CN112505640A - Time-frequency analysis method for expanded B distribution pulse signal based on parameter self-adaption - Google Patents

Time-frequency analysis method for expanded B distribution pulse signal based on parameter self-adaption Download PDF

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CN112505640A
CN112505640A CN202011258116.7A CN202011258116A CN112505640A CN 112505640 A CN112505640 A CN 112505640A CN 202011258116 A CN202011258116 A CN 202011258116A CN 112505640 A CN112505640 A CN 112505640A
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CN112505640B (en
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方世良
姚帅
方衍
安文威
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Nanjing Shihai Acoustics Technology Co ltd
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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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    • 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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Abstract

The invention discloses a parameter self-adaptive extended B distribution pulse signal time-frequency analysis method, which comprises the steps of firstly obtaining multi-component underwater sound or radar pulse signal data to be processed to generate a fuzzy function, then detecting the radial angle and the radial length of a self-item signal in a fuzzy domain to generate an extended modified B distribution kernel function, filtering the fuzzy function, and finally transforming a filtered signal to obtain a time-frequency analysis result. The method is based on the B distribution kernel function of the extended modification, is simple to realize, can set parameters of the kernel function in a self-adaptive manner according to signals, realizes better matching between the kernel function and underwater sound or radar pulse signals to be processed, and is suitable for real-time engineering application occasions.

Description

Time-frequency analysis method for expanded B distribution pulse signal based on parameter self-adaption
Technical Field
The invention relates to a time-frequency analysis method for an expanded B distribution pulse signal based on parameter self-adaptation, in particular to a time-frequency analysis method for an expanded B distribution underwater sound or radar pulse signal based on parameter self-adaptation, belonging to the technical field of signal processing.
Background
Time-frequency analysis has important significance in array signal processing applications such as radar, sonar, acoustics, voice, wireless communication and the like, and plays an extremely important role in underwater sound and electronic reconnaissance processing. The existing time frequency analysis method mainly comprises a linear time frequency analysis method and a quadratic time frequency analysis method.
The most classical linear time-frequency analysis method is short-time Fourier transform, the method is simple to implement, the operand is small, for multi-component underwater sound or radar pulse signals, the time-frequency analysis result does not have the problem of cross-term interference, the time-varying characteristics of the multi-component underwater sound or radar pulse signals can be displayed without distortion, but the time-frequency resolution cannot be improved simultaneously due to the fact that the duration time and the frequency variation range of the underwater sound or radar pulse signals reach thousands of times, and the time-frequency resolution of the short-time Fourier transform is limited by the shape and the width of a window function, so that the time-frequency resolution cannot be adapted to time-frequency analysis of the underwater sound pulse signals with extremely wide time and frequency variation ranges.
At present, scholars at home and abroad propose a plurality of quadratic time-frequency analysis methods, such as a Virgener-Viley distribution analysis method, which can obtain the best time-frequency analysis effect of instantaneous frequency for time-varying linear frequency modulation pulse signals, but for multi-component linear frequency modulation pulse signals or non-linear frequency modulation pulse signals, the method has a serious cross term problem among instantaneous frequency curves when analyzing the time-frequency characteristics of the multi-component signals; the time-frequency analysis method based on the B distribution kernel function and the modified B distribution kernel function can reduce the influence of cross terms among the instantaneous frequency curves of the multi-component pulse signals, but the parameters of the method can not self-adaptively adjust the time-frequency parameters according to the multi-component pulse signals to be processed, which can cause that the obtained time-frequency distribution is not optimal for inhibiting the cross terms.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems and the defects in the prior art, the invention provides a time-frequency analysis method for an expanded B distribution pulse signal based on parameter self-adaption. The method is based on the B distribution kernel function of the extension modification, and generates parameters according to underwater sound or radar pulse signal data to be processed so as to generate the kernel function for time-frequency analysis. Compared with other existing quadratic time-frequency analysis methods, the algorithm has stronger self-adaption performance, and has better time-frequency distribution, time-frequency resolution and interference suppression performance.
