Time-frequency analysis method for non-stationary signal

Abstract

The invention belongs to the technical field of time-frequency characteristic detection of non-stationary signals, and provides a time-frequency analysis method of non-stationary signals, which comprises the following steps: S1, designing a damping forced vibration function group, and according to a frequency range and frequency resolution precision required to be detected by a to-be-analyzed non-stationary signal, calculating a time-frequency characteristic of the to-be-analyzed non-stationary signal according to the frequency range and frequency resolution precision required to be detected by the to-be-analyzed non-stationary signal; determining the number of functions in the function group and the resonant frequency of each function; s2, converting the damped forced vibration function group into a difference equation for numerical calculation; according to the method, a group of damped forced vibration functions is designed, and the resonant frequency, the damping coefficient and the damping function of each function in the function group are set according to the actual demand of the to-be-analyzed signal, so that the time-frequency characteristics of the non-stationary signal can be accurately analyzed; in addition, the frequency resolution precision of the method is determined by the set number of functions, can be flexibly adjusted according to requirements, can be infinitely increased to improve the precision, and can also be reduced by only analyzing important frequency bands.

Description

Technical Field

[0001] The invention belongs to the technical field of time-frequency feature detection of non-stationary signals, in particular to a time-frequency analysis method of non-stationary signals. Background Art

[0002] A non-stationary signal is a signal whose distribution parameters or distribution patterns change continuously over time. Most of the signals in life, such as speech, impact vibration, etc., belong to this type of signal.

[0003] The frequency characteristics of non-stationary signals will change with time. In order to analyze the time-varying frequency characteristics, time domain analysis is usually used in the signal detection process. The time-frequency analysis methods include short-time Fourier transform, wavelet transform, Hilbert transform, and Hilbert-Huang transform.

[0004] However, the above methods have limitations in the resolution accuracy of time and frequency domains: short-time Fourier transform and wavelet transform use window functions in the time domain for frequency analysis, and cannot take into account the high resolution accuracy of both time and frequency domains; the Hilbert transform can only analyze the time-frequency characteristics of a single signal, and although the Hilbert transform can analyze mixed signals, its basic theory is still imperfect and the analysis results may be wrong.

[0005] To this end, those skilled in the art have proposed a time-frequency analysis method for non-stationary signals to solve the problems raised by the background technology. Summary of the invention

[0006] In order to solve the above technical problems, the present invention provides a time-frequency analysis method for non-stationary signals to solve the limitations of the methods in the prior art in terms of resolution accuracy in the time domain and frequency domain: short-time Fourier transform and wavelet transform use window functions in the time domain for frequency analysis, and cannot simultaneously take into account high resolution accuracy in both the time domain and the frequency domain; the Hilbert transform can only analyze the time-frequency characteristics of a single signal, and although the Hilbert-Huang transform can analyze mixed signals, its basic theory is still imperfect, and the analysis results may be erroneous.

[0007] To achieve the above-mentioned purpose, the present invention adopts a time-frequency analysis method for non-stationary signals. The working principle is that when the driving signal contains the resonant frequency of the function or a frequency component close to it, the damped forced vibration will absorb energy and make its own energy higher. When the driving signal does not contain the resonant frequency of the damped forced vibration or a frequency component close to it, the damped forced vibration will dissipate energy through damping and make itself have lower energy. The energy of the damped forced vibration at each moment is related to the difference between the amplitude and frequency value of the frequency component containing the resonant frequency of the function in the driving signal at that time. The attenuation of the amplitude detection of the frequency component with different rates is related to the quality factor of the damped forced vibration; according to the working principle, a group of damped forced vibration functions can be designed, and the resonant frequencies of the function members in the function group correspond to the frequency values ​​that need to be detected, and the damping coefficient and damping function of each function in the function group are set according to specific needs to achieve the required quality factor. The signal to be analyzed is made into the driving function of each function in the damped forced vibration function group, and the time-frequency characteristics of the signal can be accurately analyzed according to the energy time change of each function in the function group; the specific implementation steps are:

[0008] S1. Design a damped forced vibration function group, and determine the number of functions in the function group and the resonant frequency of each function according to the frequency range and frequency resolution accuracy required for the non-stationary signal to be analyzed;

[0009] S2, converting the damped forced vibration function group into a differential equation for numerical calculation to describe the state of the damped forced vibration function;

[0010] S3. According to the state value of each function in the damped forced vibration function group at each moment, the amplitude and phase of the frequency component equal to the resonant frequency of each vibration function in the non-stationary signal are analyzed and calculated.

