236 results about "Frequency resolution" patented technology

The invention relates to the technical field of fault diagnosis, in particular to a wind driven generator fault diagnosis method and system based on Mamba-ResNet. The method comprises the following steps: carrying out feature extraction and feature fusion by utilizing preprocessed data, namely constructing adaptive window short-time Fourier transform (AW-STFT) to carry out dynamic time-frequency resolution analysis, carrying out parallel feature extraction and constructing a multi-dimensional heterogeneous feature vector, and carrying out a cross-modal adaptive gating fusion mechanism based on a bidirectional cross gating unit; the method comprises the following steps: constructing a Mamba-ResNet hybrid deep network model architecture; performing model training on the constructed network model architecture; and performing fault diagnosis on the wind driven generator by using the trained model architecture. A tedious manual feature design process in a traditional method is avoided, and the automation level and adaptability of a diagnosis system are remarkably improved.

A method and apparatus for acquiring aerodynamic noise of a compressor, a medium, and a product are provided. The method includes: performing inverse Fourier transform on a known frequency-domain noise spectrum to obtain known time-domain noise data, then predicting unknown time-domain noise using a time series neural network, obtaining finer time-frequency noise data in combination with the known time-frequency noise data, and finally, performing Fourier transform on the finer time-frequency noise data to obtain new frequency-domain noise data. Limitations of a limited time step and a total simulation time on the acquisition of aerodynamic noise data in traditional numerical calculation of aerodynamic noise can be overcome. Finer aerodynamic noise data can be acquired rapidly and accurately. The frequency resolution of the noise spectrum can be increased, and reducing the consumption of computing resources and saving manpower and material resources can be achieved.

The present invention relates to the technical field of signal processing and fault diagnosis. The method of the present invention comprises: collecting a flame chemiluminescence signal, and performing adaptive filtering noise reduction processing; using an improved proper orthogonal decomposition method and a high-order mode to obtain comprehensive combustion feature information; developing a real-time synchrosqueezing transform algorithm to perform time-frequency analysis on data, and updating energy distribution in real time; taking into account sensor data to perform multi-parameter joint analysis to obtain a combustion state evaluation, using a plurality of high-speed cameras to acquire flame images from different angles, reconstructing three-dimensional flame morphology by means of a computer vision technology, and providing fault detection information; and constructing a fault prediction model to give an early warning of a combustion fault. The present method implements nondestructive and rapid detection of oscillating combustion faults, keeps rich information of flame images, reflects overall flame pulsation characteristics, increases the speed and accuracy of detection, and compensates for the defect of low frequency resolution of conventional time-frequency analysis methods.

In order to solve the problem of inaccurate classification caused by fixed time-frequency resolution and lack of physical rationality in sample enhancement in a traditional classification method, the invention relates to a partial discharge signal classification method based on a physical constraint generative adversarial network, and the method comprises the following steps: extracting a partial discharge signal and a historical partial discharge signal, and carrying out the double-window time-frequency coding of the partial discharge signal and the historical partial discharge signal; correspondingly obtaining a fused time-frequency graph and a historical fused time-frequency graph; determining a corresponding discharge type label based on the historical partial discharge signal, establishing a physical constraint generative adversarial network, and training the physical constraint generative adversarial network in the historical fusion time-frequency graph based on the discharge type label; and inputting the fusion time-frequency graph into the trained physical constraint generative adversarial network to obtain a fusion feature graph corresponding to the fusion time-frequency graph, performing time sequence modeling on the fusion feature graph, mapping the fusion feature graph into a time sequence feature vector, and performing classification on the corresponding partial discharge signals based on the time sequence feature vector.

The invention discloses a method for selecting and triggering gamma instant radiation pulse events, and belongs to the technical field of nuclear radiation detection. The method comprises the following steps: carrying out normalization preprocessing on an original gamma pulse radiation time spectrum; s time-frequency transformation is carried out on the preprocessed data, and time-frequency features are extracted; optimizing parameters of the frequency threshold and the amplitude threshold after S time-frequency transformation by adopting a deep reinforcement learning model to obtain an optimal frequency threshold and an optimal amplitude threshold; performing filtering processing on the signal of the S time-frequency conversion result, and separating noise from an effective signal; and searching a pulse radiation event for the filtered signal by applying a morphology-based peak searching method, and positioning the position and the characteristic of a real gamma instant radiation pulse event. According to the method, time-frequency analysis is carried out through S time-frequency transformation, the problem that the frequency of an analysis window cannot be adjusted through short-time window Fourier transformation is solved, the method has better frequency resolution and phase retention characteristics, and gamma pulse signal characteristics can be represented more accurately.