The technical scheme is as follows: a time-frequency analysis method for an expanded B distribution pulse signal based on parameter self-adaptation comprises the following steps:
step 1: acquiring a sampling data sequence s (N) of a multi-component underwater sound or radar pulse signal to be processed, wherein N is 0,1, …, N-1: receiving real-time multi-component underwater sound or radar pulse signal acquisition data of N sampling points as a sampling data sequence s (N) to be processed, wherein N is 0,1, … and N-1; or extracting the multi-component underwater sound or radar pulse signals of N signal sampling points received from a certain moment from a memory as a data sequence s (N) to be processed, wherein N is 0,1, …, N-1. And N is the number of sampling points corresponding to the time sequence of the multi-component underwater sound or radar pulse signal to be processed, the value is an integer power of 2, and N is required to be more than or equal to 8.
Step 2: calculating fuzzy function A of multi-component underwater sound or radar pulse signal sampling data sequence s (n) to be processedz(α, β), the method is as follows:
firstly, calculating the discrete Fourier transform S (k) of a sampling data sequence s (n) of a multi-component underwater sound or radar pulse signal to be processed, namely:
Figure BDA0002773704680000021
where k is the discrete frequency index of S (k).
Then, using s (k) to generate a fourier version z (l) of the discrete analytic signal z (n) of s (n), i.e.:
Figure BDA0002773704680000022
where l is the discrete frequency index of Z (l).
Performing discrete inverse Fourier transform on Z (l) to obtain a discrete analytic signal z (n), namely:
Figure BDA0002773704680000023
then calculating the autocorrelation function K of the analytic function z (n)z(n, β), i.e.:
Figure BDA0002773704680000024
where beta represents the discrete autocorrelation delay.
Finally calculating the autocorrelation function KzDiscrete Fourier transform of (n, beta) to obtain a fuzzy function Az(α, β), i.e.:
Figure BDA0002773704680000025
where alpha represents the discrete frequency shift.
And step 3: calculating a fuzzy function AzRadon transform of (alpha, beta) R (D)a,θb) The method comprises the following steps:
Figure BDA0002773704680000031
wherein, thetabRepresents a discrete radial angle of Radon transform, and takes the value of thetab＝-90°+0.5b，b＝0,1...,360，DaDiscrete radial distance representing Radon transform, taken as
Figure BDA0002773704680000032
[·]Represents the rounding function and δ (·) represents the impulse function.
And 4, step 4: based on Radon transform R (D)a,θb) Detecting the self-term signal and estimating the radial angle phi of the self-termpAnd radial length RDpThe method comprises the following steps:
first, the term R (0, theta) of the zero crossing point is searched for according to the following formulab) Number k corresponding to the middle peak valuepNamely:
kp＝findpeak[R(0,θb)]formula (7)
Wherein findpeak [. The]Indicating the sequence number corresponding to the search peak. Setting a threshold value RthRemoving peaks smaller than the threshold value to obtain k as 200pP1. Self-term signal R (0, theta)b) Radial angle phi ofpCan be calculated from the following formula:
Figure BDA0002773704680000036
therefore, in the fuzzy domain, the line l of the self termpThe equation of (c) can be expressed as:
Figure BDA0002773704680000033
wherein xt∈[0,N-1]，yt∈[0,N-1]；
The convolution mask H is defined as:
Figure BDA0002773704680000034
define E (x, y) as a three-dimensional matrix centered around point (x, y) in the blur domain, i.e.:
Figure BDA0002773704680000035
wherein x belongs to [1, N-2], y belongs to [1, N-2], and | is absolute value function.
Then in the fuzzy domain to
Figure BDA0002773704680000041
As a starting point along a straight line lpThe convolution mask H is moved upwards and,finding the farthest point (x) satisfying the following formulap,yp)：
Figure BDA0002773704680000042
Figure BDA0002773704680000043
The method represents two-dimensional convolution operation, and the operation process is divided into two steps: firstly, taking Hadamard products of two 3-order matrixes, and then summing all elements of the matrixes; ζ is a scaling factor set to 0.2.
Radial length RDpP1, P can be obtained by the following formula:
Figure BDA0002773704680000044
and 5: self-term radial angle phi of signal obtained according to estimationpAnd radial length RDpAdaptively generating an extended B distribution kernel function g (α, β) as follows:
first, a delay parameter ξ is calculated according to the following equation:
ξ＝max{|RDp×cos(φp) 1,. P } formula (14)
Where max (-) is the function of the maximum element;
the doppler parameter epsilon is calculated according to:
ε＝max{|RDp×sin(φp) 1,. P } formula (15)
The extended B distribution kernel function g (α, β) is then generated using the parameters ξ, ε, i.e.:
Figure BDA0002773704680000045
wherein Γ () is a gamma function, | · | represents a modulus value.
