MSTCT time-frequency analysis method and system based on multiple synchronous compression

Abstract

The present invention discloses an MSTCT time-frequency analysis method and system based on multiple synchronous compression, which includes: estimating and processing a signal through a window function to obtain an estimated instantaneous chirp rate coefficient of the signal; analyzing the chirp rate of the signal based on the estimated instantaneous chirp rate coefficient of the signal to obtain a chirplet transform and a frequency reallocation operator of the signal; obtaining a time-frequency representation result of the signal based on the chirplet transform of the signal; and performing multiple synchronous compression processing on the time-frequency representation result of the signal based on the frequency reallocation operator until the compression result meets a preset condition, and outputting a time-frequency diagram of the signal. By using the present invention, it is possible to achieve a signal time-frequency analysis result with higher resolution and energy concentration without increasing the computational cost. As an MSTCT time-frequency analysis method and system based on multiple synchronous compression, the present invention can be widely used in the field of signal processing technology.

Description

Technical Field

[0001] The present invention relates to the field of signal processing technology, and in particular to an MSTCT time-frequency analysis method and system based on multiple synchronous compression. Background Art

[0002] Time-frequency analysis (TFA) provides a powerful approach for characterizing the complex time-varying characteristics of nonstationary signals commonly found in practical applications. Therefore, developing new methods for analyzing nonstationary multicomponent signals is of great practical significance. Traditional TF analysis methods include linear TF and quadratic TF. Linear TF analysis often fails to achieve satisfactory resolution, while quadratic TF analysis, when analyzing multicomponent signals, suffers from nonlinear products that lead to cross terms, reducing the readability of the TF representation. To further improve the performance of the synchro-squeezed transform, numerous concentrated TF methods have been proposed, such as the multiple synchro-squeezed transform (MSST). However, when using MSST for time-frequency analysis of high-frequency signals, it is often difficult to accurately approximate the true IF of the signal within the number of iterations. Existing TFA methods, such as the signal chirp rate (CR) and the synchronous extraction polynomial chirplet transform, leverage high-order information to concentrate the energy of the modulated signal's TF result. However, these high-order synchro-squeezed transform methods are computationally expensive and lack robustness to noise, preventing accurate reconstruction. Summary of the Invention

[0003] In order to solve the above technical problems, the purpose of the present invention is to provide a time-frequency analysis method and system based on multiple synchronous compressed chirplet transform (MSTCT), which can achieve high resolution and energy concentration in the time-frequency analysis results of the signal without increasing the computational cost.

[0004] The first technical solution adopted by the present invention is: an MSTCT time-frequency analysis method based on multiple synchronous compression, comprising the following steps:

[0005] The signal is estimated and processed through the window function to obtain the estimated instantaneous chirp rate coefficient of the signal;

[0006] According to the estimated instantaneous chirp rate coefficient of the signal, the chirp rate of the signal is analyzed to obtain the chirplet transform and frequency redistribution operator of the signal;

[0007] Obtain the time-frequency representation of the signal based on the chirplet transform of the signal;

[0008] Based on the frequency reallocation operator, the time-frequency representation of the signal is subjected to multiple synchronous compression processes until the compression result meets the preset conditions, and the time-frequency diagram of the signal is output.

[0009] Furthermore, the step of estimating the signal by using a window function to obtain an estimated instantaneous chirp rate coefficient of the signal specifically includes:

[0010] Obtain the signal to be analyzed, the ramp function and the window function;

[0011] Preprocessing the window function according to the ramp function to obtain a preprocessed window function;

[0012] The signal to be analyzed is subjected to short-time Fourier transform and estimation processing according to the preprocessed window function to obtain the estimated instantaneous chirp rate coefficient of the signal.

