CN111198357A - S-transform time-frequency analysis method based on adjustable window function - Google Patents

S-transform time-frequency analysis method based on adjustable window function Download PDF

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CN111198357A
CN111198357A CN201911320328.0A CN201911320328A CN111198357A CN 111198357 A CN111198357 A CN 111198357A CN 201911320328 A CN201911320328 A CN 201911320328A CN 111198357 A CN111198357 A CN 111198357A
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window function
frequency
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spectrum
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芮义斌
焦碧璇
谢仁宏
李鹏
高猛
费海凤
于晴
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Nanjing University of Science and Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section

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Abstract

The invention discloses an S-transform time-frequency analysis method based on an adjustable window function, which is used for carrying out time-domain sampling on an input signal to obtain a discrete sequence; performing FFT (fast Fourier transform) on the discrete sequence to obtain a signal frequency spectrum; determining a window length control function and a window function according to the signal frequency spectrum and the resolution requirement; performing FFT on the window function to obtain a window function frequency spectrum; carrying out periodic extension on the signal frequency spectrum, and multiplying the signal frequency spectrum after dimension expansion by a window function frequency spectrum; carrying out inverse Fourier transform on the multiplied result to obtain a time distribution result of a single frequency point; and finishing the calculation of all frequency points, and finally obtaining a two-dimensional matrix time spectrum. The invention can realize high-resolution time-frequency analysis, has moderate calculation amount, is convenient for engineering realization and has good real-time performance.

