An adaptive time-frequency analysis method based on parameter estimation and energy focusing criterion

Abstract

This invention discloses an adaptive time-frequency analysis method based on parameter prediction and energy focusing criteria. The method includes the following steps: 1. Obtaining the sampled data sequence of the signal to be processed; 2. Calculating the ambiguity function A of the signal to be processed. z (m,n) and Wigner-Ville distribution ρ WVD (a,b); 3. Using Radon transform to blur the signal function A z 4. Perform detection on (m,n) and estimate the initial radial angle set Ψ of the signal ambiguity domain; 5. Design a time-frequency domain filter kernel using the initial radial angle set Ψ, and calculate the time-frequency domain filter result and its energy focusing degree; 6. Based on the energy focusing degree, expand the initial radial angle set Ψ of the self-term using the energy focusing criterion to obtain the expanded radial angle set Φ. after and through Φ after Calculate the optimal time-frequency distribution ρ(i,j) of the signal.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, specifically relating to an adaptive time-frequency analysis method based on parameter prediction and energy focusing criteria. Background Technology

[0002] Because the frequency of non-stationary signals varies with time, traditional one-dimensional time or frequency analysis cannot effectively analyze their characteristics. Therefore, time-frequency analysis was proposed and applied to the analysis of non-stationary signals in order to observe signal characteristics simultaneously in both time and frequency dimensions. The short-time Fourier transform is a traditional time-frequency analysis method, widely used in practical engineering due to its low algorithm complexity. However, the window length limits its time and frequency resolution, preventing simultaneous improvement of both. To achieve higher time and frequency resolution simultaneously, the Wigner-Ville distribution (WVD) was proposed. Although this algorithm achieves high resolution, in the analysis of multi-component and nonlinear frequency-modulated signals, it introduces cross terms into the time-frequency distribution results, affecting the accuracy of signal feature extraction. To suppress the influence of cross terms, many algorithms have been proposed, which can be mainly divided into the following two categories:

[0003] (1) Transform the signal into the fuzzy domain, utilize the property that cross terms are far from the origin of the fuzzy domain while self terms are close to the origin of the fuzzy domain, design a corresponding fuzzy domain filter kernel for filtering, and then transform the filtering result back into the time-frequency domain. Representative algorithms include extended modified B distribution and Gaussian radial kernel distribution. The advantages of this approach are: relatively low computational cost; obvious fuzzy domain characteristics of linear frequency modulated signals, making it easy to design kernel functions; cross terms of multi-component signals are far from the origin of the fuzzy domain, and cross terms between signals can also be filtered out and signal self terms can be retained by designing a low-pass fuzzy domain filter. However, its disadvantages are: poor focusing of fuzzy domain characteristics of nonlinear frequency modulated signals, signal self terms are not easy to distinguish, and it is difficult to design an ideal kernel function.

[0004] (2) Two-dimensional filtering is performed directly in the time-frequency domain, with Adaptive Directional Time-Frequency Distribution (ADTFD) being a representative algorithm. The advantage of this type of algorithm is that by designing a reasonable time-frequency domain filter, two-dimensional filtering can be performed directly in the time-frequency domain of the signal, preserving signal information to the greatest extent. However, the disadvantage is that two-dimensional time-frequency filtering often involves a large amount of computation. Summary of the Invention

[0005] Purpose of the invention: The purpose of this invention is to design the angle of the time-frequency domain filter kernel by using parameter prediction and energy focusing criteria, so as to reduce the amount of computation and obtain high-resolution time-frequency distribution results for single-component signals and multi-component signals, as well as linear frequency modulated signals and hyperbolic frequency modulated signals.

[0006] Technical Solution: To solve the above-mentioned technical problems, this invention proposes an adaptive time-frequency analysis method based on parameter prediction and energy focusing criteria. This method includes the following steps:

[0007] Step 1: Obtain the sampled data sequence s(a) of the signal to be processed, where a is the discrete index of the time quantity;

[0008] Step 2: Calculate the ambiguity function A of the sampled data sequence s(a) of the signal to be processed. z (m,n) and the Wigner-Ville distribution (WVD) ρ WVD (a,b), where m is the discrete index of frequency shift, n is the discrete index of time delay, a is the discrete index of time, and b is the discrete index of frequency.

[0009] Step 3: Use Radon transform to blur the signal function A z (m,n) are used for detection, and the initial radial angle set Ψ of the signal ambiguity domain is estimated from the term.