The invention discloses an OTFS waveform modulation method based on DFrFT time-frequency analysis, solves the problems of fixed time-frequency resolution, signal fuzziness and cross term interference existing in Heisenberg (Wigner) transformation in an OTFS system in a high dynamic scene, and belongs to the technical field of information and communication. The method provided by the invention comprises the following steps of: modulating sending data to obtain a DD domain signal, firstly performing inverse symplectic Fourier transform on the DD domain signal, then converting the DD domain signal into a time domain signal block through IDFrFT transform, adding a cyclic prefix (CP) to the time domain signal block, performing row-column transform, and then transmitting the time domain signal block; a cyclic prefix (CP) is removed from a signal received by a receiving end, the signal is converted into a time domain signal block subjected to parallel processing, a time-frequency domain signal is obtained after the time domain signal block is subjected to DFrFT transformation, then the time-frequency domain signal is mapped back to a DD domain through the Sextile Fourier transform, a DD domain signal is obtained, the DD domain signal # imgabs0 # is demodulated, and recovered sending data are obtained. The IDFrFT provided by the invention obviously reduces the calculation complexity.

The invention discloses an AD diagnosis method fusing electroencephalogram frequency spectrum standardization deviation and a brain network. The AD diagnosis method comprises the steps that S1, band-pass filtering and fragment segmentation are conducted on multi-channel EEG signals of five brain regions; s2, for each segment, calculating brain region-frequency band characteristics of five different brain regions; s3, performing standardized modeling by adopting a GAMLSS model, identifying individual deviation information of a disease group about a specific brain region rPSD, training a LightGBM classifier by utilizing the individual deviation information, and extracting a structured feature vector by utilizing an internal structure of the classifier; s4, dividing each segment into a plurality of non-overlapping frequency boxes according to frequency resolution, calculating an FCN graph in a matrix form of each frequency box, constructing a three-dimensional image according to the FCN graph, and extracting a visual feature vector by using a Swin transformer network; and S5, constructing a connection vector, and inputting the connection vector into a classifier for classification. The method provides a new technical approach for accurate diagnosis and differential diagnosis of neurodegenerative diseases.

The invention provides an inhaul cable self-vibration fundamental frequency automatic identification method and system based on a harmonic product spectrum, and relates to the technical field of structure monitoring, and the method comprises the steps: receiving vibration acceleration data of an inhaul cable, carrying out the windowing processing of the vibration acceleration data through employing a Hanning window, and generating a windowed signal; carrying out fast Fourier transform on the windowed signal, and improving the frequency resolution by implementing zero filling to obtain an initial frequency spectrum; smoothing the initial frequency spectrum to form a smooth frequency spectrum; performing passband clipping on the smooth frequency spectrum to zero the passband outer amplitude to form a clipped frequency spectrum; calculating the signal-to-noise ratio of the frequency spectrum after cutting, and comparing the signal-to-noise ratio with a preset threshold value; if the signal-to-noise ratio is lower than a preset threshold value, judging that the signal quality is unqualified and terminating the processing flow; and if the signal-to-noise ratio is equal to or higher than the preset threshold value, continuing the normal processing flow. According to the invention, automatic and high-precision identification of the self-vibration fundamental frequency of the inhaul cable can be realized.

According to embodiments, a method performed by a distributed unit (DU) may involve: transmitting, to a radio unit (RU), a first control plane message including section extension information for indicating the number of one or more signal-to-interference-plus-noise-ratio (SINR) values for each physical resource block (PRB) corresponding to a frequency resolution of an SINR report by the RU; and receiving, from the RU, a second control plane message including section type information for indicating the one or more SINR values according to the frequency resolution and the number of the one or more SINR values for each PRB.