Description

S-transform time-frequency analysis method based on adjustable window function
Technical Field
The invention relates to a radar signal processing technology, in particular to an S-transform time-frequency analysis method based on an adjustable window function.
Background
The radar echo signals are processed, and information such as the number, the types and the states of the targets can be extracted. However, most of radar echo signals are non-stationary signals and have characteristics such as time-varying property, so that a time-frequency analysis method needs to be researched to determine the change characteristic of frequency along with time. Currently, common time-frequency analysis methods include short-time fourier transform (STFT), Wavelet Transform (WT), wigner-wiler distribution (WVD), S-transform (ST), and the like. The S-transform is proposed by Stockwell on the basis of short-time fourier transform (STFT) and Wavelet Transform (WT). The method adopts a Gaussian window, and sets the window length of the Gaussian window to be inversely proportional to the frequency of a signal to be analyzed, so that the window length is adaptively changed along with the frequency of the signal, and the Gaussian window has better time-frequency analysis performance.
The Chinese patent with the patent application number of CN201710397687.0 and the name of 'synchronous extrusion generalized S transform signal time-frequency decomposition and reconstruction method' integrates four-parameter generalized S transform and synchronous extrusion transform, deduces an inverse transformation formula of the synchronous extrusion generalized S transform, combines the inverse transformation formula with different orders of fractional order Fourier transform, carries out order search by using an angle constraint method, and integrates to obtain an optimal result. The method can obtain a high-precision time-frequency analysis result, but the calculation comprises more variable parameters, the conversion performance is seriously deteriorated when the parameter setting is improper, and meanwhile, the calculation amount is large and the real-time performance is poor.
Disclosure of Invention
The invention aims to provide an S-transform time-frequency analysis method based on an adjustable window function.
The technical solution for realizing the purpose of the invention is as follows: an S-transform time-frequency analysis method based on an adjustable window function comprises the following steps:
step 1: performing time domain sampling on an input signal to obtain a discrete sequence;
step 2: performing FFT (fast Fourier transform) on the discrete sequence to obtain a signal frequency spectrum;
and step 3: determining a window length control function and a window function according to the signal frequency spectrum and the resolution requirement;
and 4, step 4: performing FFT on the window function to obtain a window function frequency spectrum;
and 5: carrying out periodic extension on the signal frequency spectrum, and multiplying the signal frequency spectrum after dimension expansion by a window function frequency spectrum;
step 6: performing inverse Fourier transform on the multiplied result of the step 5 to obtain a time distribution result of a single frequency point;
and 7: and (4) repeating the steps 4-6 until the calculation of all the frequency points is completed, and finally obtaining the time spectrum of the two-dimensional matrix.
Compared with the prior art, the invention has the following remarkable advantages: 1) the window function is adaptively adjusted according to the signal frequency, high-resolution time-frequency analysis can be realized, the calculated amount of the method is moderate, engineering realization is facilitated, and good real-time performance is achieved; 2) the Sigmoid function is introduced into the window function to limit the window length variation range, so that the time-frequency analysis performance at low frequency and high frequency is improved.
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FIG. 1 is a flow chart of the S-transform time-frequency analysis method based on the improved window function of the present invention.
FIG. 2 is a flowchart of an algorithm of the S-transform time-frequency analysis method based on the improved window function.
Fig. 3 is a time-frequency analysis result diagram of the S transform embodiment 1.
FIG. 4 is a time-frequency analysis result diagram in embodiment 1 of the present invention.
Fig. 5 is a time-frequency analysis result diagram of the S transform embodiment 2.
FIG. 6 is a time-frequency analysis result diagram in embodiment 2 of the present invention.
Fig. 7 is a time-frequency analysis result diagram of the S transform embodiment 3.
FIG. 8 is a time-frequency analysis result diagram in embodiment 3 of the present invention.
Detailed Description
The invention will be further described with reference to the accompanying drawings and specific embodiments.
Referring to fig. 1 and 2, the S-transform time-frequency analysis method based on the improved window function includes the following steps:
step 1, performing time domain sampling on an input signal s (t), wherein the sampling frequency is fsThe sampling time interval is
Figure BDA0002326974230000021
The number of sampling points is
Figure BDA0002326974230000022
Wherein t is the signal duration, obtaining a discrete sequence s [ kT ]]，k＝0,1,2,…,N-1；
Step 2, for the discrete sequence s [ kT ]]FFT to obtain signal spectrum
Figure BDA0002326974230000023
n＝0,1,2…,N-1；
Step 3, determining the values of the parameters a, b and c according to the frequency spectrum characteristics, and determining a window length control function and a window function, wherein the specific steps are as follows:
step 3-1, the signal sampling rate is fsGet it
Figure BDA0002326974230000024
Due to the fact that
Figure BDA0002326974230000025
Thus can get
Figure BDA0002326974230000026
Determining the maximum frequency f of a signalmaxMinimum frequency fminAnd the maximum and minimum values Δ f of the width of the frequency domain of the window function allowed by the practical analysismaxAnd Δ fminDetermining the value ranges of a and c by the following inequalities:
Figure BDA0002326974230000031
and 3-2, determining values of a and c in a value range, substituting each parameter value into a window length control function:
Figure BDA0002326974230000032
and 3-3, substituting the window length control function into the Gaussian window function to obtain an improved window function expression:
Figure BDA0002326974230000033
step 4, FFT is carried out on the window function to obtain a window function frequency spectrum
Figure BDA0002326974230000034
The specific formula is as follows:
Figure BDA0002326974230000035
wherein n starts to take a value from 0;
step 5, multiplying the signal frequency spectrum after the dimension expansion by a window function frequency spectrum, and the specific steps are as follows:
step 5-1, making signal frequency spectrum
Figure BDA0002326974230000036
Dimension expansion to obtain signal spectrum
Figure BDA0002326974230000037
Wherein m is 0,1,2,3 … N-1;
step 5-2, the signal frequency spectrum after dimension expansion
Figure BDA0002326974230000038
Multiplying by a window function spectrum G (m, n);
step 6, carrying out inverse Fourier transform on the multiplication result in the step 5-2 to obtain signal time domain information of the frequency point
Figure BDA0002326974230000039
And 7, repeating the step 4, the step 5 and the step 6 until all the frequency points are completely calculated, and obtaining the high-resolution time spectrum. Judging whether all frequency points are calculated or not, wherein the specific mode is to judge whether N is more than or equal to N-1 or not, if not, repeating the steps 4, 5 and 6 after adding 1 to N; and if so, outputting a time-frequency spectrum result.
On one hand, the invention realizes the self-adaptive change of the window length of the window function along with the signal frequency; on the other hand, the frequency window width is controlled to be changed within a certain range by introducing a Sigmoid function, so that the spectrum has higher resolution in the whole time.
The following describes the time-frequency analysis method of the present invention with three signals as examples.
Example 1
The simulation signal is the superposition of four single-frequency sinusoidal signals, the signal frequency is respectively 100Hz, 200Hz, 300Hz and 400Hz, and the analytic formula is as follows:
s1(t)＝ej200πt+ej400πt+ej600πt+ej800πtt∈[0,1]
signal sampling frequency fs1024Hz, so b is 50. The signal has four fixed frequency components, and for a single-frequency signal, only the frequency resolution is considered, and the width of a frequency window is controlled within a small range by taking a to 5 and c to 5. Fig. 4 is a time-frequency spectrum obtained by using an improved S-transform time-frequency analysis method in which a Sigmoid function is used as a window function control function. As can be seen from fig. 4, this method can achieve very good frequency resolution.
Example 2
The simulation signal is the superposition of two Linear Frequency Modulation (LFM) signals, and the analytic formula is as follows:
s(t)＝s1(t)+s2(t)
wherein
Figure BDA0002326974230000041
Signal sampling frequency fs1024Hz, so b is 50. The signal is when t is equal to [0,1 ]]Time fmax＝400，f min0, let the frequency resolution Δ f ∈ [5,6 ]]Therefore, the adjustment factors for improving the S-transform may be taken as a-60 and c-45, respectively. FIG. 6 shows the use of SigThe moid function is an analysis result of the LFM signal by an improved S-transform time-frequency analysis method of the window function control function, and the frequency change of the LFM signal is large. As can be seen from FIG. 6, the method solves the problems of signal divergence and poor energy aggregation at the original S-transform high frequency, and has good time-frequency performance.
Example 3
The simulation signal is a nonlinear frequency modulation signal with sine variation frequency, and the analytic formula is as follows:
s(t)＝ej2π[6cos(10πt)+260t]t∈[0,1]
signal sampling frequency fs1024Hz, so b is 50. The frequency of the signal varies sinusoidally with time, the signal fmax≈450，fminAbout 70, and let the frequency resolution delta f ∈ [10,12 ]]Therefore, the adjustment factors for improving the S-transform may be taken as a-60 and c-90, respectively. FIG. 8 is a time-frequency diagram obtained after the nonlinear frequency-modulated signal is processed by the method of the present invention, and at this time, the time-frequency result can clearly see the change track of the frequency along with the time, and the time-frequency diagram has good time-frequency analysis performance.