[0013] Furthermore, the step of preprocessing the window function according to the ramp function to obtain the preprocessed window function specifically includes:

[0014] Calculate the first-order and second-order partial derivatives of the window function with respect to time;

[0015] Multiplying the ramp function by the window function and the first-order partial derivative of the window function with respect to time respectively to obtain the product of the ramp function and the window function and the product of the ramp function and the first-order partial derivative of the window function with respect to time;

[0016] The preprocessed window function is constructed by combining the first-order partial derivative of the window function with respect to time, the second-order partial derivative of the window function with respect to time, the product of the ramp function and the window function, and the product of the ramp function and the first-order partial derivative of the window function with respect to time.

[0017] Furthermore, the expression for performing short-time Fourier transform on the signal to be analyzed according to the preprocessed window function is as follows:

[0018]

[0019] In the above formula, It represents the short-time Fourier transform result of the signal, f(t) represents the segmented signal, h(μ-t) represents the window function centered on time t after preprocessing, t represents the time variable in time-frequency analysis, and ω represents the frequency variable.

[0020] Furthermore, the calculation formula of the estimated instantaneous chirp rate coefficient of the signal is as follows:

[0021]

[0022] In the above formula, represents the estimated instantaneous chirp rate coefficient of the signal, Indicates the use of window function The short-time Fourier transform result is obtained. Indicates the use of window function The short-time Fourier transform result is obtained. Represents the short-time Fourier transform result obtained using the window function g(t), Indicates the use of window function The short-time Fourier transform result is obtained. Represents the short-time Fourier transform result obtained using the window function Tg(t,ω)=tg(t), represents taking the real part of (·), It means taking the imaginary part of (·).

[0023] Furthermore, the step of analyzing the chirp rate of the signal based on the estimated instantaneous chirp rate coefficient of the signal to obtain the chirplet transformation and frequency reallocation operator of the signal specifically includes:

[0024] Calculating the energy of the signal after short-time Fourier transform to obtain the energy of the signal after short-time Fourier transform;

[0025] The estimated instantaneous chirp rate coefficient of the signal and the energy of the signal after short-time Fourier transform are estimated and analyzed to obtain the chirp rate of the signal;

[0026] Estimate and analyze the chirp rate of the signal to obtain the chirplet transform of the signal;

[0027] Computes the frequency reallocation operator for a signal based on its chirplet transform.

[0028] Furthermore, the calculation formula of the chirplet transform of the signal is as follows:

[0029]

[0030] In the above formula, represents the chirplet transform of the signal, and f(μ) represents the signal to be processed.

[0031] Furthermore, the calculation expression of the frequency reallocation operator is as follows:

[0032]

[0033] In the above formula, represents the frequency reallocation operator, represents the chirplet transform of the signal, represents the estimate of the chirp rate of the signal, represents the partial derivative of t, represents the partial derivative with respect to ω.

[0034] The second technical solution adopted by the present invention is: an MSTCT time-frequency analysis system based on multiple synchronous compression, comprising:

[0035] The estimation module is used to estimate the signal through the window function to obtain the estimated instantaneous chirp rate coefficient of the signal;

[0036] An analysis module is used to analyze the chirp rate of the signal based on the estimated instantaneous chirp rate coefficient of the signal to obtain the chirplet transform and frequency redistribution operator of the signal;

[0037] An acquisition module is used to obtain the time-frequency representation result of the signal according to the chirplet transformation of the signal;

[0038] The output module performs multiple synchronous compression processing on the time-frequency representation of the signal based on the frequency redistribution operator until the compression result meets the preset conditions and outputs the time-frequency diagram of the signal.

[0039] The beneficial effects of the method and system of the present invention are as follows: the present invention performs prediction processing on the signal through a window function and performs chirplet transformation of the signal according to the prediction result, which can improve the transformation performance of signal synchronous compression, and self-adjusts the chirplet transformation of the signal through MSTCT, which can have better time-frequency resolution than existing transformation technologies under the condition of equal iterative calculation cost, and the output signal time-frequency diagram has better robustness to noise interference and higher resolution. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a flowchart of the steps of the MSTCT time-frequency analysis method based on multiple synchronous compression of the present invention;

[0041] Figure 2 It is a structural block diagram of the MSTCT time-frequency analysis system based on multiple synchronous compression of the present invention;

