A time-frequency analysis method based on improved S-transform combined with synchronization extraction

Abstract

The present invention discloses a time-frequency analysis method using an improved S transform combined with synchronous extraction, comprising: determining the ranges of three window parameters of an improved window function according to frequency resolution requirements for a non-stationary signal to be analyzed; determining the optimal selection of the three window parameters based on quantitative calculation of time-frequency concentration; performing an improved S transform on the signal using the optimized parameters; estimating the instantaneous frequency to obtain a synchronous extraction operator; and extracting the time-frequency spectrum of the improved S transform selected with the optimized parameters. The time-frequency analysis method using an improved S transform combined with synchronous extraction proposed by the present invention further enhances the flexibility of the S transform window function, can adapt to signals with different characteristics, has more accurate instantaneous frequency estimation, high time-frequency resolution, and better time-frequency analysis results.

Description

Technical Field

[0001] The invention belongs to signal processing technology, and in particular relates to a time-frequency analysis method for improving S-transformation combined with synchronization extraction. Background Art

[0002] Non-stationary signals are widely present in fields such as radar, communications, sonar, and medicine. The simple Fourier transform (TFA) can only transform signals from the time domain to the frequency domain, which is insufficient for analyzing non-stationary signals. Time-frequency analysis (TFA) is widely used to convert time series signals into a two-dimensional time-frequency plane to obtain information about the signal's time-varying characteristics. Classic time-frequency analysis methods include the short-time Fourier transform (STFT), wavelet transform (WT), Wigner-Ville distribution (WVD), and S-transform (ST). The STFT assumes that the signal within a short time window is stationary and obtains the signal's time-frequency information through a piecewise Fourier transform of a sliding window. However, when the window function is fixed, the time-frequency resolution is fixed, resulting in very low time-frequency aggregation. The wavelet transform (WT) addresses the issue of fixed resolution to some extent, but its use is limited by its shortcomings, such as the lack of a clear physical meaning for the scale parameter, the constraints imposed by admissibility conditions, and the difficulty in designing the wavelet basis. The Wigner-Ville distribution has good time-frequency aggregation, but it can generate cross terms for multi-component signals, which can interfere with the resolution of useful signals. The S-transform is a combination of the short-time Fourier transform and the wavelet transform. Its time window width is inversely proportional to frequency, resulting in high frequency resolution at low frequencies and low frequency resolution but high temporal resolution at high frequencies. However, because the window length varies only slightly with frequency, the time-frequency resolution is not ideal. Therefore, many experts and scholars have made improvements based on the S-transform, modifying the window function and introducing several window parameters to increase its flexibility. However, there is still room for improvement in time-frequency aggregation, and artificially selected parameter values ​​do not necessarily lead to optimal time-frequency analysis results.

[0003] A common problem with the aforementioned time-frequency analyses is that they fail to overcome the Heisenberg uncertainty principle, resulting in ambiguous results. To accurately describe the time-frequency characteristics of nonstationary signals, recent methods such as the synchronized compression short-time Fourier transform (SST) and synchronized extraction short-time Fourier transform (SET) have been proposed. Both are post-processing techniques based on the STF, estimating the instantaneous frequency from the STF results. The difference lies in that synchronized compression "squeezes" the time-frequency coefficients within a certain frequency range to the instantaneous frequency, while synchronized extraction directly extracts the time-frequency coefficients at the instantaneous frequency as the result of the time-frequency transform, resulting in a higher degree of time-frequency convergence. However, because they are based on the STF, they suffer from inaccurate time-frequency estimates.

[0004] Chinese patent publication number CN108694392A discloses a high-precision synchronous extraction generalized S-transform time-frequency analysis method. This method combines synchronous extraction with the generalized S-transform, allowing for adjustable window length based on signal frequency, resulting in high time-frequency resolution. However, its performance is affected by parameters, making optimal parameters difficult to determine, and there is still room for improvement in time-frequency analysis performance. Summary of the Invention

[0005] The object of the present invention is to provide a time-frequency analysis method for improving S-transform combined with synchronization extraction.

[0006] The technical solution for achieving the purpose of the present invention is as follows: In a first aspect, the present invention provides a time-frequency analysis method for improving S-transform combined with synchronization extraction, comprising the following steps:

[0007] Step 1: Input the non-stationary signal to be analyzed;

[0008] Step 2: Determine the range of three window parameters of the improved window function according to the frequency resolution requirement;

[0009] Step 3: Based on the quantitative calculation of time-frequency aggregation, the optimal selection of the three window parameters is determined;

[0010] Step 4: Perform improved S transform on the signal using the optimized parameters;

[0011] Step 5: Estimate the instantaneous frequency by using the improved S transform selected according to the obtained optimization parameters to obtain a synchronous extraction operator;

[0012] Step 6: Use the synchronous extraction operator to extract the improved S-transform time-frequency spectrum selected by the optimized parameters.

[0013] In a second aspect, the present invention provides a computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the method described in the first aspect when executing the program.

[0014] In a third aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in the first aspect.

