An adaptive window length time-frequency transform method based on minimum information entropy criterion

Abstract

The application provides a minimum information entropy criterion-based adaptive window length time-frequency transform algorithm, comprising: obtaining an input signal sequence, and calculating a correlation function of the signal; summing the correlation function to obtain S; setting multiple thresholds based on S; searching a peak width of the correlation function according to the thresholds to obtain the peak width corresponding to each threshold; taking the peak width corresponding to each threshold as a window length, calculating a time-frequency transform of the signal to obtain a plurality of time-frequency spectrums; calculating information entropy of the plurality of time-frequency spectrums respectively; selecting a minimum value in the information entropy; and taking a time-frequency spectrum corresponding to the minimum value as a time-frequency transform result. The window length can be adaptively adjusted, a time-frequency spectrum graph with better energy focusing performance is obtained, and more accurate extraction of signal components is realized.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of signal processing, and particularly relates to an adaptive window length time-frequency transform method based on a minimum information entropy criterion. BACKGROUND

[0002] The frequency change in a signal carries important information, and the traditional Fourier transform can convert the signal from the time domain to the frequency domain, but it does not have positioning information in the time domain and the frequency domain. The time-frequency transform can obtain the time-frequency spectrum of the signal by windowing the signal to obtain the local characteristics of the signal, but the resolution of the time domain and the frequency domain is mutually restricted, and selecting a suitable window length to consider the resolution of the time domain and the frequency domain is of great significance to the characteristic analysis of the signal.

[0003] In the traditional time-frequency transform method, a fixed window length is generally set in advance to calculate the time-frequency spectrum, and in the case that the window length does not match the signal frequency, it is difficult to obtain a time-frequency spectrum with good energy focusing, which is not conducive to accurate extraction of signal components. SUMMARY

[0004] The present application aims to solve the problems existing in the prior art, to adaptively adjust the window length, to obtain a time-frequency spectrum with good energy focusing, and to provide an adaptive window length time-frequency transform method based on a minimum information entropy criterion.

[0005] In order to achieve the above-mentioned purpose, the present application adopts the following technical scheme: an adaptive window length time-frequency transform method based on a minimum information entropy criterion, comprising:

[0006] Step one: obtaining an input signal sequence, calculating the correlation function of the input signal sequence;

[0007] Step two: summing up the correlation function to obtain , based on Setting a plurality of thresholds, searching the peak width of the correlation function according to the thresholds, and obtaining the peak width corresponding to each threshold;

[0008] Step three: taking the peak width corresponding to each threshold as the window length, calculating the time-frequency transform of the input signal sequence, and obtaining a plurality of time-frequency spectrums;

[0009] Step four: calculating the information entropy of each time-frequency spectrum;

[0010] Step five: selecting the minimum value in the information entropy, and taking the time-frequency spectrum corresponding to the minimum value as the time-frequency transform result.

[0011] Further, the correlation function is:

[0012]

[0013] in, Given the input signal sequence, ,in Integers greater than 0 greater than or equal to 0 and less than or equal to integers, yes right Modulo operation.

[0014] Furthermore, the aforementioned for:

[0015]

[0016] in, For the correlation function, greater than or equal to 0 and less than or equal to Integers.

[0017] Furthermore, the expression for the threshold is:

[0018]

[0019] in , This is the threshold.

[0020] Furthermore, the specific steps for searching the peak width of the relevance function based on the threshold are as follows: searching for a suitable peak width from 1 to N. , making Satisfy the following formula:

[0021]

[0022] in, This represents the peak width corresponding to each threshold.

[0023] Furthermore, the time-frequency transform of the calculated input signal sequence is specifically represented as follows:

[0024]

[0025] in, , , This indicates the floor function. This represents the time spectrum.

[0026] Furthermore, the specific steps for calculating the information entropy of several time-frequency spectra include:

[0027] Step A1: Time spectrum Summation yields The calculation method is as follows:

[0028]

[0029] Step A2: to time-frequency spectrum After normalization, the following is obtained The specific expression is as follows:

[0030] ;

[0031] Step A3: calculate the information entropy of The calculation formula of the information entropy of is as follows:

[0032] .