[0042] Figure 3 is a time domain waveform diagram of a signal obtained by the present invention;

[0043] Figure 4 It is a time-frequency diagram obtained by performing time-frequency analysis on the signal using the synchronous compression transform method;

[0044] Figure 5 It is a time-frequency diagram obtained by applying the method of the present invention to perform time-frequency analysis on the signal;

[0045] Figure 6 It is a time-frequency diagram obtained by performing time-frequency analysis on a signal containing noise using the synchronous compression transform method;

[0046] Figure 7It is a time-frequency diagram obtained by performing time-frequency analysis on a signal containing noise using the method of the present invention. DETAILED DESCRIPTION

[0047] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. The step numbers in the following embodiments are provided for ease of description only and do not limit the order of the steps. The order of execution of the steps in the embodiments can be adaptively adjusted based on the understanding of those skilled in the art.

[0048] Reference Figure 1 The present invention provides an MSTCT time-frequency analysis method based on multiple synchronous compression, which includes the following steps:

[0049] S1. Estimation processing is performed on the signal through the window function to obtain the estimated instantaneous chirp rate coefficient of the signal;

[0050] S11, obtaining a signal to be analyzed, a ramp function, and a window function;

[0051] S111, reference Figure 3 , obtaining the signal to be analyzed, which includes a signal with noise and a signal without noise. From the figure, it can be seen that the signal f(t) is a signal in the time domain. The part before 600 seconds is a single-frequency signal, and the part after 600 seconds is a nonlinear frequency-modulated signal;

[0052] Specifically, the noise-free signal is as follows:

[0053]

[0054] The signal with noise is specifically as follows:

[0055] f0(t)=f(t)+n(t)

[0056] In the above formula, f(t) represents the signal without noise, f0(t) represents the signal with noise, n(t) represents Gaussian white noise, t represents the time variable in time-frequency analysis, and the sampling frequency is 1 Hz;

[0057] S12, preprocessing the window function according to the ramp function to obtain a preprocessed window function;

[0058] S121, preset a window function and a ramp function, and calculate the first-order partial derivative and the second-order partial derivative of the window function with respect to time;

[0059] Specifically, the input window function is as follows:

[0060]

[0061] In the above formula, g(t) represents the window function, σ 2 represents variance;

[0062] Where σ = 0.32, number of iterations M = 10;

[0063] The calculation process of the first-order partial derivative of the window function with respect to time is as follows:

[0064]

[0065] In the above formula, Dg(t) represents the first-order partial derivative of the window function with respect to time;

[0066] The calculation process of the second-order partial derivative of the window function with respect to time is as follows:

[0067]

[0068] In the above formula, D 2 g(t) represents the second-order partial derivative of the window function with respect to time;

[0069] S122. Performing multiplication operations on the ramp function, the window function, and the first-order partial derivative of the window function with respect to time, respectively, to obtain a product of the ramp function and the window function and a product of the ramp function and the first-order partial derivative of the window function with respect to time;

[0070] Specifically, the product calculation process of the ramp function and the window function is as follows:

[0071] Tg(t)=tg(t)

[0072] In the above formula, Tg(t) represents the product of the ramp function and the window function;

[0073] The calculation process of the product of the ramp function and the first-order partial derivative of the window function with respect to time is as follows:

[0074]

[0075] In the above formula, DTg(t) represents the product of the ramp function and the first-order partial derivative of the window function with respect to time.

[0076] S123. Construct a preprocessed window function by combining the first-order partial derivative of the window function with respect to time, the second-order partial derivative of the window function with respect to time, the product of the ramp function and the window function, and the product of the ramp function and the first-order partial derivative of the window function with respect to time.

[0077] S13. Perform short-time Fourier transform and estimation processing on the signal to be analyzed according to the pre-processed window function to obtain an estimated instantaneous chirp rate coefficient of the signal.