[0011] Preferably, the step S1 is specifically described as follows: a damped forced vibration function group is designed: for non-stationary signals, the number of functions in the vibration function group and the resonant frequency of each vibration function are determined according to the frequency range to be detected and the required frequency resolution accuracy.

[0012] Preferably, in step S1, when designing a damped forced vibration function group, it also includes determining the damping coefficient and damping function of each function to achieve the required quality factor. The specific operation is: determining the number of damped vibration functions included in the function group: when the frequency resolution accuracy is fixed, the number of functions in the function group = frequency analysis range / frequency resolution accuracy; or determining the number of functions in the function group according to requirements to correspond to the number of frequency components in the non-stationary signal that needs to be analyzed.

[0013] Preferably, the damping coefficient and damping function are determined: the undamped natural frequency of the function, the damping coefficient and the damping function determine the quality factor of the damped vibration function. The higher the quality factor is, the stronger the anti-"beating" performance of the vibration function is when performing time-frequency analysis, and the frequency resolution accuracy is enhanced, but the startup time will become longer, and the time resolution accuracy will be reduced, which may miss the frequency components that appear briefly; therefore, the damping coefficient and damping function of each function should be set according to the actual needs of the signal to be analyzed.

[0014] Preferably, the step S2 is specifically described as follows: converting the damped forced vibration function into a differential equation for numerical calculation; the non-stationary signal sequence F t The time interval ΔT of the differential operation can be set according to the sampling frequency of the non-stationary signal, or the time interval ΔT can be set according to the signal frequency component to be analyzed; the displacement x is set for each function in the function group k and speed v k Two variables describe the state of the damped forced function, k is the sequence number of the function in the damped forced vibration function, m k is the mass parameter of the kth vibration function, ω k is the undamped natural frequency ω of the kth vibration function, and each function corresponds to a detection frequency; the differential equation for the transformation of the damped forced vibration function starts from the 0 state, and the driven non-stationary signal sequence is calculated from time 0.

[0015] Preferably, the step S3 is specifically described as follows: Analyze and calculate the resonance frequency ω of K vibration functions in the non-stationary signal according to the state value of each function in the damped forced vibration function group at each moment C The amplitude and phase of the frequency component; Frequency component estimation: Estimate the frequency amplitude of each frequency component in the signal according to the energy of each function in the damped forced vibration function group, and then analyze the frequency components in the signal; At the same time, interpolation can be performed according to the quality factor of each function to increase the frequency resolution accuracy without increasing the number of functions.

[0016] The present invention proposes a time-frequency analysis method for non-stationary signals. In view of the defects of current time-frequency analysis methods, such as short-time Fourier transform and wavelet transform, which cannot take into account the resolution accuracy of time domain and frequency domain at the same time, and Hilbert transform and Hilbert-Huang transform, which cannot accurately analyze the frequency components of non-stationary signals, the present invention aims to enable the time-frequency analysis method to have high-precision resolution attributes in both time domain and frequency domain, and accurately obtain the frequency classification, amplitude value and phase parameters contained in the non-stationary signal at each moment.

[0017] A time-frequency analysis system for non-stationary signals, applicable to the above-mentioned time-frequency analysis method for non-stationary signals, comprising:

[0018] A design module is used to design a damped forced vibration function group, determine the number of functions in the function group and the resonant frequency of each function according to the frequency range and frequency resolution accuracy required for the non-stationary signal to be analyzed, and determine the damping coefficient and damping function of each function to achieve the required quality factor;

[0019] A numerical calculation module, used for converting the damped forced vibration function group into a differential equation for numerical calculation to describe the state of the damped forced vibration function, wherein the differential operation time interval of the non-stationary signal sequence is set according to the sampling frequency of the non-stationary signal or the signal frequency component to be analyzed;

[0020] The analysis and calculation module is used to analyze and calculate the amplitude and phase of the frequency component equal to the resonance frequency of each vibration function in the non-stationary signal according to the state value of each function in the damped forced vibration function group at each moment.