Claims (8)

1. An S-transform time-frequency analysis method based on an adjustable window function is characterized by comprising the following steps:
step 1: performing time domain sampling on an input signal to obtain a discrete sequence;
step 2: performing FFT (fast Fourier transform) on the discrete sequence to obtain a signal frequency spectrum;
and step 3: determining a window length control function and a window function according to the signal frequency spectrum and the resolution requirement;
and 4, step 4: performing FFT on the window function to obtain a window function frequency spectrum;
and 5: carrying out periodic extension on the signal frequency spectrum, and multiplying the signal frequency spectrum after dimension expansion by a window function frequency spectrum;
step 6: performing inverse Fourier transform on the multiplied result of the step 5 to obtain a time distribution result of a single frequency point;
and 7: and (4) repeating the steps 4-6 until the calculation of all the frequency points is completed, and finally obtaining the time spectrum of the two-dimensional matrix.
2. The adjustable window function-based S-transform time-frequency analysis method of claim 1, wherein in step 1, time-domain sampling is performed on the input signal S (t) at a sampling frequency fsThe sampling time interval is
Figure FDA0002326974220000011
The number of sampling points is
Figure FDA0002326974220000012
Wherein t is the signal duration, obtaining a discrete sequence s [ kT ]]，k＝0,1,2,…,N-1。
3. The adjustable window function-based S-transform time-frequency analysis method of claim 1, wherein in step 2, S [ kT ] is applied to the discrete sequence]FFT to obtain signal spectrum
Figure FDA0002326974220000013
4. The adjustable window function-based S-transform time-frequency analysis method of claim 1, wherein in step 3, the specific method for determining the window length control function and the window function is as follows:
step 3-1, determining parameters a, b and c according to the signal spectrum and the resolution requirement;
let the signal sampling rate be fsDue to the fact that
Figure FDA0002326974220000014
Thus taking
Figure FDA0002326974220000015
Let the maximum and minimum frequencies of the signal be fmaxAnd fminMaximum and minimum values Δ f of the width of the frequency domain of the window function allowed by the practical analysismaxAnd Δ fminThen, the value ranges of a and c are determined by the following inequalities:
Figure FDA0002326974220000016
and 3-2, determining values of a and c in a value range, substituting each parameter value into a window length control function:
Figure FDA0002326974220000017
and 3-3, substituting the window length control function into the Gaussian window function to obtain an improved window function expression:
Figure FDA0002326974220000021
wherein the content of the first and second substances,
where α (f) is the window function scale factor.
5. The adjustable window function-based S-transform time-frequency analysis method of claim 1, wherein in step 4, the window function spectrum is
Figure FDA0002326974220000022
The specific formula is as follows:
Figure FDA0002326974220000023
wherein N starts to take a value from 0, N is the number of frequency points, and T is the sampling period.
6. The adjustable window function-based S-transform time-frequency analysis method according to claim 1, wherein in step 5, the signal spectrum after dimension expansion is multiplied by a window function spectrum, specifically:
step 5-1, making signal frequency spectrum
Figure FDA0002326974220000024
Dimension expansion to obtain signal spectrum
Figure FDA0002326974220000025
Wherein m is 0,1,2,3 … N-1;
step 5-2, the signal frequency spectrum after dimension expansion
Figure FDA0002326974220000026
Multiplied by the window function spectrum G (m, n).
7. The adjustable window function-based S-transform time-frequency analysis method of claim 1, wherein in step 6, inverse Fourier transform is performed on the multiplication result to obtain time-domain information of the nth frequency point
Figure FDA0002326974220000027
Wherein m is 0,1,2,3 … N-1.
8. The improved S-transform time-frequency analysis method based on the adjustable window function as claimed in claim 1, wherein the specific judgment manner for judging whether all frequency points are calculated in step 7 is: judging whether N is larger than or equal to N-1, if not, adding 1 to N, and repeating the steps 4, 5 and 6; and if so, outputting a time-frequency spectrum result.
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CN113280963A (en) * 2021-05-26 2021-08-20 南通河海大学海洋与近海工程研究院 Real-time cable force identification method based on improved S transformation
CN113295923A (en) * 2021-04-16 2021-08-24 西安交通大学 VFTO signal spectrum analysis method based on improved s-transform
CN115267548A (en) * 2022-07-22 2022-11-01 苏州元启动力科技有限公司 Lithium battery voltage sampling method, system and readable storage medium

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CN113295923A (en) * 2021-04-16 2021-08-24 西安交通大学 VFTO signal spectrum analysis method based on improved s-transform
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CN115267548A (en) * 2022-07-22 2022-11-01 苏州元启动力科技有限公司 Lithium battery voltage sampling method, system and readable storage medium

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