Step 6: adaptively generating an extended B distribution kernel function g (alpha, beta) and a signal blurring function AzMultiplication of (. alpha.,. beta.) byObtaining a fuzzy domain filtered signal AF(α, β), the formula is as follows:
AF(α,β)＝Az(α, β) · g (α, β), α ═ 0,1, …, N-1, β ═ 0,1, …, N-1, formula (17).
And 7: the blurred domain filtered signal AFAnd (alpha, beta) transforming to a time-frequency domain to obtain a time-frequency analysis result T (n, m) of the underwater sound pulse signal, namely:
Figure BDA0002773704680000051
where n represents the discrete sampling instant and m represents the discrete sampling frequency.
Further, in step 2 of the method, calculating discrete fourier transform s (k) of a multi-component underwater sound or radar pulse signal sampling data sequence s (n) to be processed is obtained by using fast fourier transform; calculating the discrete inverse Fourier transform z (n) of Z (l) by inverse fast Fourier transform; calculating an autocorrelation function KzDiscrete Fourier transform of (n, beta) to obtain a fuzzy function AFThe (alpha, beta) is implemented using a fast fourier transform.
Further, in step 7 of the method of the present invention, the blurred field filtered signal a is processedFAnd (alpha, beta) transforming to a time-frequency domain to obtain a time-frequency analysis result T (n, m) of the signal, wherein the time-frequency analysis result T (n, m) is obtained by adopting fast Fourier transform.
The method comprises the steps of firstly obtaining multi-component underwater sound or radar pulse signal data to be processed to generate a fuzzy function, then detecting the radial angle and the radial length of a self-item signal in a fuzzy domain to generate an expansion modification B distribution kernel function, filtering the fuzzy function, and finally transforming a filtering signal to obtain a time-frequency analysis result.
Has the advantages that: compared with the prior art, the technical scheme of the invention has the following beneficial technical effects:
the invention adopts a self-adaptive parameter setting method, and the time-frequency parameters can realize better matching of multi-component underwater sound or radar pulse signals. Compared with other existing quadratic time-frequency analysis methods, the method can better inhibit cross interference terms generated among instantaneous frequencies for multi-component underwater sound pulse signals on the premise of keeping the instantaneous frequency self terms.
Compared with the element expansion B distribution time-frequency analysis method, the method has the advantages that the added operation amount is small, and the multi-component underwater sound or radar pulse signal to be analyzed has better self-adaptability of the time-frequency parameter.
The processing procedure of the time frequency analysis kernel function parameter used by the method of the invention which is self-adaptively adjusted according to the signal can be applied to other quadratic time frequency analysis methods.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a diagram showing a fuzzy function distribution of multi-component underwater sound pulse signal data to be processed in example 1;
FIG. 3 shows a Radon transform profile of the blur function in example 1;
FIG. 4 is a diagram showing an adaptively generated extended B-distribution kernel function distribution map in example 1;
FIG. 5 is a time-frequency distribution diagram of the underwater acoustic pulse signals obtained by the processing in example 1;
FIG. 6 is a diagram showing a fuzzy function distribution of multi-component underwater sound pulse signal data to be processed in example 2;
fig. 7 shows the distribution of the Radon transform of the blur function in example 2.
FIG. 8 is a diagram showing an adaptively generated extended B-distribution kernel function distribution in example 2;
fig. 9 is a time-frequency distribution diagram of the underwater acoustic pulse signal processed in embodiment 2.
Detailed Description
The present invention is further illustrated by the following examples, which are intended to be purely exemplary and are not intended to limit the scope of the invention, as various equivalent modifications of the invention will occur to those skilled in the art upon reading the present disclosure and fall within the scope of the appended claims.