The invention discloses a bearing fault diagnosis method based on wavelet time-frequency coding and a convolution visual converter. The method comprises the following steps: collecting vibration signals of a bearing under different working conditions; performing continuous wavelet transform on the one-dimensional vibration signal to generate a two-dimensional time-frequency diagram with high time-frequency resolution; carrying out coding and image enhancement on the time-frequency graph through an enhanced color mapping mode; inputting the time-frequency graph into a convolution visual converter model, and realizing local and global combined extraction of vibration features through convolution projection, a self-attention mechanism and a multi-stage feature fusion structure; the features are classified to identify a state of health or type of fault of the bearing. According to the method, the diagnosis precision and robustness in a complex working condition and high-noise environment are effectively improved, and the method is suitable for state monitoring and early fault early warning of various types of rotary mechanical equipment.

The invention discloses a ship signal adaptive time-frequency analysis method based on instantaneous frequency direction self-adjustment. The ship signal adaptive time-frequency analysis method comprises the steps of collecting ship signals to be subjected to time-frequency analysis and performing short-time Fourier transform; estimating the instantaneous frequency of the ship signal based on short-time Fourier transform time-frequency distribution in combination with time-frequency narrow-band features; calculating the instantaneous frequency and the optimal window length after smoothing; segmenting the smoothed instantaneous frequency in time, calculating time-frequency domain direction pre-guidance of each time period, and constructing a Chirp atomic direction over-complete dictionary; segmenting the ship signal in time, and calculating the matching direction of the ship signal in each time period so as to calculate and improve Chirplet transformation time-frequency distribution; and calculating the optimal short-time Fourier transform in combination with the optimal window length, and correcting and improving Chirplet transform time-frequency distribution. According to the method, the robustness of short-time Fourier transform and the anisotropy of improved Chirplet transform are utilized at the same time, and time-frequency distribution with high robustness and high time-frequency resolution is obtained.

The invention discloses an electric wire and cable partial discharge online detection and insulation defect evaluation system. The system comprises a distributed sensor array, a signal preprocessing unit, a feature extraction module, a defect evaluation unit, a positioning module and an early warning unit. Multiple sensors cooperatively detect, a distributed sensor array realizes full-line coverage, weak discharge signals are effectively captured, and the detection sensitivity reaches a picobank (pC) level. According to the dual positioning algorithm, an improved TDOA algorithm and a PSO algorithm are combined, and the positioning error is smaller than or equal to 0.5 m (laboratory environment) and smaller than or equal to 1.5 m (actual engineering environment) and is improved by 30%-50% compared with a traditional method. Time-frequency feature depth extraction: wavelet packet transformation and S transformation are combined to realize 0.1 microsecond-level time resolution and 5kHz-level frequency resolution of discharge signals, and different types of discharge are accurately identified.

The invention discloses a phase modifier bearing fault diagnosis method, which belongs to the technical field of power equipment fault diagnosis, and comprises the following steps of: analyzing independent components, performing blind source separation on a received phase modifier bearing vibration signal, and extracting three types of independent source signals of impact, abrasion and noise; the gradient driving window length is self-adaptive, and the window length of short-time Fourier transform is dynamically adjusted based on the instantaneous frequency gradient of the independent source signal; wavelet packet frequency band energy screening: performing wavelet packet decomposition on the signal after window length adaptive processing, screening a fault characteristic frequency band based on an energy contribution rate, and reconstructing the signal; and enhancing stochastic resonance, and inputting the reconstructed signal into a stochastic resonance system. According to the method, independent component analysis, gradient driving window length self-adaption, wavelet packet frequency band energy screening and stochastic resonance enhanced fourth-order diagnosis chain are constructed, so that multi-stage cooperative processing of phase modifier bearing faults is realized, and the technical problems of time-frequency resolution contradiction, insufficient feature decoupling and weak generalization ability are effectively solved.

The invention discloses a time-frequency analysis method based on local entropy optimization synchronous demodulation reassignment transformation, relates to the technical field of signal processing, and solves the problem that a traditional time-frequency analysis method is not easy to carry out when complex non-stable vibration signals generated by rotating machinery and the like are processed. The problems of difficulty in balancing time and frequency resolution, easiness in energy diffusion, difficulty in multi-component signal separation and the like exist; according to the method, zero padding is carried out on the two ends of a target signal, a discrete Gaussian window is constructed to generate a sliding windowing signal matrix, a projection angle sequence is generated in an angle space, a time axis and a frequency axis are discretized, a demodulation function containing undetermined parameters is constructed to generate a complex number time-frequency representation matrix, the Renyi entropy value of time-frequency sub-blocks is calculated to determine an optimal demodulation parameter, and the optimal demodulation parameter is obtained. And setting a frequency difference threshold to construct a frequency redistribution operator to generate an optimized time-frequency matrix. The method is mainly used for time-frequency analysis of complex non-stationary vibration signals in the fields of rotating machinery and the like, and high-precision frequency modulation feature extraction and enhancement processing are achieved.