[0010] Step 4: Design a time-frequency domain filter kernel using the initial radial angle set Ψ, and calculate the time-frequency domain filtering results and their energy focusing degree;

[0011] Step 5: Based on the energy focusing degree calculated in Step 4, expand the initial radial angle set Ψ of the self-term using the energy focusing criterion to obtain the expanded radial angle set Φ. after and through Φ after Calculate the optimal time-frequency distribution ρ(i,j) of the signal, where i is the discrete index of the time quantity in the time-frequency domain and j is the discrete index of the frequency quantity in the time-frequency domain.

[0012] Further, in step 1, the sampled data sequence s(a) of the signal to be processed is obtained using the following method, specifically including the following steps: receiving data from L sampling points from the sensor as the sampled data sequence s(a) of the signal to be processed, a = 0, 1, ..., L-1, where a is the discrete index of the time quantity, and L is the number of sampling points corresponding to the entire signal duration, L = 2. r r is an integer greater than or equal to 10.

[0013] Furthermore, in step 2, the ambiguity function A of the sampled data sequence s(a) of the signal to be processed is calculated using the following method. z (m,n) and Wigner-Ville distribution ρWVD (a,b), specifically including the following steps:

[0014] Step 2.1: Calculate the discrete Fourier transform S(α) of the sampled data sequence s(a) of the signal to be processed:

[0015]

[0016] Where α is the discrete index of the frequency of S(α), and j is the imaginary unit, i.e.

[0017] Step 2.2: Generate the Fourier transform Z(β) of the discrete analytic signal z(a) of s(a) using the discrete Fourier transform S(α) of the signal to be processed:

[0018]

[0019] Where β is the frequency discrete index of Z(β);

[0020] Step 2.3: Perform a discrete inverse Fourier transform on Z(β) to obtain the discrete analytic signal z(a) of the signal to be processed:

[0021]

[0022] Where 'a' is the time-based discrete index;

[0023] Step 2.4: Calculate the autocorrelation function K of the discrete analytic signal z(a). z (a,n):

[0024]

[0025] in, express The conjugate form of the time delay is n, where n = 0, 1, ..., L-1, and a = 0, 1, ..., L-1.

[0026] Step 2.5: Based on the autocorrelation function K of the discrete analytic signal z(a) z (a,n), calculate the ambiguity function A of the signal to be processed. z (m,n):

[0027]

[0028] Where m is the discrete index of frequency shift and n is the discrete index of time delay;

[0029] Step 2.6: Based on the autocorrelation function K of the discrete analytic signal z(a) z (a,n), calculate the Wigner-Ville distribution ρ of the signal to be processed. WVD(a,b):

[0030]

[0031] Where a is the discrete index for time and b is the discrete index for frequency.

[0032] Furthermore, in step 3, the Radon transform is used to ambiguate the signal ambiguity function A using the following method. z The detection is performed on (m,n), and the initial radial angle set Ψ of the signal ambiguity domain is estimated. The specific steps include:

[0033] Step 3.1: Initialize the parameters of the initial radial angle set Ψ of the fuzzy domain of the predicted signal, specifically including the initialization of the following parameters:

[0034] ① The number of discrete radial angles K in the Radon transform is initialized to a positive integer of 21 ≤ K ≤ 181;

[0035] ②The discrete radial angle set of the Radon transform is initialized as follows:

[0036] Θ=[θ1,θ2,…,θ k ,…,θ K ]

[0037] Where k is the discrete index of the radial angle, k = 1, 2, ..., K, and the k-th discrete radial angle θ k Initialize to:

[0038] θ k = -π / 2 + kπ / K;

[0039] ③ Extracting the threshold R from the initial radial angle in the signal ambiguity domain th Initialize to: 0.1≤R th Positive real numbers ≤ 0.5;

[0040] Step 3.2: Calculate the ambiguity function A of the signal to be processed. z The Radon transform of (m,n) at a radial distance of 0 yields the Radon transform set R(Θ) = [R(θ1), R(θ2), ..., R(θ)]. k ),…,R(θ K )], where the k-th discrete radial angle θ k The Radon transform result R(θ) at the corresponding radial distance of 0 k )for:

[0041]

[0042] Where K is the discrete radial angle number of the Radon transform, whose value has been initialized in step 3.1, and δ() is expressed as:

[0043]

[0044] Where x is a real number, when x = 0, δ(x) = 1, and when x ≠ 0, δ(x) = 0;

[0045] Step 3.3: Estimate the initial radial angle set Ψ of the signal ambiguity domain using the Radon transform set R(Θ) at radial distance 0.