[0021] Preferably, the design module is further used to: determine the quality factor of the damped vibration function based on the undamped natural frequency, damping coefficient and damping function of the function; determine the number of functions in the function group based on the frequency resolution accuracy and the frequency analysis range; set the resonant frequency of each vibration function in the damped forced vibration function group as the frequency component that needs to be detected by the signal to be analyzed.

[0022] Preferably, the numerical calculation module is further used to: set two variables, displacement and velocity, for each function in the function group to describe the state of the damped forced function; starting from state 0, the driven non-stationary signal sequence is calculated from time 0, and numerical calculation is performed through the steps of calculating acceleration, updating velocity and updating displacement.

[0023] Preferably, the analysis and calculation module is further used to: estimate the amplitude-frequency value of each frequency component in the signal based on the energy of each function in the damped forced vibration function group, and then analyze the frequency components in the signal; interpolate according to the quality factor of each function, and then increase the frequency resolution accuracy without increasing the number of functions.

[0024] Preferably, it also includes: a display module, which is used to display the amplitude and phase information of each frequency component in the non-stationary signal obtained by the analysis and calculation module.

[0025] Preferably, it also includes: a storage module for storing the damped forced vibration function group designed by the design module, the numerical calculation results obtained by the numerical calculation module, and the amplitude and phase information of each frequency component in the non-stationary signal obtained by the analysis and calculation module.

[0026] A processor is configured to execute the above-mentioned time-frequency analysis method for non-stationary signals.

[0027] A machine-readable storage medium stores instructions, which, when executed by a processor, configure the processor to execute the above-mentioned time-frequency analysis method for non-stationary signals.

[0028] Compared with the prior art, the present invention has the following beneficial effects:

[0029] The time-frequency analysis method of non-stationary signals proposed in the present invention can significantly improve the resolution accuracy in the time domain and frequency domain; by designing a group of damped forced vibration functions, and setting the resonant frequency, damping coefficient and damping function of each function in the function group according to the actual needs of the signal to be analyzed, the present invention can accurately analyze the time-frequency characteristics of the non-stationary signal; in addition, the frequency resolution accuracy of the present method is determined by the set number of functions, which can be flexibly adjusted according to needs, and can be increased infinitely to improve the accuracy, or only important frequency bands can be analyzed to reduce the amount of calculation; at the same time, the time resolution accuracy of the present method can reach up to the sampling period of the signal, thereby realizing high-precision resolution attributes in both the time domain and the frequency domain, and accurately obtaining the frequency classification and its amplitude value and phase parameters contained in the non-stationary signal at each moment. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a flow chart of the time-frequency analysis method of non-stationary signals of the present invention;

[0031] Figure 2 A schematic diagram of an example speech signal for time-frequency analysis of the present invention;

[0032] Figure 3 Spectrogram for time-frequency analysis of an example speech signal;

[0033] Figure 4 Short-time Fourier time-frequency analysis spectrogram for the example speech;

[0034] Figure 5 It is a framework diagram of the time-frequency analysis system of the non-stationary signal of the present invention. DETAILED DESCRIPTION

[0035] The following embodiments of the present invention are described in further detail in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0036] Embodiment: The present invention provides a time-frequency analysis method for a non-stationary signal, such as Figure 1 As shown, the following steps are included:

[0037] S1. Design a damped forced vibration function group, and determine the number of functions in the function group and the resonant frequency of each function according to the frequency range and frequency resolution accuracy required for the non-stationary signal to be analyzed;

[0038] S2, converting the damped forced vibration function group into a differential equation for numerical calculation to describe the state of the damped forced vibration function;

[0039] S3. According to the state value of each function in the damped forced vibration function group at each moment, the amplitude and phase of the frequency component equal to the resonant frequency of each vibration function in the non-stationary signal are analyzed and calculated.