The time-frequency analysis method of the expanded B distribution pulse signal based on parameter self-adaption comprises the following steps:
step 1: acquiring a sampling data sequence s (N) of a multi-component underwater sound or radar pulse signal to be processed, wherein N is 0,1, …, N-1: receiving real-time multi-component underwater sound or radar pulse signal acquisition data of N sampling points as a sampling data sequence s (N) to be processed, wherein N is 0,1, … and N-1; or extracting the multi-component underwater sound or radar pulse signals of N signal sampling points received from a certain moment from a memory as a data sequence s (N) to be processed, wherein N is 0,1, …, N-1. And N is the number of sampling points corresponding to the time sequence of the multi-component underwater sound or radar pulse signal to be processed, the value is an integer power of 2, and N is required to be more than or equal to 8.
Step 2: calculating fuzzy function A of multi-component underwater sound or radar pulse signal sampling data sequence s (n) to be processedz(α, β), the method is as follows:
firstly, calculating the discrete Fourier transform S (k) of a sampling data sequence s (n) of a multi-component underwater sound or radar pulse signal to be processed, namely:
Figure BDA0002773704680000061
where k is the discrete frequency index of S (k).
Then, using s (k) to generate a fourier version z (l) of the discrete analytic signal z (n) of s (n), i.e.:
Figure BDA0002773704680000062
where l is the discrete frequency index of Z (l).
Performing discrete inverse Fourier transform on Z (l) to obtain a discrete analytic signal z (n), namely:
Figure BDA0002773704680000071
then calculating the autocorrelation function K of the analytic function z (n)z(n, β), i.e.:
Figure BDA0002773704680000072
where beta represents the discrete autocorrelation delay.
Finally calculating the autocorrelation function KzDiscrete Fourier transform of (n, beta) to obtain a fuzzy function Az(α, β), i.e.:
Figure BDA0002773704680000073
where alpha represents the discrete frequency shift.
And step 3: calculating a fuzzy function AzRadon transform of (alpha, beta) R (D)a,θb) The method comprises the following steps:
Figure BDA0002773704680000074
wherein, thetabRepresents a discrete radial angle of Radon transform, and takes the value of thetab＝-90°+0.5b，b＝0,1...,360，DaDiscrete radial distance representing Radon transform, taken as
Figure BDA0002773704680000075
[·]Represents the rounding function and δ (·) represents the impulse function.
And 4, step 4: based on Radon transform R (D)a,θb) Detecting the self-term signal and estimating the radial angle phi of the self-termpAnd radial length RDpThe method comprises the following steps:
first, the term R (0, theta) of the zero crossing point is searched for according to the following formulab) Number k corresponding to the middle peak valuepNamely:
kp＝findpeak[R(0,θb)]formula (7)
Wherein findpeak [. The]Indicating the sequence number corresponding to the search peak. Setting a threshold value RthRemoving peaks smaller than the threshold value to obtain k as 200pP1. Self-term signal R (0, theta)b) Radial angle phi ofpCan be calculated from the following formula:
Figure BDA0002773704680000076
therefore, in the fuzzy domain, the line l of the self termpThe equation of (c) can be expressed as:
Figure BDA0002773704680000081
wherein xt∈[0,N-1]，yt∈[0,N-1]；
The convolution mask H is defined as:
Figure BDA0002773704680000082
define E (x, y) as a three-dimensional matrix centered around point (x, y) in the blur domain, i.e.:
Figure BDA0002773704680000083
wherein x belongs to [1, N-2], y belongs to [1, N-2], and | is absolute value function.
Then in the fuzzy domain to
Figure BDA0002773704680000084
As a starting point along a straight line lpMoving convolution mask H upward, find the farthest point (x) satisfying the following equationp,yp)：
Figure BDA0002773704680000085
Figure BDA0002773704680000086
The method represents two-dimensional convolution operation, and the operation process is divided into two steps:firstly, taking Hadamard products of two 3-order matrixes, and then summing all elements of the matrixes; ζ is a scaling factor set to 0.2.
Radial length RDpP1, P can be obtained by the following formula:
Figure BDA0002773704680000087
and 5: self-term radial angle phi of signal obtained according to estimationpAnd radial length RDpAdaptively generating an extended B distribution kernel function g (α, β) as follows:
first, a delay parameter ξ is calculated according to the following equation:
ξ＝max{|RDp×cos(φp) 1,. P } formula (14)
Where max (-) is the function of the maximum element;
the doppler parameter epsilon is calculated according to:
ε＝max{|RDp×sin(φp) 1,. P } formula (15)
The extended B distribution kernel function g (α, β) is then generated using the parameters ξ, ε, i.e.:
Figure BDA0002773704680000091
wherein Γ () is a gamma function, | · | represents a modulus value.