The invention relates to the technical field of crossing of medical instruments and artificial intelligence, and provides a hearing threshold detection method based on multi-mode hearing electrophysiological signal fusion. Comprising stimulation frequency otoacoustic emission and auditory brainstem response induced by sweep frequency stimulation sound, distortion product otoacoustic emission induced by dual-tone stimulation and middle ear sound immittance / reflection signals, and a multi-task deep learning model is constructed to perform fusion analysis on the signals. According to the method, accurate quantitative regression prediction of hearing thresholds with any frequency resolution and automatic classification and discrimination of hearing loss properties are synchronously realized, the problems of single evaluation dimension and insufficient complex hearing loss analysis ability in the prior art are effectively solved, the comprehensiveness, accuracy and clinical operation efficiency of objective hearing evaluation are remarkably improved, and the method is suitable for popularization and application. And an innovative system solution is provided for fine diagnosis of the auditory function.

The invention provides a radar interference signal identification method and system based on a deep fusion neural network, and the method comprises the steps: obtaining an echo signal of a radar, carrying out the generalized S transformation of the echo signal to generate a time-frequency image, carrying out the preprocessing of the time-frequency image, and obtaining a preprocessed time-frequency image; and identifying the preprocessed time-frequency image by using a pre-trained deep fusion neural network model, and outputting an interference signal type. According to the method, the time-frequency image of the radar interference signal with high time-frequency resolution is obtained by adopting generalized S transformation, the time-frequency domain characteristics of the radar interference signal can be flexibly described, and the quality of a learning sample is ensured.

The invention discloses an ISAR imaging method based on a low-rank adaptive stable diffusion model, and the method comprises the steps: carrying out the motion compensation, range compression and short-time Fourier transform processing of an ISAR radar echo signal of a rigid target, and generating a low-resolution TFR; inputting the low-resolution TFR into a low-rank adaptive stable diffusion model (LoRA-SD) to carry out TFR super-resolution processing, and improving the frequency resolution by refining the curve characteristics of the TFR to generate a high-resolution TFR; wherein the low-rank adaptive model (LoRA-SD) is obtained by performing fine adjustment on a pre-trained SD-Turbo large model by using a LoRA adapter; and finally, generating a high-resolution ISAR image by using a distance-instantaneous Doppler algorithm. The method breaks through the frequency resolution limit of traditional time-frequency analysis, significantly improves the resolution and quality of ISAR imaging, and has good generalization ability and robustness.

The invention relates to the technical field of wireless carrier communication, in particular to a cluster unmanned aerial vehicle mixed signal separation and identification method, which comprises the following steps of: extracting a receiving strength time sequence from a received cluster unmanned aerial vehicle mixed wireless carrier communication signal, and calculating the sum of absolute values of difference values between continuous points of the sequence under a plurality of time scales, and linear fitting is carried out to establish a mixed channel fractal dimension. According to the method, difference absolute value accumulation and calculation under a plurality of time scales are carried out on a mixed wireless carrier communication signal receiving strength sequence, a mixed channel fractal dimension is established, and the fractal dimension is utilized to realize adaptive setting of an analysis window length and a stepping amount, so that the time-frequency resolution capability of subsequent segmented Fourier transform is improved; after a mixed signal time-frequency spectrogram is generated, a complete discrete time-frequency trajectory set is constructed through multi-frequency unit peak energy detection and association along a time axis, and unmanned aerial vehicle signals with closely overlapped frequencies can be distinguished.