[0078] Specifically, a short-time Fourier transform is performed on the signal to be analyzed according to the preprocessed window function. The preprocessed window function includes the original window function and has a total of five forms. The short-time Fourier transform is performed on the signal to be analyzed respectively. The specific transformation process is as follows:

[0079]

[0080]

[0081]

[0082]

[0083]

[0084] The signal is estimated based on the Fourier transform result. The specific process of the estimation process is as follows:

[0085]

[0086] In the above formula, represents the estimated instantaneous chirp rate coefficient of the signal, Indicates the use of window function The short-time Fourier transform result is obtained. Indicates the use of window function The short-time Fourier transform result is obtained. Represents the short-time Fourier transform result obtained using the window function g(t), Indicates the use of window function The short-time Fourier transform result is obtained. Represents the short-time Fourier transform result obtained using the window function Tg(t,ω)=tg(t), represents taking the real part of (·), It means taking the imaginary part of (·).

[0087] S2. Analyze the chirp rate of the signal based on the estimated instantaneous chirp rate coefficient of the signal to obtain the chirplet transform and frequency redistribution operator of the signal;

[0088] S21. Calculate the energy of the signal after the short-time Fourier transform to obtain the energy of the signal after the short-time Fourier transform. Specifically, the calculation formula for the energy of the signal after the short-time Fourier transform is as follows:

[0089]

[0090] In the above formula, Represents the energy of the signal after short-time Fourier transform;

[0091] S22, estimating and analyzing the estimated instantaneous chirp rate coefficient of the signal and the energy of the signal after short-time Fourier transform to obtain the chirp rate of the signal;

[0092] Specifically, the chirp rate is the instantaneous frequency change rate of the signal, which describes the changing trend and speed of the instantaneous frequency of the signal. The chirp rate of the signal is estimated again based on the estimated instantaneous chirp rate coefficient of the signal and the energy of the signal after short-time Fourier transform, as shown below:

[0093]

[0094] In the above formula, Indicates the chirp rate of the signal to be analyzed;

[0095] S23, estimating and analyzing the chirp rate of the signal to obtain the chirplet transform of the signal;

[0096] Specifically, the chirplet transform of the signal is estimated based on the chirp rate of the signal, which is as follows:

[0097]

[0098] In the above formula, represents the chirplet transform of the signal, and f(μ) represents the signal to be processed.

[0099] S24. Calculate a frequency reallocation operator of the signal according to the chirplet transform of the signal.

[0100] Specifically, the calculation process of the frequency reallocation operator is as follows:

[0101]

[0102] In the above formula, represents the frequency reallocation operator, represents the chirplet transform of the signal, represents the estimate of the chirp rate of the signal, represents the partial derivative of t, represents the partial derivative with respect to ω.

[0103] S3. Based on the frequency redistribution operator, the chirplet transform of the signal is subjected to multiple synchronous compression processing to output the time-frequency diagram of the signal.

[0104] S31, obtaining a time-frequency representation result of the signal according to the chirplet transformation of the signal;

[0105] S32. Based on the frequency reallocation operator, perform multiple synchronous compression processing on the time-frequency representation result of the signal until the compression result meets the preset conditions, and output the time-frequency diagram of the signal.

[0106] Specifically, the multiple synchronous compression processing is the MSTCT transformation. The number of iterations is set manually. The more iterations, the better the signal compression, but the corresponding computational complexity is also greater. On the contrary, if the number of iterations is small, the effect is not so good and the computational complexity is small. When the number of iterations reaches a certain value, the signal compression level tends to be stable, and increasing the number of iterations will not improve the effect much. The time-frequency representation obtained by the chirplet transformation is subjected to multiple synchronous compression based on the frequency redistribution operator to obtain a time-frequency representation result with high energy concentration. The specific process of the MSTCT transformation is as follows:

[0107]

[0108]

[0109] In the above formula, Ts [M] (t,ω) represents the result after M times of MSTCT, ω and a both represent frequency;

[0110] The above formula only integrates a but not ω.