Step 6: adaptively generating an extended B distribution kernel function g (alpha, beta) and a signal blurring function AzMultiplying (alpha, beta) to obtain a fuzzy domain filtered signal AF(α, β), the formula is as follows:
AF(α,β)＝Az(α, β) · g (α, β), α ═ 0,1, …, N-1, β ═ 0,1, …, N-1, formula (17).
And 7: the blurred domain filtered signal AFAnd (alpha, beta) transforming to a time-frequency domain to obtain a time-frequency analysis result T (n, m) of the underwater sound pulse signal, namely:
Figure BDA0002773704680000092
where n represents the discrete sampling instant and m represents the discrete sampling frequency.
The method comprises the steps of firstly obtaining multi-component underwater sound or radar pulse signal data to be processed to generate a fuzzy function, then detecting the radial angle and the radial length of a self-item signal in a fuzzy domain to generate an expansion modification B distribution kernel function, filtering the fuzzy function, and finally transforming a filtering signal to obtain a time-frequency analysis result.
In the embodiment of the invention, the multi-component underwater sound pulse signal to be processed consists of two linear frequency modulation signals, and the model is as follows:
s(n)＝s(n1)+s(n2)
Figure BDA0002773704680000093
Figure BDA0002773704680000094
where a is the multi-component hydroacoustic pulse signal amplitude to be processed,
Figure BDA0002773704680000095
for the initial phase of the signal to be processed, N is the number of sampling points of the chirp signal, flIs an initial frequency, fsMu is the modulation rate for the sampling frequency.
Example 1
The parameters of the simulated multi-component underwater sound pulse signal are respectively set as follows: signal amplitude a 1, initial phase
Figure BDA0002773704680000096
2048 samples N, signal initial frequency fl400Hz, sampling frequency fsThe modulation rates are 4000Hz respectively: 0Hz/s and 781.25Hz/s, the pulse width length is 0.256s, and the received signal length is 0.512 s.
Firstly, the methodCalculating fuzzy function A of multi-component underwater sound pulse signal data s (n) to be processedz(α, β), the calculation results are shown in fig. 2.
Then, a fuzzy function A is calculatedzRadon transform of (alpha, beta) R (D)a,θb) The calculation results are shown in fig. 3.
Then, the radial angle and the radial length of the self-term are estimated to obtain
Figure BDA0002773704680000101
Then, a delay parameter ξ 0.0533 and a doppler parameter ε 0.2742 are obtained. The extended B distribution kernel function g (α, β) is generated using the parameters ξ, ε, as shown in fig. 4.
Then, the adaptively generated extended B distribution kernel function g (alpha, beta) and the signal fuzzy function A are combinedzMultiplying (alpha, beta) to obtain a fuzzy domain filtered signal AF(α, β), and finally filtering the blurred domain signal aFAnd (alpha, beta) transforming to a time-frequency domain to obtain a time-frequency analysis result T (n, m) of the multi-component underwater sound pulse signal, as shown in FIG. 5.
Example 2
The parameters of the simulated multi-component underwater sound pulse signal are respectively set as follows: signal amplitude a 1, initial phase
Figure BDA0002773704680000103
2048 samples N, signal initial frequency fl400Hz, sampling frequency fsThe modulation rates are 4000Hz respectively: 0Hz/s and-781.25 Hz/s, the pulse width length is 0.256s, and the received signal length is 0.512 s.
Firstly, calculating a fuzzy function A of multi-component underwater sound pulse signal data s (n) to be processedz(α, β), the calculation results are shown in fig. 6.
Then, a fuzzy function A is calculatedzRadon transform of (alpha, beta) R (D)a,θb) The calculation results are shown in fig. 7.
Then, the radial angle and the radial length of the self-term are estimated to obtain
Figure BDA0002773704680000102
Then, a delay parameter ξ 0.0399 and a doppler parameter ε 0.2748 are obtained. The extended B distribution kernel function g (α, β) is generated using the parameters ξ, ε, as shown in fig. 8.
