-dimensional spherical axis of the ECG signal created with the invention system. Each layer shows the distribution of the FFT of the received signal in angular phases for frequency values between [0-125Hz], REFERENCES

[0366] 1. Constantine A. Balanis, “Antenna Theory: Analysis and design”, 4th edition, John Wiley & sons, 2016, ISBN:978.111.864.206.01

[0367] 2. Rangaraj M. Rangayyan, Sridnar Krishnan, “Biomedical Signal analysis”, IEEE press, Wiley Blackwell, 2024, ISBN: 978.982.585.2

[0368] 3. https: / / deprem.afad.gov.tr / last-earthquakes.html

[0369] 4. https: / / www.kaggle.com / datasets / bjoernjostein / georgia-12lead-ecg-chalienge- database

[0370] 5. Goldberger AL, Amaral LAN, Glass L, Hausdorff JM, Ivanov PCh, Mark RG, Mietus JE, Moody GB, Peng CK, Stanley HE. PhysioBank, PhysioToolkit, and PhysioNet: Components of a New Research Resource for Complex Physiologic Signals. Circulation 101 (23):pp215-220, 2000, (June13). doi: 10.1161 / 01. CIR.101,23.e215

[0371] 6. https: / / physionet.org / content / siena-scalp-eeg / 1.0.0 /

[0372] 7. Detti, P. (2020). Siena Scalp EEG Database (version 1.0.0). PhysioNet. https: / / doi.org / 10.13026 / 5d4a-j060.

[0373] 8. https: / / en.wikipedia.org / wiki / 10-20_system_(EEG)

Claims

CLAIMS1. A method for modeling single-phase or multiphase signals in a graph on an angular coordinate axis depending on phase angles and independent variables, characterized by comprising the following process steps;• Input signal receiving unit (S01), which receives digital input signals from a data source, pre-processes them, and receives the signal vectors into an array variable in accordance with the phase angle directions in which they will be modelled on the angular axis;• Signal analysis window identifier (S02), which enables the identification of parameters such as a signal window analysis method, window analysis time, etc., in order to model and analyze input signals in analysis windows;• Layer and segment identifier (S03), which enables the identification of the number of segments and layers that will form a graphic pattern depending on the changing parameters such as the amount of signal resolution, linear or non-linear increase of the signal, lower and upper limit values of the signal to be displayed on a graph on an angular coordinate axis during the analysis period;• Angular axis and graphic identifier (S04), which enables the identification of the parameters related to the calculation methods of the boundary regions of each of the segments and layers where the signals will be added in the graph and that enables the determination of an angular coordinate axis and the geometric shape and pattern of the graph in which the signal is desired to be displayed on this axis, depending on the independent variables and phase angles of the signals to be displayed on the angular axis, in accordance with the number of layers and segments identified in step (S03),• Signal analysis loop unit (S05), which starts a loop to display the signal data within the analysis period in the graph defined in step (S04),• Signal vector estimation unit (S06), which enables the signal to be received in an array variable so that it can be displayed in all layers and segments of the graph in step (S04), and which enables the calculation of unknown signal vectors using a vector signal estimation method, if signal vectors at phase angles not given as input signals need to be calculated in this context,• Signal parameters identifier (S07), which enables the identification of these feature parameters and if it is desired to continue with the signal in the array variable in step (S06) or to show the signal feature parameters obtained by some calculations from the signal instead of said signal in the graph,• Signal representation format identifier (S08), which identifies the display type of the signal to be displayed on the graph defined in step (S04), and in this context, identifies the variables required to represent the signal with numerical values, colour tones, symbols, special signs or other visual elements in the relevant segments and layers of the graph on the angular coordinate axis,• Graphic display continuity provider (S09), which enables the graphic display to remain on the screen throughout the loops in step (S11) so that the signal values to be displayed on the graphic in step (S04) can be added to all segments and layers in the graphic,• Loop initial values unit (S10), which enables the identification of the initialization parameters needed during layer and segment loops;• Layer and segment loops unit (S11), which enables the initiation of loops related to layers and segments for the representation of the signal in each layer and segment of the graph;• Layer and segment boundary identifier (S12), which enables the calculation of the variables defining the boundary regions of the relevant layer and segment of the graph in order to display the signal variables in the relevant layers and segments in the graph defined in step (S04) on the angular axis, according to the graphical calculations defined in step (S04) during the loop in step (S11 ),• Signal to be displayed identifier (S13), which enables the identification of the signal parameters to be displayed in the relevant layer and segment of the graph in step (S12),Signal visualization unit (S14), which enables the signal parameters in step (S13) to be displayed on the graph, according to the location of the graph determined in step (S12) and the signal display shape in step (S08),Layer and segment loops continuation unit (S15), which enables the continuation of segment and layer loops and the updating of the relevant index variables for processing signal variables in each layer and segment of the graph,• Graphic display continuity disabler (S16), which enables the continuity feature of the graphic display to be disable after the completion of the graphical expression of the signal parameters within the analysis window,• Signal analysis window progressor (S17), which enables the continuation of the signal analysis loop in step (S05) to repeat the operations for the graphical display of signal variables in the next analysis window,• Program terminator (S18), which enables that the processes are terminated when the loop in step (S05) is completed or terminated by the user.