[0015] Compared with the prior art, the present invention has the following significant advantages: 1) the present invention adopts an improved window function with three parameters, so that the frequency window width of the window function can be changed along with the concavity of the frequency change curve, which greatly improves the flexibility of the S transform in adapting to different signals; 2) the present invention introduces quantitative calculation of time-frequency aggregation to determine the optimal selection of window function parameters, avoiding the randomness of artificially determining window parameters based on parameter ranges and experience, thereby achieving the optimal overall time-frequency aggregation of the signal; 3) the present invention performs synchronous extraction based on the improved S transform with optimized parameter selection, combining the advantages of both, making the instantaneous frequency estimation more accurate and the time-frequency resolution higher, and improving the fuzzy phenomenon of the time-frequency graph of multi-component instantaneous frequency overlapping signals.

[0016] The present invention is further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 This is a flow chart of the time-frequency analysis method for improving S-transform combined with synchronization extraction according to the present invention.

[0018] Figure 2 1 is a diagram showing the time-frequency analysis results of the improved S-transform embodiment 1.

[0019] Figure 3 This is a diagram of the time-frequency analysis results of synchronous extraction embodiment 1.

[0020] Figure 4 This is a diagram of the time-frequency analysis results of Example 1 of the present invention.

[0021] Figure 5 This is a diagram of the time-frequency analysis results of the improved S-transform embodiment 2.

[0022] Figure 6 This is a diagram of the time-frequency analysis results of synchronous extraction embodiment 2.

[0023] Figure 7 This is a diagram of the time-frequency analysis results of Example 2 of the present invention. DETAILED DESCRIPTION

[0024] Combine Figure 1 As shown, the present invention is a time-frequency analysis method for improving S transform combined with synchronization extraction, comprising the following steps:

[0025] Step 1: Input the non-stationary signal s(t) to be analyzed;

[0026] Step 2: Determine the range of the three window parameters of the improved window function according to the frequency resolution requirements. The specific steps are as follows:

[0027] Step 2-1: Determine the maximum value of the frequency resolution Δf required for actual analysis max and minimum value Δf minAnd the value range R of parameters a, b, c a 、R b 、R c ;

[0028] Step 2-2: Determine the value range set Γ of parameters a, b, and c according to the following inequality: abc :

[0029]

[0030] Among them, f s is the sampling frequency;

[0031] Step 3: Based on the quantitative calculation of time-frequency aggregation, the optimal selection of the three window parameters is determined. The specific steps are as follows:

[0032] Step 3-1: From the value set Γ abc Take a set of a, b, and c values ​​and substitute them into the following formula to calculate the modified S transform MST of the non-stationary signal s(t): (a,b,c) (τ,f):

[0033]

[0034] Where t is the time variable, f is the frequency variable, τ is the time axis displacement parameter, i is the imaginary unit, and σ(f) is the scale factor of the improved window function, which is expressed as follows:

[0035]

[0036] Step 3-2: Calculate the modified S transform MST (a,b,c) The result of (τ,f) energy normalization:

[0037]

[0038] Step 3-3: Quantitatively calculate the time-frequency aggregation TFD of the improved S transform corresponding to this group a, b, and c (a,b,c) :

[0039]

[0040] Step 3-4: Repeat steps 3-1 to 3-3 until all the sets Γ are obtained. abc All combinations of a, b, and c values;

[0041] Step 3-5: Make the time-frequency aggregation TFD (a,b,c) The values ​​of a, b, and c that correspond to the maximum value are used as the optimization parameters of the improved S transform:

[0042]

[0043] Step 4: Use the optimized parameters (a, b, c) opt Perform an improved S transform on the input signal s(t) to obtain the improved S transform MST with optimized parameter selection opt (τ,f), specifically:

[0044]

[0045] Where t is the time variable, f is the frequency variable, τ is the time axis displacement parameter, i is the imaginary unit, and a, b, and c are the optimization parameters obtained in steps 3-5;

[0046] Step 5: Estimate the instantaneous frequency using the improved S transform selected based on the obtained optimization parameters Get the synchronous extraction operator SEO. The specific steps are:

[0047] Step 5-1: Improved S transform MST selected based on optimized parameters opt (τ,f) estimates the instantaneous frequency of the signal s(t)

[0048]

[0049] in, is the symbol of partial derivative;

[0050] Step 5-2: Estimate the instantaneous frequency based on the obtained Calculate the synchronous extraction operator SEO:

[0051]

[0052] Step 6: Use the synchronization extraction operator SEO(τ,f) to select the improved S transform time spectrum MST of the optimization parameters opt (τ,f) is extracted:

[0053]

[0054] Among them, SEMST(τ,f) is the result of improved S transform combined with synchronization extraction.

[0055] The present invention is further described in detail below with reference to two embodiments.