Then, the adaptively generated extended B distribution kernel function g (alpha, beta) and the signal fuzzy function A are combinedzMultiplying (alpha, beta) to obtain a fuzzy domain filtered signal AF(α, β), and finally filtering the blurred domain signal aFAnd (alpha, beta) transforming to a time-frequency domain to obtain a time-frequency analysis result T (n, m) of the multi-component underwater sound pulse signal, as shown in FIG. 9.

Claims (10)

1. A time-frequency analysis method for an expanded B distribution pulse signal based on parameter self-adaptation is characterized by comprising the following steps:
step 1: acquiring a sampling data sequence s (N) of a multi-component underwater sound or radar pulse signal to be processed, wherein N is 0,1, … and N-1; the N is the number of sampling points corresponding to the time sequence of the multi-component underwater sound or radar pulse signal to be processed, the value is an integer power of 2, and the N is more than or equal to 8;
step 2: calculating fuzzy function A of multi-component underwater sound or radar pulse signal sampling data sequence s (n) to be processedz(α,β)；
And step 3: calculating a fuzzy function AzRadon transform of (alpha, beta) R (D)a,θb)；
And 4, step 4: based on Radon transform R (D)a,θb) Detecting the self-term signal and estimating the radial angle phi of the self-termpAnd radial length RDp；
And 5: self-term radial angle phi of signal obtained according to estimationpAnd radial length RDpAdaptively generating an extended B distribution kernel function g (α, β);
step 6: adaptively generating an extended B distribution kernel function g (alpha, beta) and a signal blurring function AzMultiplying (alpha, beta) to obtain a fuzzy domain filtered signal AF(α,β)；
And 7: the blurred domain filtered signal AFTime-frequency analysis node for converting (alpha, beta) to time-frequency domain to obtain underwater sound pulse signalFruit T (n, m).
2. The time-frequency analysis method for the expanded B distribution pulse signal based on the parameter self-adaptation as claimed in claim 1, wherein in the step 2, the discrete Fourier transform S (k) for calculating the sampling data sequence s (n) of the multi-component underwater sound or radar pulse signal to be processed is obtained by fast Fourier transform; calculating the discrete inverse Fourier transform z (n) of Z (l) by inverse fast Fourier transform; calculating an autocorrelation function KzDiscrete Fourier transform of (n, beta) to obtain a fuzzy function AFThe (alpha, beta) is implemented using a fast fourier transform.
3. The method for time-frequency analysis of extended B-distribution pulse signals based on parameter adaptation as claimed in claim 1, wherein in step 7, the fuzzy domain filtered signal A is filteredFAnd (alpha, beta) transforming to a time-frequency domain to obtain a time-frequency analysis result T (n, m) of the signal, wherein the time-frequency analysis result T (n, m) is obtained by adopting fast Fourier transform.
4. The time-frequency analysis method for the expanded B distribution pulse signal based on the parameter self-adaptation as claimed in claim 1, wherein in the step 2, the fuzzy function A of the multi-component sampling data sequence s (n) of the underwater acoustic or radar pulse signal to be processed is calculatedz(α, β), the method is as follows:
firstly, calculating the discrete Fourier transform S (k) of a sampling data sequence s (n) of a multi-component underwater sound or radar pulse signal to be processed, namely:
Figure FDA0002773704670000021
wherein k is the discrete frequency index of S (k);
then, using s (k) to generate a fourier version z (l) of the discrete analytic signal z (n) of s (n), i.e.:
Figure FDA0002773704670000022
wherein l is the discrete frequency index of Z (l);
performing discrete inverse Fourier transform on Z (l) to obtain a discrete analytic signal z (n), namely:
Figure FDA0002773704670000023
then calculating the autocorrelation function K of the analytic function z (n)z(n, β), i.e.:
Figure FDA0002773704670000024
wherein β represents a discrete autocorrelation delay;
finally calculating the autocorrelation function KzDiscrete Fourier transform of (n, beta) to obtain a fuzzy function Az(α, β), i.e.:
Figure FDA0002773704670000025
where alpha represents the discrete frequency shift.
5. The method as claimed in claim 1, wherein in step 3, a fuzzy function A is calculatedzRadon transform of (alpha, beta) R (D)a,θb) The method comprises the following steps:
Figure FDA0002773704670000031
wherein, thetabRepresents a discrete radial angle of Radon transform, and takes the value of thetab＝-90°+0.5b，b＝0,1...,360，DaDiscrete radial distance representing Radon transform, taken as
Figure FDA0002773704670000037
[·]Represents the rounding function and δ (·) represents the impulse function.