[0046] Ψ={Θ:R(Θ)≥R th}

[0047] Among them, R th The threshold for extracting the initial radial angle in the signal ambiguity domain is given by R(Θ), which was initialized in step 3.1. R(Θ) = [R(θ1), R(θ2), ..., R(θ)]. k ),…,R(θ K [] represents the Radon transform set obtained in step 3.2. Let Ψ be the initial set of radial angles in the estimated fuzzy domain, where Ψ represents the Radon transform set R(Θ) containing angles greater than or equal to the extraction threshold R. th The set of angles corresponding to the Radon transform values. It is the estimated initial radial angle of the p-th fuzzy domain term, where p = 1, 2, ..., P, and P is the number of angles contained in the set Ψ of the initial radial angles of the fuzzy domain term.

[0048] Furthermore, in step 4, the time-frequency domain filter kernel is designed using the initial radial angle set Ψ of the signal term, and the time-frequency domain filter result and its energy focusing degree are calculated. Specifically, this includes the following steps:

[0049] Step 4.1: Initialize the parameters for designing the time-frequency domain filter kernel, calculating the time-frequency domain filter results, and their energy focusing degree. Specifically, this includes initializing the following parameters:

[0050] ① The time dimension length parameter v of the time-frequency domain filter kernel t Initialize as: 1≤v t Positive integers ≤ 5;

[0051] ② Frequency dimension length parameter v of the time-frequency domain filter kernel f Initialize as: 1≤v f Positive integers ≤15;

[0052] ③ Time-frequency domain filter kernel length L γ Initialize as: ceil(L / 16)≤L γ A positive odd number ≤ ceil(L / 8), where ceil() is the floor function;

[0053] ④ Time quantity t(a) of the time-frequency domain filter kernel γ Initialize to: t(a) γ )=-1+a γ (2 / L γ ), where a γ For the discrete index of the filter kernel time quantity, a γ =0,1,…,L γ -1;

[0054] ⑤ Time-frequency domain filtering kernel frequency quantity f(b) γ Initialized as: f(b) γ )=-1+b γ (2 / L γ ), where b γ For the discrete index of the filter kernel frequency quantity, b γ =0,1,…,L γ -1;

[0055] Step 4.2, set the initial radial angle of the term. The discrete index p = 1;

[0056] Step 4.3: Utilize the estimated initial radial angle of the self-terminus. Design the time-frequency domain filter kernel γ as follows: p (a γ ,b γ ):

[0057]

[0058] Among them, v t The time dimension length parameter of the time-frequency domain filter kernel has been initialized in step 4.1, v f The frequency dimension length parameter of the time-frequency domain filter kernel has been initialized in step 4.1. p (a γ ) and f p (b γ ) are the initial radial angles of the p-th term. The corresponding time and frequency components of the time-frequency domain filter kernel are expressed as follows:

[0059]

[0060]

[0061] Wherein, t(a γ ) is the time quantity of the time-frequency domain filter kernel, whose value has been initialized in step 4.1, a γ For the discrete index of the filter kernel time quantity, a γ =0,1,…,Lγ -1, f(b) γ ) is the time-frequency domain filter kernel frequency, whose value has been initialized in step 4.1, b γ For the discrete index of the filter kernel frequency quantity, b γ =0,1,…,L γ -1,L γ This is the length of the time-frequency domain filter kernel, whose value has been initialized in step 4.1;

[0062] Step 4.4: Utilize the time-frequency domain filtering kernel γ p (a γ ,b γ ) and the Wigner-Ville distribution ρ of the signal WVD (a,b), calculate the time-frequency domain filtering result ρ as follows: p (i,j):

[0063]

[0064] Where i is the discrete index of time quantity in the time-frequency domain, and j is the discrete index of frequency quantity in the time-frequency domain. This represents the summation of each element in all computable numerical matrices within the parentheses, where a and b are non-negative integer values ​​that satisfy the following condition:

[0065]

[0066] Where L is the number of sampling points covering the entire signal duration, and its value has been initialized in step 1. γ This is the length of the time-frequency domain filter kernel, whose value has been initialized in step 4.1;

[0067] Step 4.5: Calculate the time-frequency domain filtering result ρ p The degree of energy focusing E of (i,j) p :

[0068]

[0069] Among them, the averaged time-frequency domain filtering result ρ avg (i,j) uses the time-frequency domain filtering result ρ p (i,j) is calculated to be:

[0070]

[0071] Step 4.6: Let p = p + 1, and determine whether the following conditions are true:

[0072]

[0073] Where p is the initial radial angle of the term. The discrete index is P, which is the number of initial radial angles of the term estimated in step 3.3. If the above conditions are met, proceed to step 5; if the conditions are not met, return to step 4.3.