[0040] Furthermore, a damped forced vibration function group is designed: for non-stationary signals, the number of functions in the vibration function group and the resonant frequency of each vibration function are determined according to the frequency range to be detected and the required frequency resolution accuracy. The damped forced vibration function formula of the function group is as follows:

[0041]

[0042] Where: Damping coefficient Damping function for A polynomial function with undamped natural frequency F is the signal to be analyzed.

[0043] Furthermore, in step S1, when designing a damped forced vibration function group, it also includes determining the damping coefficient and damping function of each function to achieve the required quality factor. The specific operation is: determining the number of damped vibration functions included in the function group: when the frequency resolution accuracy is fixed, the number of functions in the function group = frequency analysis range / frequency resolution accuracy; or determining the number of functions in the function group according to requirements to correspond to the number of frequency components in the non-stationary signal that needs to be analyzed.

[0044] Determine the damping coefficient and damping function: The undamped natural frequency, damping coefficient and damping function of the function determine the quality factor of the damped vibration function. The higher the quality factor, the stronger the vibration function's anti-"beating" performance during time-frequency analysis, and the frequency resolution accuracy is enhanced, but the startup time will become longer, and the time resolution accuracy will be reduced, which may cause the omission of short-lived frequency components. Therefore, the damping coefficient and damping function of each function should be set according to the actual needs of the signal being analyzed.

[0045] Specifically, the resonant frequency of each vibration function in the damped forced vibration function group is set as the frequency component that needs to be detected by the signal to be analyzed. The resonant frequency of the damped forced vibration function is determined by the function's undamped natural frequency ω, the damping coefficient γ and the damping function Determine; The resonant frequency can be calculated by solving the damped forced vibration equation, or it can be estimated by numerical calculation results; The numerical calculation method for estimating the resonant frequency is to first set the damping coefficient and damping equation according to specific needs, and then set a set of damped forced vibration function groups according to the resonant frequency error ε allowed by the actual time-frequency analysis algorithm; The driving signal of the function in the damped forced vibration function group is the resonant frequency ω to be solved r The undamped natural frequency ω of each function in the damped forced vibration function group is estimated by numerical calculation. The specific steps for determining the undamped natural frequency ω of each function are as follows: C =ω r A set of damped forced vibration functions is set as the center, and the undamped natural frequencies ω of the functions are ω C -nε,ω C -(n-1)ε,……,ω C , ..., ω C +(n-1)ε,ω C +nε; through similar steps S2 and S3, if the damped forced vibration function with the highest energy is at both ends of the function group when stable, then ω C Set it as this value and recalculate the estimate. When the function with the highest energy is in the middle of the function group, the undamped natural frequency ω of the function is taken as the estimated value. The undamped natural frequency ω satisfies the requirement that the resonant frequency of the damped forced function is the detection frequency.

[0046] Further, the step S2 is specifically described as follows: converting the damped forced vibration function into a differential equation for numerical calculation; the non-stationary signal sequence F t The time interval ΔT of the differential operation can be set according to the sampling frequency of the non-stationary signal, or the time interval ΔT can be set according to the signal frequency component to be analyzed; the displacement x is set for each function in the function group k and speed v k Two variables describe the state of the damped forced function, k is the sequence number of the function in the damped forced vibration function, m k is the mass parameter of the kth vibration function, ω k is the undamped natural frequency ω of the kth vibration function, and each function corresponds to a detection frequency; the differential equation for the transformation of the damped forced vibration function starts from the 0 state, and the driven non-stationary signal sequence is calculated from time 0, and the calculation steps are:

[0047] Calculate the acceleration:

[0048] Update speed:

[0049] Update displacement:

[0050] Further, the step S3 is specifically described as follows: according to the state value of each function in the damped forced vibration function group at each moment, the resonance frequency ω of the K vibration functions in the non-stationary signal is calculated. C The amplitude and phase of the frequency components of

[0051] Amplitude estimation: Calculate the energy of each vibration function

[0052] The amplitude of the corresponding frequency component in the non-stationary signal is calculated based on the damping coefficient, damping function and vibration function energy:

[0053] For example: Damping function: When, the amplitude:

[0054] Damping function: When, the amplitude:

[0055] It is the maximum speed value corresponding to the current energy of the Kth function.