The invention provides a direct drinking water equipment fault intelligent diagnosis and real-time alarm control method, and relates to the technical field of intelligent monitoring and fault diagnosis, and the method comprises the steps: collecting pressure, flow, conductivity, turbidity and temperature parameters through a multi-source sensor, and transmitting the parameters to a central processing unit; the method comprises the following steps: preprocessing data by adopting dynamic wavelet transform, optimizing a mother wavelet function and a decomposition scale based on a time-frequency resolution index, and filling an abnormal value in combination with sliding window detection and linear interpolation to generate a standardized data set; extracting significant frequency band characteristics of a time domain mean value, a variance and frequency domain energy, and performing dynamic dimension reduction and normalization through principal component analysis; inputting the feature vector into a support vector machine and random forest hybrid model, and outputting a fault type and probability; dynamically adjusting an alarm threshold according to the probability, introducing a water quality anomaly index to evaluate a conductivity and turbidity collaborative risk, triggering graded alarm and pushing the graded alarm to a terminal; model parameters are updated by adopting an incremental learning algorithm, and a response strategy is optimized in combination with equipment load and environment temperature.

The application discloses a numerically controlled oscillator based on double modulus accumulation and a method for improving frequency resolution, and the numerically controlled oscillator comprises a parameter configuration module, a carry processing module and a main phase accumulator. The parameter configuration module is used for configuring an integer part and a fractional part of a frequency control word based on a target output frequency, and the fractional part comprises a numerator modulus and a denominator modulus. The carry processing module is used for accumulating the fractional part of the frequency control word. On the basis of expanding an arithmetic logic bit width, a parallel pre-judgment architecture is adopted to generate a carry signal to the main phase accumulator according to the numerator modulus and the denominator modulus. The main phase accumulator is used for accumulating the integer part of the frequency control word and simultaneously updating a phase value according to the carry signal, so that a high-resolution frequency output is realized. The application decomposes the frequency control word into the integer part and the fractional part through the double modulus accumulation architecture, dynamically corrects the integer phase by using an accumulation carry mechanism of the fractional part, and realizes a frequency resolution much higher than that of a traditional structure without significantly increasing the bit width of the main phase accumulator.

A method for noise suppression in a hearing instrument includes using an acousto-electric input transducer of the hearing instrument to generate an input signal from ambient sound. A frequency-band-wise noise suppression is applied to a processing signal derived from the input signal. Stationary noise is detected in the respective frequency band, and depending on the detected stationary noise, an amplification factor of the processing signal is set for the relevant frequency band. An analysis adapted to detect stationary and non-stationary noise is applied to the processing signal. The analysis has a lower frequency resolution than the frequency-band-wise noise suppression and, upon detected presence of stationary and / or non-stationary noise in the analysis of the processing signal, the stationary noise in the frequency-band-wise noise suppression is presumed to be detected in each frequency band, and the corresponding amplification factors are set.

A decoder audio device comprises a receiver (101) and an audio signal generator (103). The receiver receives an audio data signal, the audio data signal comprising: a downmix audio signal that is a downmix of a first multi-channel audio signal; an upmix parameter set for a time-frequency segment of the downmix audio signal, the upmix parameter set comprising a level difference parameter, a correlation parameter and a phase difference parameter; and at least one transient parameter indicative of a transient characteristic of the first multi-channel audio signal. The audio signal generator generates an output multi-channel audio signal by upmixing the downmix audio signal according to the upmix parameter and the transient parameter. The decoder audio device uses an artificial neural network (105) having an input node that receives the upmix parameter and the transient parameter. The transient parameter has a different time-frequency resolution than the upmix parameter, and typically has a much roughened frequency resolution. An improved multi-channel audio signal can be generated with little need for additional overhead in terms of processing complexity, resources, and data rate.

The application discloses a high-speed sampling data real-time extraction method based on parallel digital filters, which comprises the following steps: collecting a measured signal through a collection system of a mixed domain oscilloscope to obtain parallel multi-channel signals; realizing large-multiple real-time extraction filtering through a parallel CIC filter and a cascaded parallel half-band filter to obtain serial data; and finally performing serial extraction on the serial data to obtain output data, so that the frequency resolution of the spectrum analysis function of the oscilloscope can be significantly improved without increasing the FFT length.

A wireless communication device includes one or more antenna arrays that receives RF signals across a plurality of frequency bands. The wireless communication device applies band-specific filtering operation to the received RF signals to obtain filtered RF signals. The wireless communication device converts and digitizes the filtered RF signals to obtain digitized intermediate frequency (IF) signals. The wireless communication device executes a plurality of spectrum measurements for the digitized IF signals. Each spectrum measurement of the plurality of spectrum measurements is based on a different offset frequency of a sequence of offset frequencies. Each spectrum measurement is associated with a first frequency resolution. The processor stores phase coherence information for each spectrum measurement. The processor combines the plurality of spectrum measurements based on the stored phase coherence information to generate a spectrum analysis output with a second frequency resolution that exceeds the first frequency resolution.