[0056] Example 1

[0057] The simulation signal is the superposition of two line frequency modulation signals s1(t) and s2(t) and a nonlinear signal s3(t). The analytical expressions are:

[0058] s1(t)=sin(2π(60-20t)t)

[0059] s2(t)=sin(2π(250+25t)t)

[0060] s3(t)=sin(2π(150t+3sin(15t)))

[0061] The sampling frequency is 1024 Hz, the sampling time is 1 s, the frequency resolution Δf∈[2,11], and the value range of parameters a, b, and c is R a 、R b 、R c 0 respectively <a<100,0<b<100,-200<c<600。 Figure 2 The time-frequency diagram obtained by improving the S transform is relatively fuzzy overall. Figure 3 is the result of the original synchronous extraction transformation, Figure 4 To improve the analysis results of S transform combined with synchronization extraction, the optimized parameters a=40, b=45, c=10 are used. Figure 2 、 Figure 3 and Figure 4 After adding synchronous extraction, the time-frequency analysis results have better time-frequency aggregation, but the instantaneous frequency estimation of the original synchronous extraction transformation is not accurate enough. The instantaneous frequency estimation error of the present invention is smaller and the time-frequency aggregation is higher.

[0062] Example 2

[0063] The simulation signal is a superposition of a linear frequency modulated signal s1(t) and a nonlinear frequency modulated signal s2(t), but the instantaneous frequencies of the two overlap. Their analytical expressions are:

[0064] s1(t)=sin(2π(100+100t)t)

[0065] s2(t)=sin(2π(300t+4sin(20t)))

[0066] The sampling frequency is 1024 Hz, the sampling time is 1 s, the frequency resolution Δf∈[2,11], and the value range of parameters a, b, and c is R a 、R b 、R c 0 respectively <a<200,0<b<200,-200<c<600。 Figure 5 The time-frequency diagram obtained by improving the S transform is also relatively fuzzy overall. Figure 6 is the result of the original synchronous extraction transformation, Figure 7 To improve the analysis results of S transform combined with synchronization extraction, the optimized parameters a=106, b=150, c=185 are used. Figure 6 and Figure 7The original synchronous extraction transformation has serious fuzzy time-frequency diagrams at the intersection of the instantaneous frequencies of the signal components. The present invention improves this phenomenon and has better time-frequency analysis effects.

Claims

1. A time-frequency analysis method combining improved S-transform and synchronization extraction, characterized in that: The following steps are involved: Step 1: Input the non-stationary signal to be analyzed; Step 2: Determine the range of the three window parameters of the improved window function according to the frequency resolution requirements. The specific steps are as follows: Step 2-1: Determine the maximum value of the frequency resolution Δf required for actual analysis max and minimum value Δf min And the value range R of parameters a, b, c a 、R b 、R c ; Step 2-2: Determine the value range set Γ of parameters a, b, and c according to the following inequality: abc : Among them, f s is the sampling frequency; Step 3: Based on the quantitative calculation of time-frequency aggregation, the optimal selection of the three window parameters is determined. The specific steps are as follows: Step 3-1: From the value set Γ abc Take a set of a, b, and c values ​​and substitute them into the following formula to calculate the modified S transform MST of the non-stationary signal s(t): (a,b,c) (τ,f): Where t is the time variable, f is the frequency variable, τ is the time axis displacement parameter, i is the imaginary unit, and σ(f) is the scale factor of the improved window function, which is expressed as follows: Step 3-2: Calculate the modified S transform MST (a,b,c) The result of (τ,f) energy normalization: Step 3-3: Quantitatively calculate the time-frequency aggregation TFD of the improved S transform corresponding to this group a, b, and c (a,b,c) : Step 3-4: Repeat steps 3-1 to 3-3 until all the sets Γ are obtained. abc All combinations of a, b, and c values; Step 3-5: Make the time-frequency aggregation TFD (a,b,c) The values ​​of a, b, and c that correspond to the maximum value are used as the optimization parameters of the improved S transform: Step 4: Use the optimized parameters (a, b, c) opt Perform an improved S transform on the input signal s(t) to obtain the improved S transform MST with optimized parameter selection opt (τ,f), specifically: Where t is the time variable, f is the frequency variable, τ is the time axis displacement parameter, i is the imaginary unit, and a, b, and c are the optimization parameters obtained in steps 3-5; Step 5: Estimate the instantaneous frequency by using the improved S transform selected according to the obtained optimization parameters to obtain a synchronous extraction operator; Step 6: Use the synchronous extraction operator to extract the improved S-transform time-frequency spectrum selected by the optimized parameters.

2. The time-frequency analysis method of improved S transform combined with synchronization extraction according to claim 1 is characterized in that: Step 5: Estimate the instantaneous frequency using the improved S transform selected based on the obtained optimization parameters. Get the synchronous extraction operator SEO. The specific steps are: Step 5-1: Improved S transform MST selected based on optimized parameters opt (τ,f) estimates the instantaneous frequency of the signal s(t) in, is the symbol of partial derivative; Step 5-2: Estimate the instantaneous frequency based on the obtained Calculate the synchronous extraction operator SEO:

3. The time-frequency analysis method of improved S transform combined with synchronization extraction according to claim 2 is characterized in that: Step 6: Use the synchronization extraction operator SEO(τ,f) to select the improved S transform time spectrum MST of the optimization parameters opt (τ,f) is extracted: Among them, SEMST(τ,f) is the result of improved S transform combined with synchronization extraction.

4. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the method according to any one of claims 1 to 3 are implemented.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method according to any one of claims 1 to 3 are implemented.

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