[0074] Furthermore, in step 5, the initial radial angle set Ψ of the self-term is expanded based on the degree of energy focusing using the energy focusing criterion, resulting in the expanded radial angle set Φ. after and through Φ after Calculating the optimal time-frequency distribution ρ(i,j) of a signal involves the following steps:

[0075] Step 5.1: Based on the degree of energy focusing, expand the initial radial angle set Ψ of the self-term using the energy focusing criterion to obtain the expanded radial angle set Φ of the self-term. after and through Φ after The parameters of the optimal time-frequency distribution ρ(i,j) of the signal are initialized, specifically including the initialization of the following parameters:

[0076] ① Expand the radial angle step of the terminator Initialize to: A positive real number, where C is a positive integer satisfying 1 ≤ C ≤ 20;

[0077] ② The flag flag1, which controls the radial angular direction of the extended term, is initialized to: flag1 = 1;

[0078] ③ The proportional threshold r for the termination angle expansion th Initialize to: 0.2≤r th Positive real numbers ≤ 0.8;

[0079] ④ The set of radial angles Φ before self-expansion before Initialized to: Φ before =Ψ;

[0080] ⑤ Maximum time-frequency distribution ρ max (i,j) is initialized as follows:

[0081] ρ max (i,j)=0,i=0,1,…,L-1,j=0,1,…,L-1

[0082] Where i is the discrete index of time quantity in the time-frequency domain, and j is the discrete index of frequency quantity in the time-frequency domain;

[0083] ⑥ The optimal time-frequency distribution ρ(i,j) is initialized as follows:

[0084] ρ(i,j)=0,i=0,1,…,L-1,j=0,1,…,L-1

[0085] Where i is the discrete index of time quantity in the time-frequency domain, and j is the discrete index of frequency quantity in the time-frequency domain;

[0086] Step 5.2, set the initial radial angle of the term. The discrete index p = 1;

[0087] Step 5.3: Utilize the time-frequency domain filtering result ρ p (i,j), calculate the time-frequency distribution ρ of the maximum value. max (i,j):

[0088] ρ max (i,j)=max(ρ(i,j),ρ p (i,j)),i=0,1,…,L-1,j=0,1,…,L-1

[0089] Where max(ρ(i,j),ρ p (i,j)) represents the expression for ρ(i,j) and ρ p Compare (i,j) and take the element with the largest modulus value. ρ(i,j) is the optimal time-frequency distribution, and its value has been initialized in step 5.1. p (i,j) represents the time-frequency domain filtering result calculated in step 4.4, where i is the discrete index of the time quantity in the time-frequency domain and j is the discrete index of the frequency quantity in the time-frequency domain. After completing the above steps, let ρ(i,j) = ρ max (i,j);

[0090] Step 5.4: Calculate the radial angle before self-expansion.

[0091]

[0092] in, The p-th self-term initial radial angle is obtained from step 3.3;

[0093] Step 5.5: Based on the radial angle before self-expansion After obtaining the radial angle of the self-expansion

[0094]

[0095] Here, flag1 is a flag that controls the radial angular direction of the extended term, and its value has been initialized in step 5.1. The angular step of the radial angle of the term has been initialized in step 5.1 to extend the step.

[0096] Step 5.6: Calculate the radial angle after self-expansion. Extended time-frequency domain filter kernel γ after (a γ ,bγ ):

[0097]

[0098] Among them, v t The time dimension length parameter of the time-frequency domain filter kernel has been initialized in step 4.1, v f The frequency dimension length parameter of the time-frequency domain filter kernel has been initialized in step 4.1. after (a γ ) and f after (b γ The radial angles after self-expansion are respectively. The corresponding extended time-frequency domain filter kernel time and frequency quantities are expressed as follows:

[0099]

[0100]

[0101] Wherein, t(a γ ) is the time quantity of the time-frequency domain filter kernel, whose value has been initialized in step 4.1, a γ For the discrete index of the filter kernel time quantity, a γ =0,1,…,L γ -1, f(b) γ ) is the time-frequency domain filter kernel frequency, whose value has been initialized in step 4.1, b γ For the discrete index of the filter kernel frequency quantity, b γ =0,1,…,L γ -1,L γ This is the length of the time-frequency domain filter kernel, whose value has been initialized in step 4.1;