2. The method according to Claim-1, characterized by comprising the following process steps: determining the digital signals that are desired to be displayed on an angular coordinate axis; sequencingthe signals in accordance with the angular directions in which they will be modelled on the angular coordinate axis; identification an angular coordinate axis depending on the independent variables and phase angles of the signals to be displayed on the angular axis and defining a graphic pattern with the number of segments and layers determined according to the variables such as the resolution amount of the signal, the amount of linear or non-linear increase, and the lower and upper limit values; identification the calculation methods of the boundary areas of the segments and layers in this graph; if there are unknown signal variables at the phase angles desired to be displayed on the angular axis, calculating the relevant parameters with a signal estimation method; expressing signal variables in the relevant segments and layers of the graph defined on the angular coordinate axis, with numerical values, colour tone, sign, symbols or other visual elements.

3. A signal modeling system according to Claim-1 or Claim-2, a signal modeling system for modeling the variation of digital signals versus their arguments and phase angles, operating on a device capable of processing information and using the method of Claim-1, wherein the signal modelingsystem models the signals in segments and layers divided on a linear or nonlinear scale in a graph on a two-dimensional or three- dimensional angular axis, the modeled system is characterized by comprising the following process steps;• An input signal acquisition unit (301), which receives a digital input signal at a sampling rate Fs from an input device managed by a processor, preprocesses it, and receives the signal vectors into an array of variables in accordance with the phase angle directions in which they are to be modeled on the angular axis,• Signal analysis window identifier (302), which enables the identification of parameters such as a signal window analysis method, window analysis time, etc., in order to model and analyze input signals in analysis windows,• Layer and segment identifier (303), which identifies the number of segments and layers that will form a graphic pattern depending on the changing parameters such as the amount of signal resolution, the amount of linear or non-linear increase of the signal, the lower and upper limit values of the signal to be displayed on a graph on an angular coordinate axis during the analysis period,• Angular axis and graphic identifier (304), which enables the identification of an angular coordinate axis and the methods for calculating the graphic pattern on which the signal will be displayed on this axis and the boundary values of the segments and layers, depending on the independent variables and phase angles of the signals to be displayed on the angular axis, in accordance with the number of layers and segments determined in step (303) and by using the equations between Equation-4 and Equation-12 or which enables user-defined graphic patterns to be defined on demand,• Signal analysis loop unit (305), which starts a loop to display the signal data within the analysis period in the graph defined in step (304),• Signal vector estimation unit (306), which enables the signal to be received in an array variable so that the graph in step (304) can be displayed in all layers and which enables the unknown signal vectors to be calculated using a vector signal estimation method, if signal vectors at phase angles not provided as input signals need to be calculated in this context;• Signal parameters identifier (307), which enables for either proceeding with the signal in the array variable from step (306) or, if signal feature parameters derived from the signal through certain calculations are to be displayed on the graph instead of the signal itself, determines these feature parameters,• Signal representation format identifier (308), that identifies the representation style of the signal to be displayed in the graph defined in step (304) and within this scope, it facilitates the determination of the variables required to represent the signal with numerical values, color tones, symbols, special markers, or other visual elements in the relevant segments and layers of the graph on the angular coordinate axis,• Graphic display continuity provider (309), which enables the graphic display to remain on the screen continuously so that the signal values to be displayed in the graphic in the angular axis described in step (304) can be added in all segments and layers in the graphic,• Loop initial values unit (310), which enables the identification of the initialization parameters needed during layer and segment loops,• Layer and segment loops unit (311), which enables the initiation of loops related to layers and segments for displaying the signal in each layer and segment on the graphic display,• Layer and segment boundary identifier (312), which enables the calculation of the variables defining the boundary regions of the relevant layer and segment of the graph for the purpose of displaying the signal variables in the relevant layers and segments in the graph defined in step (304) on the angular axis during the loop in step (311) according to the graphical calculations defined in step (304),• Signal to be displayed identifier (313), which identifies the signal parameters to be displayed in the relevant layer and segment of the graph in step (312),• Signal visualization unit (314), which enables the signal parameters in step (313) to be displayed on the graph, according to the location of the graph identified in step (312) and the signal display shape in step (308),• Layer and segment loops continuation unit (315), which enables the continuation of segment and layer loops for processing signal variables in each layer and segment of the graph and the updating of relevant index variables,Graphic display continuity disabler (316), which enables the continuity feature of the graphic display to be disabled after the graphical representation of the signal parameters within the analysis window is completed,Signal analysis window stepper (317), which enables the continuation of the signal analysis loop in step (305) to repeat the operations for the graphical display of signal variables in the next analysis window,• Program terminator (318), which enables the processes are terminated when the loop in step (305) is completed or terminated by the user.