[0111] Finally, refer to Figure 5 and Figure 7 , the time-frequency diagram of the output signal f(t) after MSTCT. The time-frequency diagram allows us to observe the time domain information and frequency domain information of a signal at the same time, and can effectively characterize the change law of the frequency component of the non-stationary signal over time; the time-frequency analysis method can be applied to fields such as earthquake, astronomy, gravitational waves, radar, sonar, biomedicine, speech and mechanical engineering. The time-frequency diagram obtained by time-frequency analysis can provide a very intuitive display of signal processing in these fields, such as Figure 4 and Figure 6 As shown in the figure, it is the time-frequency diagram of the signal obtained by the synchronous compression transform method. It can be seen from the figure that although the time-frequency diagram obtained after the synchronous compression transform method is used for time-frequency analysis has a good energy concentration in the single-frequency part of the signal, the energy smearing phenomenon in the nonlinear frequency modulation part of the signal is still not well solved, and the faster the frequency of the signal changes, the worse the resolution of the obtained curve. This also shows that the synchronous compression transform method has poor noise robustness when performing time-frequency analysis on noise-contaminated signals.

[0112] Reference Figure 2 , the MSTCT time-frequency analysis system based on multiple synchronous compression includes:

[0113] The estimation module is used to estimate the signal through the window function to obtain the estimated instantaneous chirp rate coefficient of the signal;

[0114] An analysis module is used to analyze the chirp rate of the signal based on the estimated instantaneous chirp rate coefficient of the signal to obtain the chirplet transform and frequency redistribution operator of the signal;

[0115] An acquisition module is used to obtain the time-frequency representation result of the signal according to the chirplet transformation of the signal;

[0116] The output module performs multiple synchronous compression processing on the time-frequency representation of the signal based on the frequency redistribution operator until the compression result meets the preset conditions and outputs the time-frequency diagram of the signal.

[0117] The contents of the above method embodiments are all applicable to the present system embodiments. The functions specifically implemented by the present system embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0118] The above is a specific description of the preferred implementation of the present invention, but the invention is not limited to the embodiments. Those skilled in the art can make various equivalent modifications or substitutions without violating the spirit of the present invention. These equivalent modifications or substitutions are all included in the scope defined by the claims of this application.

Claims

1. The MSTCT time-frequency analysis method based on multiple synchronous compression is characterized by: The following steps are involved: The signal is estimated and processed through the window function to obtain the estimated instantaneous chirp rate coefficient of the signal; According to the estimated instantaneous chirp rate coefficient of the signal, the chirp rate of the signal is analyzed to obtain the chirplet transform and frequency redistribution operator of the signal; Obtain the time-frequency representation of the signal based on the chirplet transform of the signal; Based on the frequency redistribution operator, the time-frequency representation of the signal is subjected to multiple synchronous compression processing until the compression result meets the preset conditions and the time-frequency diagram of the signal is output; The step of estimating the signal by using a window function to obtain an estimated instantaneous chirp rate coefficient of the signal specifically includes: Obtain the signal to be analyzed, the ramp function and the window function; Preprocessing the window function according to the ramp function to obtain a preprocessed window function; Perform short-time Fourier transform and estimation processing on the signal to be analyzed according to the pre-processed window function to obtain the estimated instantaneous chirp rate coefficient of the signal; The step of preprocessing the window function according to the ramp function to obtain the preprocessed window function specifically includes: Calculate the first-order and second-order partial derivatives of the window function with respect to time; Multiplying the ramp function by the window function and the first-order partial derivative of the window function with respect to time respectively to obtain the product of the ramp function and the window function and the product of the ramp function and the first-order partial derivative of the window function with respect to time; The preprocessed window function is constructed by combining the first-order partial derivative of the window function with respect to time, the second-order partial derivative of the window function with respect to time, the product of the ramp function and the window function, and the product of the ramp function and the first-order partial derivative of the window function with respect to time.