6. The time-frequency analysis method for the expanded B distribution pulse signal based on the parameter self-adaptation as claimed in claim 1, wherein in the step 4, R (D) is transformed based on Radona,θb) Detecting the self-term signal and estimating the radial angle phi of the self-termpAnd radial length RDpThe method comprises the following steps:
first, the term R (0, theta) of the zero crossing point is searched for according to the following formulab) Number k corresponding to the middle peak valuepNamely:
kp＝findpeak[R(0,θb)]formula (7)
Wherein findpeak [. The]Indicating the sequence number corresponding to the search peak. Setting a threshold value RthRemoving peaks smaller than the threshold value to obtain k as 200pP1., P; self-term signal R (0, theta)b) Radial angle phi ofpCan be calculated from the following formula:
Figure FDA0002773704670000033
therefore, in the fuzzy domain, the line l of the self termpThe equation of (c) can be expressed as:
Figure FDA0002773704670000034
wherein xt∈[0,N-1]，yt∈[0,N-1]；
The convolution mask H is defined as:
Figure FDA0002773704670000035
define E (x, y) as a three-dimensional matrix centered around point (x, y) in the blur domain, i.e.:
Figure FDA0002773704670000036
wherein x belongs to [1, N-2], y belongs to [1, N-2], and | is absolute value function;
then in the fuzzy domain to
Figure FDA0002773704670000041
As a starting point along a straight line lpMoving convolution mask H upward, find the farthest point (x) satisfying the following equationp,yp)：
Figure FDA0002773704670000042
Figure FDA0002773704670000043
The method represents two-dimensional convolution operation, and the operation process is divided into two steps: firstly, taking Hadamard products of two 3-order matrixes, and then summing all elements of the matrixes; ζ is a scaling factor set to 0.2;
radial length RDpP1, P can be obtained by the following formula:
Figure FDA0002773704670000044
7. the time-frequency analysis method for expanded B distribution pulse signals based on parameter adaptation as claimed in claim 1, wherein in step 5, the radial angle φ of the signal term obtained according to estimationpAnd radial length RDpAdaptively generating an extended B distribution kernel function g (α, β) as follows:
first, a delay parameter ξ is calculated according to the following equation:
ξ＝max{|RDp×cos(φp) 1,. P } formula (14)
Where max (-) is the function of the maximum element;
the doppler parameter epsilon is calculated according to:
ε＝max{|RDp×sin(φp) 1,. P } formula (15)
The extended B distribution kernel function g (α, β) is then generated using the parameters ξ, ε, i.e.:
Figure FDA0002773704670000045
wherein Γ () is a gamma function, | · | represents a modulus value.
8. The time-frequency analysis method for extended B distribution pulse signals based on parameter adaptation as claimed in claim 1, wherein in step 6, the adaptively generated extended B distribution kernel function g (α, β) and the signal fuzzy function A are appliedzMultiplying (alpha, beta) to obtain a fuzzy domain filtered signal AF(α, β), the formula is as follows:
AF(α,β)＝Az(α, β) · g (α, β), α ═ 0,1, …, N-1, β ═ 0,1, …, N-1, formula (17).
9. The method for time-frequency analysis of extended B-distribution pulse signals based on parameter adaptation as claimed in claim 1, wherein in step 7, the fuzzy domain filtered signal A is filteredFAnd (alpha, beta) transforming to a time-frequency domain to obtain a time-frequency analysis result T (n, m) of the underwater sound pulse signal, namely:
Figure FDA0002773704670000051
where n represents the discrete sampling instant and m represents the discrete sampling frequency.
10. The extended B-distribution pulse signal time-frequency analysis method based on parameter adaptation according to claim 1, wherein in step 1, the sampling data sequence s (N) of the multi-component underwater sound or radar pulse signal, where N is 0,1, …, and N-1 is obtained by: receiving real-time multi-component underwater sound or radar pulse signal acquisition data of N sampling points as a sampling data sequence s (N) to be processed, wherein N is 0,1, … and N-1; or extracting the multi-component underwater sound or radar pulse signals of N signal sampling points received from a certain moment from a memory as a data sequence s (N) to be processed, wherein N is 0,1, …, N-1.
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