4. A method of generating a signal from a graphic image, according to claim-1 or claim-2 or claim-3, characterized by comprising the following process steps;• Taking a picture or graphic image as input data (201 ),• Defining an angular coordinate system for the part of a picture or graphic image in a loop within a signal analysis window that is to be converted into a signal, according to the arguments and phase angles of the signal to be converted (202),• Dividing the graph on the angular coordinate axis into segments and layers according to variables such as the amount of resolution, limit values, linear or non-linear change amounts, and phase angles of the signal to be converted (203),• Starting a loop through the segments and layers of the graph (204),• Converting the colour tones in the relevant segments into numerical values to represent the signal variables according to a colour palette defined in the resolution and limit range to represent the signal and transferring them to an array if each segment of the graph and each part of the graph remaining in its layers are defined in terms of colour tones (205),• Converting these symbols, signs and numerical values into numerical values to represent the signal variables and transferring them to an array according to a defined range of variables with the resolution and limit range to represent the signal if each segment of the graph and each remaining part of its layers have symbols, signs and numerical values that can be associated with numerical values (206),• Providing a loop continuation unit for segments and layers of the graph and conversion of all segments and layers into signal variables (207),• Storing the signal fragment in memory in accordance with the layer and segment in the larger signal and its angular orientation on the coordinate axis, andreturning to the beginning of the analysis window loop (step 202) if the graphic image, as part of a larger graphic, is converted into a signal during the analysis time (208),• Combining the signal data and storing the same in a multidimensional signal array according to their angular orientation, and completing the signal extraction from the graphic image, once the analysis is complete (209).

5. Method of estimating signal vectors at phase angles not given as signal vectors according to claim-1 or claim-2 or claim-3, characterized by comprising the following process steps;In order to find (n-1) vector components y(i), (y(i), i=1,2,3,..., n-1) between any vectors x1 and x2 of length L with an angle 0 between them and each of which has an angle (0 / n) between them, and calculating (n-1) vectors y(i) and adding them to a matrix Bx of size (L x (n-1 )),Bx (j,i)= [ (n-i) *x1(j) + (i) * x2(j) ] / n, j=1,... L, and i = 1,...,n -1) (3)Obtaining unknown signal vectors by the signal vector estimation unit in the step (S06) in Claim-1 or in the step (306) in Claim-3, using the calculations in Equation-3; or obtaining unknown signal vectors by using another calculation method when desired.