[0033] Further, in the information entropy , find the index corresponding to the minimum value, and according to the index , find the time-frequency spectrum corresponding to the minimum value from the time-frequency spectrum obtained in step four, and take the time-frequency spectrum corresponding to the minimum value as the final output time-frequency analysis result.

[0034] Beneficial effects: the time domain and frequency domain resolutions of the time-frequency spectrum obtained by time-frequency transformation are mutually restricted, the traditional method adopts a pre-set fixed window length to analyze data, and in the case that the signal parameters are unknown, it is difficult to better realize the focusing of the signal on the time-frequency spectrum. The method adopts a group of peak widths of the signal correlation function as the window length of time-frequency transformation for calculation, and selects the optimal time-frequency transformation window length through the method of calculating the information entropy of the time-frequency spectrum, so that the time-frequency spectrum with good energy focusing characteristics is obtained. Compared with the existing technology, the method can adaptively adjust the window length, obtain the time-frequency spectrum with good energy focusing characteristics, and is helpful for more accurate extraction of signal components. BRIEF DESCRIPTION OF DRAWINGS

[0035] Figure 1 is the flowchart of the present application;

[0036] Figure 2 is the correlation function of the signal in the embodiment of the present application;

[0037] Figure 3 is the time-frequency spectrum corresponding to the first peak width obtained in the embodiment of the present application; ;

[0038] Figure 4 is the time-frequency spectrum corresponding to the second peak width obtained in the embodiment of the present application; ;

[0039] ​Figure 5 The third peak width corresponds to the time-frequency spectrum obtained in the embodiment of the present application . DETAILED DESCRIPTION

[0040] The present application will be further explained in connection with the accompanying drawings.

[0041] As Figure 1 shown, the present application provides an adaptive window length time-frequency transform method based on minimum information entropy criterion, comprising:

[0042] Step one: obtaining an input signal sequence, calculating the correlation function of the input signal sequence.

[0043] Step two: summing the correlation function to obtain , based on setting multiple thresholds, searching the peak width of the correlation function according to the thresholds, obtaining the peak width corresponding to each threshold.

[0044] Step three: taking the peak width corresponding to each threshold as the window length, calculating the time-frequency transform of the input signal sequence, obtaining several time-frequency spectrums.

[0045] Step four: calculating the information entropy of the several time-frequency spectrums respectively.

[0046] Step five: selecting the minimum value in the information entropy, taking the time-frequency spectrum corresponding to the minimum value as the time-frequency transform result.

[0047] In step one, an input signal sequence is obtained, wherein is an integer greater than 0. The correlation function of the input signal sequence is calculated , wherein is an integer greater than or equal to 0 and less than or equal to . The calculation formula of the correlation function is:

[0048]

[0049] wherein, is the modulo operation on .

[0050] In step two, the correlation function in step one is summed to obtain , based on setting thresholds , wherein is an integer greater than 0, Threshold The expression is Wherein According to the threshold, the peak width of the correlation function is searched, and the peak width corresponding to each threshold is obtained And the peak width corresponding to each threshold The following formula must be satisfied:

[0051] .

[0052] In step three, the peak width corresponding to multiple thresholds As the window length, the time-frequency transform is performed on the input signal sequence to obtain the time-frequency spectrum The formula of the time-frequency spectrum

[0053]

[0054] Wherein, , , Indicates the floor operation.

[0055] In step four, the sum of the time-frequency spectrum Is obtained The calculation method is:

[0056]

[0057] Several time-frequency spectra Are normalized respectively to obtain several , The specific expression is:

[0058] .

[0059] The information entropy Of several Is calculated, and the calculation formula of the information entropy

[0060] .

[0061] In step five, among the several information entropies The index Corresponding to the minimum value is found, and the time-frequency spectrum Corresponding to the minimum value is found from the several time-frequency spectra Obtained in step four according to the index The time-frequency spectrum Corresponding to the minimum value is taken as the final output time-frequency analysis result.