[0056] Other forms of damping functions can be used as required. When the damping function is in other forms, the maximum velocity function of the vibration function of the frequency amplitude can be obtained by solving the damped forced vibration equation, or it can be estimated by numerical calculation; the estimation method can be based on the damping function being a polynomial equation of several times, and a linear regression equation can be designed to estimate the equation parameters of the amplitude of the corresponding frequency component of the driving signal;

[0057] Phase estimation:

[0058] Frequency component estimation: The amplitude-frequency value of each frequency component in the signal is estimated based on the energy of each function in the damped forced vibration function group, and then the frequency components in the signal are analyzed; at the same time, interpolation can be performed based on the quality factor of each function to increase the frequency resolution accuracy without increasing the number of functions.

[0059] As can be seen from the above, the present invention is a time-frequency analysis method for non-stationary signals. When analyzing the time-frequency characteristics of non-stationary signals, the method can set the frequency resolution accuracy and time resolution accuracy according to requirements; the frequency resolution accuracy of the method is determined by the set number of functions, which can be increased infinitely as long as the equipment allows, and can also be analyzed only in important frequency bands according to requirements to reduce the amount of calculation; the time resolution accuracy of the method is at most the sampling period of the signal.

[0060] The embodiments are further described below in conjunction with the accompanying drawings:

[0061] like Figure 2 As shown, Figure 2It shows an original non-stationary signal, such as a speech signal (the sampling rate of the speech signal is 44100Hz), which shows the change of its amplitude over time in the time domain. As can be seen from the figure, the figure provides an intuitive representation of the signal to be analyzed, illustrating the complexity and time-varying nature of non-stationary signals (such as speech); it is the starting point of the analysis, showing the different frequency components contained in the signal and their time-varying characteristics.

[0062] like Figure 3 As shown, Figure 3 The spectrogram obtained by analyzing the example speech signal using the present technical solution (i.e., the time-frequency analysis method for non-stationary signals) is shown (the frequency resolution accuracy of the figure is 5 Hz, and the time resolution accuracy is adjusted to 3 ms); the spectrogram is a two-dimensional representation, with the horizontal axis representing time, the vertical axis representing frequency, and the depth of color representing the strength or energy of the signal. It can be seen from the figure that the present technical solution can accurately analyze the time-frequency characteristics of non-stationary signals; through the spectrogram, it can be clearly seen how the different frequency components in the signal change over time, such as the appearance, disappearance, and amplitude changes of frequency; this reflects the advantage of the present technical solution in both time domain and frequency domain with high resolution accuracy.

[0063] like Figure 4 As shown, Figure 4 The conventional short-time Fourier transform (STFT) Figure 2 The spectrogram obtained by analyzing the speech signal in (the figure is obtained by using the MATLAB specgram function, the frame length parameter of the function is set to 2048, which is about 46ms, the theoretical maximum frequency resolution accuracy is 21.5Hz, and the frame overlap parameter of the function is 1536, so the displayed time resolution accuracy of the figure is 11.5ms, which is actually 46ms); Figure 3 Similarly, it is also a two-dimensional representation with the horizontal axis representing time and the vertical axis representing frequency, but the signal strength represented by the depth of the color may be different from Figure 3 Different, by Figure 3 As shown, this figure is used to compare with the analysis results of the present technical solution; due to the limitations of short-time Fourier transform in time domain and frequency domain resolution accuracy, its analysis results may not be as clear and accurate as those of the present technical solution; by comparison Figure 3 and Figure 4 , we can intuitively see the advantages of this technical solution in improving the accuracy of time-frequency analysis.

[0064] The time-frequency analysis method of a non-stationary signal according to an embodiment of the present invention is compared with the current conventional technology to obtain the following table:

[0065]

[0066] It can be seen from the above table that the present invention is superior to the existing technology in terms of time domain and frequency domain resolution accuracy, multi-signal analysis capability, flexibility, computational complexity, and applicable scenarios. This method is suitable for large-scale promotion and application.