[0102] Step 5.7: Utilize the extended time-frequency domain filter kernel γ after (a γ ,b γ ) and the Wigner-Ville distribution ρ of the signal WVD (a,b), calculate the extended time-frequency domain filtering result ρ as follows: after (i,j):

[0103]

[0104] Where i is the discrete index of time quantity in the time-frequency domain, and j is the discrete index of frequency quantity in the time-frequency domain. This represents the summation of each element in all computable numerical matrices within the parentheses, where a and b are non-negative integer values ​​that satisfy the following condition:

[0105]

[0106] Where L is the number of sampling points covering the entire signal duration, and its value has been initialized in step 1. γ This is the length of the time-frequency domain filter kernel, whose value has been initialized in step 4.1;

[0107] Step 5.8: Calculate the extended time-frequency domain filtering result ρ after The degree of energy focusing E of (i,j) after :

[0108]

[0109] Among them, the averaged extended time-frequency domain filtering result ρ′ avg (i,j) utilizes the extended time-frequency domain filtering result ρ after (i,j) is calculated to be:

[0110]

[0111] Step 5.9: Determine whether the following conditions are true:

[0112] E after >E p ·r th and and

[0113] Among them, E p For step 4.5, the initial radial angle is obtained using the p-th self-term. The calculated energy focusing degree, r th The proportional threshold for terminating angle expansion, whose value was initialized in step 5.1, Φ before The set of radial angles before self-expansion is initialized in step 5.1. If the above condition is not met, proceed to step 5.10; if the condition is met, calculate the set of radial angles Φ after self-expansion as follows. after With the time-frequency distribution of the maximum value ρ max (i,j):

[0114]

[0115] ρ max (i,j)=max(ρ(i,j),ρ after (i,j)),i=0,1,…,L-1,j=0,1,…,L-1

[0116] Where, Φ before It is the set of radial angles before the self-expansion, and its values ​​have been initialized in step 5.1. Let be the radial angle after self-expansion calculated in step 5.5, and let ∪ denote the union of the sets on both sides of the sign. max(ρ(i,j),ρ after (i,j)) represents the expression for ρ(i,j) and ρ after Compare (i,j) and take the element with the largest modulus value. ρ(i,j) is the optimal time-frequency distribution, and its value has been initialized in step 5.1. after (i,j) represents the extended time-frequency domain filtering result calculated in step 5.7. After completing the above steps, let Φ before =Φ after , ρ(i,j)=ρ max (i,j), and return to step 5.5;

[0117] Step 5.10: Determine whether the following conditions are true:

[0118] flag1>0

[0119] Here, flag1 is a flag that controls the radial angle direction of the extended term. Its value has been initialized in step 5.1. If the condition is true, set flag1 = -1 and return to step 5.5; if the condition is false, set flag1 = 1 and proceed to step 5.11.

[0120] Step 5.11: Let p = p + 1, and determine whether the following conditions are true:

[0121] p > P

[0122] Where p is the initial radial angle of the term. The discrete index is P, which is the number of initial radial angles of the self-term estimated in step 3.3. If the condition is met, step 5 ends and the optimal time-frequency distribution ρ(i,j) of the signal to be detected is obtained; otherwise, return to step 5.3.

[0123] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:

[0124] 1. The time-frequency analysis method of this invention employs parameter prediction, which effectively reduces the computational load. According to step 3, the signal ambiguity domain distribution is detected through Radon transform, and the initial radial angle of the signal is predicted. Based on this, subsequent angle expansion is performed, and the time-frequency domain filter kernel is designed using the expanded angle. This parameter prediction method overcomes the limitations of traditional time-frequency filtering methods that use all angles for filter kernel design, using only angles representing the signal's intrinsic characteristics for filter design, thus reducing the computational load.