The invention describes a method for noise reduction in a hearing instrument (1), wherein an acousto-electrical input transducer (E1) of the hearing instrument (1) generates an input signal (E1) from ambient sound (2), wherein a frequency-bandwise noise reduction (21) is applied to a processing signal (V1) derived from the input signal (E1), in which stationary noise in the respective frequency band (Bj, Bk) is detected, and depending on the detected stationary noise, a gain factor (Gk) of the processing signal (V1) for the respective frequency band (Bj, Bk) is set, wherein an analysis (12) is applied to the processing signal (V1), which is configured to detect both stationary and non-stationary noise, wherein said analysis (12) has a lower frequency resolution than the frequency-bandwise noise reduction (21).and wherein, in the case of a detected presence (Y) of stationary and / or non-stationary noise in said analysis (12) of the processing signal (V1), the stationary noise is assumed to be detected in the frequency-bandwise noise suppression (21) in each frequency band (Bj, Bk), and the corresponding gain factors (Gk) are set.

The invention discloses a microwave electric field detection method based on three-light-excited Rydberg atom eight-wave mixing, and the method comprises the steps: building a microwave electric field detection device based on three-light-excited Rydberg atom eight-wave mixing, enabling a transmission path of decoration light Kd and a transmission path of coupling light Kc to reversely coincide with a transmission path of detection light KP in an atomic gas chamber, and enabling the transmission path of the coupling light Kc to be a transmission path of the detection light KP; a local oscillation microwave electric field KL is emitted to the atomic gas chamber from one side of the atomic gas chamber through the horn antenna; the horn antenna passively receives a signal microwave electric field KS in a free space and loads the signal microwave electric field KS to the atomic gas chamber; by observing the beat frequency electric signal output by the photoelectric detector, it is confirmed that the horn antenna receives the signal microwave electric field KS. Through a three-light excitation Rydberg atom scheme and an eight-wave mixing technology, the frequency resolution and sensitivity of electric field detection are remarkably improved, and a brand new technical path is provided for high-precision microwave electric field detection.

The application discloses a kind of hyperpolarized inert gas FID signal resonance frequency accurate measurement method, belong to atomic molecule and optical physics, signal detection and analysis field.For the FID signal of hyperpolarized inert gas, since signal itself oscillation decay with time, the length of sampling time is limited therefore the resolution of spectrum is limited, in turn, the precision of magnetic field measurement is influenced.The present application significantly improves the frequency resolution by refining spectrum and frequency estimation in succession, and has important significance for improving the precision of magnetic field measurement.

The purpose of the present disclosure is to provide a frequency analysis device capable of determining a frequency with a higher accuracy than a frequency resolution. A frequency analysis device according to the present disclosure divides a signal wave in the time domain into a plurality of sections at predetermined time intervals, and performs discrete Fourier transform on each of the plurality of sections into which the signal wave has been divided. Furthermore, the frequency analysis device calculates a frequency spectrum by combining the signal waves subjected to the discrete Fourier transform in the plurality of sections, and determines a provisionally determined frequency from the frequency spectrum. Furthermore, the frequency analysis device calculates a section phase difference, which is a phase difference between the signal waves in adjacent sections, for at least one set of the plurality of sections. The frequency analysis device corrects the provisionally determined frequency using the section phase difference.

In order to solve the problem of insufficient time-frequency resolution of the existing fractional-order wavelet transform, the invention provides a generalized fractional-order wavelet transform time-frequency analysis method, which comprises the following steps of: converting a fractional-order rotation angle parameter of the fractional-order wavelet transform into a free variable based on a fractional-order wavelet transform theory; according to the generalized fractional order wavelet transform time-frequency analysis method, the time-frequency characteristics of signals are extracted through maximum operation, and therefore the new generalized fractional order wavelet transform time-frequency analysis method can be obtained, and when the method is used for processing multi-component non-stationary signals, the time-frequency resolution higher than that of a traditional time-frequency analysis method (such as short-time Fourier transform and wavelet transform) can be obtained.