[0067] like Figure 5 As shown, a time-frequency analysis system for non-stationary signals is applicable to the above-mentioned time-frequency analysis method for non-stationary signals, comprising:

[0068] A design module is used to design a damped forced vibration function group, determine the number of functions in the function group and the resonant frequency of each function according to the frequency range and frequency resolution accuracy required for the non-stationary signal to be analyzed, and determine the damping coefficient and damping function of each function to achieve the required quality factor;

[0069] A numerical calculation module, used for converting the damped forced vibration function group into a differential equation for numerical calculation to describe the state of the damped forced vibration function, wherein the differential operation time interval of the non-stationary signal sequence is set according to the sampling frequency of the non-stationary signal or the signal frequency component to be analyzed;

[0070] The analysis and calculation module is used to analyze and calculate the amplitude and phase of the frequency component equal to the resonance frequency of each vibration function in the non-stationary signal according to the state value of each function in the damped forced vibration function group at each moment.

[0071] Furthermore, the design module is further used to: determine the quality factor of the damped vibration function based on the undamped natural frequency, damping coefficient and damping function of the function; determine the number of functions in the function group based on the frequency resolution accuracy and the frequency analysis range; set the resonant frequency of each vibration function in the damped forced vibration function group as the frequency component that needs to be detected by the signal to be analyzed.

[0072] Furthermore, the numerical calculation module is further used to: set two variables, displacement and velocity, for each function in the function group to describe the state of the damped forced function; starting from state 0, the driven non-stationary signal sequence is calculated from time 0, and numerical calculation is performed through the steps of calculating acceleration, updating velocity and updating displacement.

[0073] Furthermore, the analysis and calculation module is further used to: estimate the amplitude-frequency value of each frequency component in the signal according to the energy of each function in the damped forced vibration function group, and then analyze the frequency components in the signal; interpolate according to the quality factor of each function, and then increase the frequency resolution accuracy without increasing the number of functions.

[0074] Furthermore, it also includes: a display module, which is used to display the amplitude and phase information of each frequency component in the non-stationary signal obtained by the analysis and calculation module.

[0075] Furthermore, it also includes: a storage module for storing the damped forced vibration function group designed by the design module, the numerical calculation results obtained by the numerical calculation module, and the amplitude and phase information of each frequency component in the non-stationary signal obtained by the analysis and calculation module.

[0076] In this embodiment, the time-frequency analysis system for non-stationary signals includes a processor and a memory, wherein the processor includes a kernel, and the kernel retrieves the corresponding program unit from the memory. One or more kernels may be provided, and the time-frequency analysis method for non-stationary signals is implemented by adjusting kernel parameters.

[0077] The memory may include non-permanent memory in a computer-readable medium, random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM, and the memory includes at least one memory chip.

[0078] An embodiment of the present application provides a processor configured to execute the above-mentioned time-frequency analysis method of non-stationary signals.

[0079] An embodiment of the present application provides a machine-readable storage medium, on which instructions are stored. When the instructions are executed by a processor, the processor is configured to execute the above-mentioned time-frequency analysis method for non-stationary signals.

[0080] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0081] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0082] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0083] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0084] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0085] The memory may include non-permanent memory in a computer-readable medium, random access memory (RAM) and / or non-volatile memory in the form of read-only memory (ROM) or flash RAM. The memory is an example of a computer-readable medium.

[0086] Computer readable media include permanent and non-permanent, removable and non-removable media, and can be implemented by any method or technology to store information. Information can be computer readable instructions, data structures, program modules or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, compact disk read-only memory (CD-ROM), digital versatile disk (DVD) or other optical storage, magnetic cassettes, magnetic disk storage or other magnetic storage devices or any other non-transmission media that can be used to store information that can be accessed by a computing device. As defined herein, computer readable media does not include temporary computer readable media (transitory media), such as modulated data signals and carrier waves.

[0087] It should also be noted that the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, commodity or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, commodity or device. In the absence of more restrictions, the elements defined by the sentence "comprises a ..." do not exclude the existence of other identical elements in the process, method, commodity or device including the elements.

[0088] The embodiments of the present invention are provided for the purpose of illustration and description. Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and cannot be understood as limitations of the present invention. Ordinary technicians in this field can change, modify, replace and modify the above embodiments within the scope of the present invention.

[0089] The embodiments of the present invention are provided for the purpose of illustration and description. Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and cannot be understood as limitations of the present invention. Ordinary technicians in this field can change, modify, replace and modify the above embodiments within the scope of the present invention.