[0062] In a specific embodiment, the input signal sequence​​ For the linear frequency modulation signal, the duration is 2 seconds, the frequency varies from 100 Hz to 200 Hz in the duration, the sampling frequency is 8000 Hz, and the correlation function is calculated as shown in Figure 2 .

[0063] Set thresholds , wherein , the peak width corresponding to each threshold is calculated . Set , and obtain , and further obtain .

[0064] Then, the peak width corresponding to each threshold is taken as the window length, the time-frequency transform of the input signal sequence is calculated, and three time-frequency spectrums are obtained, as shown in Figure 3 , Figure 4 , Figure 5 .

[0065] Then, the information entropy of the three time-frequency spectrums is calculated, the minimum value of the information entropy of the three time-frequency spectrums is selected, and finally the minimum value is 7.5620, and the index corresponding to the time-frequency spectrum corresponding to the minimum value is , that is, the time-frequency analysis result is taken as the final output.

[0066] The resolution of the time domain and the frequency domain of the time-frequency spectrum obtained by time-frequency transform is mutually restricted, and the traditional method adopts a pre-set fixed window length to analyze data, and in the case of not knowing the signal parameters, it is difficult to better realize the focusing of the signal on the time-frequency spectrum. The present application calculates by taking a group of peak widths of the signal autocorrelation function as the window length of time-frequency transform, and selects the optimal time-frequency transform window length by calculating the information entropy of the time-frequency spectrum, so as to obtain a time-frequency spectrum with good energy focusing characteristics. Thus, in the case of large amount of signal data or real-time observation of the time-frequency spectrum, more accurate extraction of signal components is realized.

[0067] The above only describes the preferred embodiments of the present application, and it should be noted that for ordinary skilled in the art, without departing from the principles of the present application, a number of improvements and refinements can be made, and these improvements and refinements should also be considered as the protection scope of the present application.​

Claims

1. An adaptive window-length time-frequency transform method based on the minimum information entropy criterion, used to adaptively adjust the window length to obtain a time-frequency spectrum with optimized energy focusing, characterized in that, include: Step 1: Obtain the input signal sequence and calculate the correlation function of the input signal sequence; the signal sequence is a linear frequency modulated signal. The correlation function is: in, Given the input signal sequence, ,in Integers greater than 0 greater than or equal to 0 and less than or equal to integers, yes right Modulo operation; Step 2: Sum the correlation functions to obtain ,based on Multiple thresholds are set, and the peak width of the correlation function is searched according to the thresholds to obtain the peak width corresponding to each threshold; The for: in, For the correlation function, greater than or equal to 0 and less than or equal to Integers; The expression for the threshold is: in , For threshold; The specific steps for searching the peak width of the correlation function based on the threshold are as follows: search for a suitable peak width from 1 to N. , making Satisfy the following formula: in, The peak width corresponding to each threshold; Step 3: Using the peak width corresponding to each threshold as the window length, calculate the time-frequency transformation of the input signal sequence to obtain several time-frequency spectra; Step 4: Calculate the information entropy of the aforementioned time-frequency spectra respectively; Step 5: Select the minimum value in the information entropy, and use the time spectrum corresponding to the minimum value as the time-frequency transformation result.

2. The adaptive window length time-frequency transform method based on the minimum information entropy criterion according to claim 1, characterized in that, The time-frequency transform of the calculated input signal sequence is specifically represented as follows: in, , , This indicates the floor function. This represents the time spectrum.

3. The adaptive window length time-frequency transform method based on the minimum information entropy criterion according to claim 2, characterized in that, The specific steps for calculating the information entropy of several time-frequency spectra include: Step A1: Time spectrum Summation yields The calculation method is as follows: Step A2: Time spectrum After normalization, we get The specific representation is as follows: ； Step A3: Calculation Information entropy Information entropy The calculation formula is: 。 4. The adaptive window length time-frequency transform method based on the minimum information entropy criterion as described in claim 3, characterized in that, The specific steps of step five are as follows: In information entropy Find the index of the minimum value in the table. and indexed by subscript The time spectrum obtained from step four Find the time spectrum corresponding to the minimum value The time spectrum corresponding to the minimum value The time-frequency analysis results are the final output.

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