2. The MSTCT time-frequency analysis method based on multiple synchronous compression according to claim 1 is characterized in that: The expression for performing short-time Fourier transform on the signal to be analyzed according to the preprocessed window function is as follows: In the above formula, It represents the short-time Fourier transform result of the signal, f(t) represents the segmented signal, h(μ-t) represents the window function centered on time t after preprocessing, t represents the time variable in time-frequency analysis, and ω represents the frequency variable.

3. The MSTCT time-frequency analysis method based on multiple synchronous compression according to claim 1 is characterized in that: The calculation formula of the estimated instantaneous chirp rate coefficient of the signal is as follows: In the above formula, represents the estimated instantaneous chirp rate coefficient of the signal, Indicates the use of window function The short-time Fourier transform result is obtained. Indicates the use of window function The short-time Fourier transform result is obtained. Represents the short-time Fourier transform result obtained using the window function g(t), Indicates the use of window function The short-time Fourier transform result is obtained. Represents the short-time Fourier transform result obtained using the window function Tg(t,ω)=tg(t), represents taking the real part of (·), It means taking the imaginary part of (·).

4. The MSTCT time-frequency analysis method based on multiple synchronous compression according to claim 3 is characterized in that: The step of analyzing the chirp rate of the signal according to the estimated instantaneous chirp rate coefficient of the signal to obtain the chirplet transformation and frequency reallocation operator of the signal specifically includes: Calculating the energy of the signal after short-time Fourier transform to obtain the energy of the signal after short-time Fourier transform; The estimated instantaneous chirp rate coefficient of the signal and the energy of the signal after short-time Fourier transform are estimated and analyzed to obtain the chirp rate of the signal; Estimate and analyze the chirp rate of the signal to obtain the chirplet transform of the signal; Computes the frequency reallocation operator for a signal based on its chirplet transform.

5. The MSTCT time-frequency analysis method based on multiple synchronous compression according to claim 4 is characterized in that: The calculation formula of the time-frequency representation result obtained by chirplet transformation of the signal is as follows: In the above formula, represents the chirplet transform of the signal, and f(μ) represents the signal to be processed.

6. The MSTCT time-frequency analysis method based on multiple synchronous compression according to claim 5 is characterized in that: The calculation expression of the frequency reallocation operator is as follows: In the above formula, represents the frequency reallocation operator, represents the chirplet transform of the signal, represents the estimate of the chirp rate of the signal, represents the partial derivative of t, represents the partial derivative with respect to ω.

7. The MSTCT time-frequency analysis system based on multiple synchronous compression is characterized by: Includes the following modules: The estimation module is used to estimate the signal through the window function to obtain the estimated instantaneous chirp rate coefficient of the signal; An analysis module is used to analyze the chirp rate of the signal based on the estimated instantaneous chirp rate coefficient of the signal to obtain the chirplet transform and frequency redistribution operator of the signal; An acquisition module is used to obtain the time-frequency representation result of the signal according to the chirplet transformation of the signal; The output module performs multiple synchronous compression processing on the time-frequency representation of the signal based on the frequency redistribution operator until the compression result meets the preset conditions and outputs the time-frequency diagram of the signal; The process of estimating the signal by using a window function to obtain the estimated instantaneous chirp rate coefficient of the signal specifically includes: Obtain the signal to be analyzed, the ramp function and the window function; Preprocessing the window function according to the ramp function to obtain a preprocessed window function; Perform short-time Fourier transform and estimation processing on the signal to be analyzed according to the pre-processed window function to obtain the estimated instantaneous chirp rate coefficient of the signal; The step of preprocessing the window function according to the ramp function to obtain the preprocessed window function specifically includes: Calculate the first-order and second-order partial derivatives of the window function with respect to time; According to the multiplication operation of the ramp function with the window function and the first-order partial derivative of the window function with respect to time, the product of the ramp function and the window function and the product of the ramp function and the first-order partial derivative of the window function with respect to time are obtained; the first-order partial derivative of the window function with respect to time, the second-order partial derivative of the window function with respect to time, the product of the ramp function and the window function and the product of the ramp function and the first-order partial derivative of the window function with respect to time are combined to construct the preprocessed window function.

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