Claims

1. A time-frequency analysis method for non-stationary signals, characterized in that: The following steps are involved: S1. Design a damped forced vibration function group, and determine the number of functions in the function group and the resonant frequency of each function according to the frequency range and frequency resolution accuracy required for the non-stationary signal to be analyzed; S2, converting the damped forced vibration function group into a differential equation for numerical calculation to describe the state of the damped forced vibration function; S3. According to the state value of each function in the damped forced vibration function group at each moment, the amplitude and phase of the frequency component equal to the resonant frequency of each vibration function in the non-stationary signal are analyzed and calculated.

2. The time-frequency analysis method for a non-stationary signal as claimed in claim 1, characterized in that: The specific description of step S1 is as follows: Design a damped forced vibration function group: For non-stationary signals, determine the number of functions in the vibration function group and the resonant frequency of each vibration function according to the frequency range to be detected and the required frequency resolution accuracy.

3. The time-frequency analysis method for a non-stationary signal as claimed in claim 1, characterized in that: In step S1, when designing a damped forced vibration function group, it also includes determining the damping coefficient and damping function of each function to achieve the required quality factor. The specific operation is: determining the number of damped vibration functions included in the function group: when the frequency resolution accuracy is fixed, the number of functions in the function group = frequency analysis range / frequency resolution accuracy; or determining the number of functions in the function group according to requirements to correspond to the number of frequency components in the non-stationary signal that needs to be analyzed.

4. The time-frequency analysis method for a non-stationary signal as claimed in claim 1, characterized in that: The specific description of step S2 is as follows: converting the damped forced vibration function into a differential equation for numerical calculation; t The time interval ΔT of the differential operation can be set according to the sampling frequency of the non-stationary signal, or the time interval ΔT can be set according to the signal frequency component to be analyzed; the displacement x is set for each function in the function group k and speed v k Two variables describe the state of the damped forced function, k is the sequence number of the function in the damped forced vibration function, m k is the mass parameter of the kth vibration function, ω k is the undamped natural frequency ω of the kth vibration function, and each function corresponds to a detection frequency; the differential equation for the transformation of the damped forced vibration function starts from the 0 state, and the driven non-stationary signal sequence is calculated from time 0.

5. The time-frequency analysis method for a non-stationary signal as claimed in claim 1, characterized in that: The specific description of step S3 is as follows: Analyze and calculate the resonance frequency ω of K vibration functions in the non-stationary signal according to the state value of each function at each moment in the damped forced vibration function group. C The amplitude and phase of the frequency component; Frequency component estimation: Estimate the amplitude-frequency value of each frequency component in the signal according to the energy of each function in the damped forced vibration function group, and then analyze the frequency components in the signal; At the same time, interpolation can be performed according to the quality factor of each function to increase the frequency resolution accuracy without increasing the number of functions.

6. A time-frequency analysis system for non-stationary signals, characterized in that: A time-frequency analysis method for a non-stationary signal according to any one of claims 1 to 5, comprising: A design module is used to design a damped forced vibration function group, determine the number of functions in the function group and the resonant frequency of each function according to the frequency range and frequency resolution accuracy required for the non-stationary signal to be analyzed, and determine the damping coefficient and damping function of each function to achieve the required quality factor; A numerical calculation module, used for converting the damped forced vibration function group into a differential equation for numerical calculation to describe the state of the damped forced vibration function, wherein the differential operation time interval of the non-stationary signal sequence is set according to the sampling frequency of the non-stationary signal or the signal frequency component to be analyzed; The analysis and calculation module is used to analyze and calculate the amplitude and phase of the frequency component equal to the resonance frequency of each vibration function in the non-stationary signal according to the state value of each function in the damped forced vibration function group at each moment.

7. A processor, characterized in that: The method is configured to perform the time-frequency analysis method of a non-stationary signal according to any one of claims 1 to 5.

8. A machine-readable storage medium having instructions stored thereon, characterized in that: When the instruction is executed by a processor, the processor is configured to perform the time-frequency analysis method for a non-stationary signal according to any one of claims 1 to 5.

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