6. Method according to claim-5, in order to run the relevant process steps in the calculation of all y(i) vectors (Bx=[y(1), y(2),,...,y(n-1]) in the content of a Bx matrix in Equality-3 as instructions, dividing the space between any x1 and x2 vectors with an angle 6 and a length of L into n equal segments, and finding n-1 vectors in these segments, characterized by comprising the following process steps;• Taking the vectors x1 and x2 with L elements as input data,• Identifying an integer n greater than 1, which is the value of the segments in the range of two vectors,• Initializing an empty matrix Bx(L, (n -1)), each column of which will contain n-1 vectors,Starting the loop for each vector y(i) to be calculated from i = 1 to (n-1 ),Starting the loop for each element of vector y(i) from j = 1 to L,o Calculating the jth element values of the vector y(i) with Bx(j,i) = ((n- i) / n)*x1 (j) + (i / n) *x2(j)),o j-loop continuing until the operations on all elements of the ith vectors of the Bx matrix are completed,o Repeating the i loop until the operations are completed for (n-1) vectors y(i) of the Bx matrix,• loops ending and the Bx matrix is being created then the operation is completed for all y(i) vectors and element.

7. Method of claim-1 or claim-2 or claim-3, wherein the method of estimating the unknown signal vectors is an implementation of the methods of claim-5 or claim-6, wherein the method of generating a signal matrix comprising Ni*Nj signal vectors using and including Ni signal vectors each having an angle 0 between them, characterized by a method of dividing Ni vectors of vector length L each into (Nj-1 ) equal segments and calculating (Nj-1) vectors in these segments, according to Claim- 1, Claim-2 or Claim-3, by an application that extends the signal vectors estimation algorithm of Equation-3 and claim-5 to obtain Nj-1 new vectors from a sequence of Ni vectors xi ([x1,x2,...,x(Ni]), between each of them, by the following process steps;• Taking an AA matrix array of size (Ni x L) containing Ni vectors, each of which is of length L and has an angle 6 between them (AA = [x1,x2,...,x(Ni]), from the AA matrix array to form a BA matrix array of size (Sf x L) (Here, (Nj-1) new vectors are added between every two adjacent vectors in the AA matrix and this corresponds to the value Nj*Ni = Sf) (401);• Initializing the BA matrix as empty and starting with a value of k = 1 (402);• Starting a loop for Ni input vectors in matrix AA (i=1: Ni) (403);• Transferring the ith vector of the AA matrix array to an A2 array (A2(:)=AA(:,i)) (404);• Checking whether the index value i is less than Ni (405);If i< Ni, taking it as B2(:)=AA(:,i+1) (405a);If i>=Ni, it is taken as B2(:)=AA(:,1) (405b).Initializing a loop for Nj prediction vectors (j=1: Nj) (406).• Calculating the kth vector of the BA matrix with the formula BA(:,k)=(Nj- j1) / Nj)*A2+((j1) / Nj)*B2 and increasing the k value with k=k+1 (407);• Checking whether the index value j is less than Nj (408);• If j< Nj, returning to step (406), or if j>=Ni, checking whether the index value i is less than Ni (409);• If i< Ni, returning to step (403), or if i>=Ni, completing the loop operations and form the BA matrix of size (Sf x L) (410).

8. Method according to claim-1 or claim-2 or claim-3, characterized by comprising the following process steps; for determining the angular axis types and graphic patterns of the input signal, in step (S04) in Claim-1 or in step (304) in Claim-2; within the scope of determining the coordinate boundaries of the angular axis, graphic pattern and layers and segments in the graphic pattern; using the calculations in equations from Equation-4 to Equation-12; or specifying a user-defined angular axis type and chart pattern using the option in step (304).

9. An implementation of a signal modeling method according to Claim-1 for operation on various devices comprises the following mechanisms and process steps: Obtaining digital samples of an input signal from an input terminal (501); After operating an application of the inventive method according to Claim-1 or Claim-2 or Claim-3 on a processor connected to the input and output terminals, transmitting the input signal to an output terminal connected to the processor (for example, displaying it on a graphic screen (502a); or recording the obtained information in the memory (502b); or transmitting it to another device via the I / O interface (502c)).

10. Method according to Claim-1 or Claim-2 or Claim-3, characterized by the signal spectrum modeling method comprising the following process steps; In the analysis of the spectrum analysis of an input signal in angular coordinates using the methods in Claim-1 or Claim-2 and Claim-3, dividing all angular frequency components of an input signal into frequency segments and layers by increasing them according to the logarithm base between the minimum and maximum frequencies of the signal in order to create logarithmic-based frequency layers; modeling the fundamental frequency components of the signal spectrum in a graph on the angular axis by associating them with all their harmonics.

11. Method according to Claim-1 or Claim-2 or Claim-3, characterized by comprising the following process steps; modeling the changes of a multi-phase digital signal depending on at least one independent variable in a linear or non-linear rate against its independent variables, using the methods in Claim-1 or Claim-2 and Claim-3, in a graph having segments and layers depending on the phase angles and independent variables of the signal in the angular coordinate axis; thus modeling the changes of the signal according to the independent variables in all phase angles in a graph on the angular axis.

12. Method according to Claim-1 or Claim-2 or Claim-3, wherein for another embodiment of modeling a signal on a graph on the angular coordinate axis in the signal modeling method, the signal modeling system may be adapted to model a signal on the same graph without increasing the coordinate axis size, such that the graph performs the following process steps:o If the behaviour of a signal against other independent variables is desired to be expressed in the same graph,o If other signal property parameters of the same signal using the same independent variables are desired to be expressed in the same graph,o If different signals using the same independent variable are to be expressed on the same angular graph,showing the new signals that are intended to be expressed with expressions such as numerical value, symbol, sign, and colour tone within the segments in the existing graph, or by creating sub-layers connected to the layers in the graph or subsegments connected to the segments, defining new areas for the new signal variables, expressing them with various visual elements in the newly created layers and segments, and modeling them in the same graph.

13. Method according to claim-1 or claim-2 or claim-3, characterized in that; another application of modeling the angular coordinate axis in the signal modeling method comprises the following process steps: obtaining the graphics created in each analysis window in any picture or graphic image format using the process steps in claim-1 or claim-2 or claim-3, so that using them as data in machine learning and deep learning algorithms; recording the graphics in successive analysis windows in video image format when desired; using the said graphic models as input data in deep learning or machine learning algorithms or storing them in a data device.

14. Another implementation of the signal modeling method according to Claim-1 for modeling antenna radiated power signals, characterized by comprising the following steps; in the power analysis of an antenna with the methods according to Claim-1 or Claim-2 or Claim-3; modeling a graph on an angular coordinate axis in order to define the measured distance or different frequency values at which the antenna is operated in segments and layers, and modeling the power values measured in all angular directions and all distances towards the center between the transmitter and receiver antennas in segments and layers in the graph on the angular coordinate axis.

15. Further embodiments of the graphical pattern modeling in the procedures according to claim-1 or claim-2 or claim-3, characterized by comprising any one or a combination of the following processing steps: In step (S06) of claim-1 or step (306) of claim-2 or graphic pattern modeling on the angular axis of claim-3, for graphic modeling of a multiphase input signal on the angular axis, the signal modeling system may be adapted to perform the following operations:• For any signal vector at any phase angle, by defining a different graphic pattern on the angular axis, the signal is modeled in different graphic patterns at different phase angles, thereby expressing the signal on a variable-featured graphic pattern background that represents the patterns changing according to the phase angles of the signal;For signal modeling within analysis windows, in a new analysis loop, preserving the graphic pattern in the previous analysis window, creating a new graphic pattern on the graphic pattern, and modeling the signal on this pattern

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