[0125] 2. The time-frequency analysis method of this invention employs an energy focusing criterion, enabling adaptive signal analysis and achieving excellent results. According to step 5, during the angle expansion process, the energy focusing degree of the time-frequency domain filtering result is calculated based on the energy focusing criterion. Through conditional decision-making without human intervention, all angles reflecting the signal's intrinsic characteristics can be adaptively obtained and used to design the time-frequency domain filter kernel. The angles obtained through the energy focusing criterion effectively reflect the signal's intrinsic characteristics, thus the filtered time-frequency distribution better reduces the impact of noise and cross-terms on the identification of the signal's intrinsic distribution. This invention optimizes the direction design of the time-frequency domain filter kernel based on parameter prediction and the energy focusing criterion, reducing computational load while ensuring the quality of time-frequency analysis. It provides high-resolution time-frequency analysis for both linear frequency modulation (LFM) and hyperbolic frequency modulation (HFM) signals. Attached Figure Description

[0126] Figure 1 This is a schematic diagram of the adaptive time-frequency analysis method based on parameter prediction and energy focusing criteria of the present invention;

[0127] Figure 2 The signal ambiguity domain distribution is shown in Example 1;

[0128] Figure 3 The signal Wigner-Ville distribution is shown in Example 1;

[0129] Figure 4 The optimal time-frequency distribution of the signal in Example 1;

[0130] Figure 5 The signal ambiguity domain distribution in Example 2;

[0131] Figure 6 The signal Wigner-Ville distribution is shown in Example 2;

[0132] Figure 7 This is the optimal time-frequency distribution of the signal in Example 2. Detailed Implementation

[0133] To better understand the purpose, structure, and function of this invention, the invention will be further described below with reference to the accompanying drawings.

[0134] like Figure 1 As shown, this invention proposes an adaptive time-frequency analysis method based on parameter prediction and energy focusing criteria, comprising the following steps:

[0135] Step 1: Obtain the sampled data sequence s(a) of the signal to be processed, where a is the discrete index of the time quantity;

[0136] Step 2: Calculate the ambiguity function A of the sampled data sequence s(a) of the signal to be processed. z(m,n) and the Wigner-Ville distribution (WVD) ρ WVD (a,b), where m is the discrete index of frequency shift, n is the discrete index of time delay, a is the discrete index of time, and b is the discrete index of frequency.

[0137] Step 3: Use Radon transform to blur the signal function A z (m,n) are used for detection, and the initial radial angle set Ψ of the signal ambiguity domain is estimated from the term.

[0138] Step 4: Design a time-frequency domain filter kernel using the initial radial angle set Ψ, and calculate the time-frequency domain filtering results and their energy focusing degree;

[0139] Step 5: Based on the energy focusing degree calculated in Step 4, expand the initial radial angle set Ψ of the self-term using the energy focusing criterion to obtain the expanded radial angle set Φ. after and through Φ after Calculate the optimal time-frequency distribution ρ(i,j) of the signal, where i is the discrete index of the time quantity in the time-frequency domain and j is the discrete index of the frequency quantity in the time-frequency domain.

[0140] Further, in step 1, the sampled data sequence s(a) of the signal to be processed is obtained using the following method, specifically including the following steps: receiving data from L sampling points from the sensor as the sampled data sequence s(a) of the signal to be processed, a = 0, 1, ..., L-1, where a is the discrete index of the time quantity, and L is the number of sampling points corresponding to the entire signal duration, L = 2. r r is an integer greater than or equal to 10.

[0141] Furthermore, in step 2, the ambiguity function A of the sampled data sequence s(a) of the signal to be processed is calculated using the following method. z (m,n) and Wigner-Ville distribution ρ WVD (a,b), specifically including the following steps:

[0142] Step 2.1: Calculate the discrete Fourier transform S(α) of the sampled data sequence s(a) of the signal to be processed:

[0143]

[0144] Where α is the discrete index of the frequency of S(α), and j is the imaginary unit, i.e.

[0145] Step 2.2: Generate the Fourier transform Z(β) of the discrete analytic signal z(a) of s(a) using the discrete Fourier transform S(α) of the signal to be processed:

[0146]

[0147] Where β is the frequency discrete index of Z(β);

[0148] Step 2.3: Perform a discrete inverse Fourier transform on Z(β) to obtain the discrete analytic signal z(a) of the signal to be processed:

[0149]

[0150] Where 'a' is the time-based discrete index;

[0151] Step 2.4: Calculate the autocorrelation function K of the discrete analytic signal z(a). z (a,n):

[0152]

[0153] in, express The conjugate form of the time delay is n, where n = 0, 1, ..., L-1, and a = 0, 1, ..., L-1.

[0154] Step 2.5: Based on the autocorrelation function K of the discrete analytic signal z(a) z (a,n), calculate the ambiguity function A of the signal to be processed. z (m,n):

[0155]

[0156] Where m is the discrete index of frequency shift and n is the discrete index of time delay;

[0157] Step 2.6: Based on the autocorrelation function K of the discrete analytic signal z(a) z (a,n), calculate the Wigner-Ville distribution ρ of the signal to be processed. WVD (a,b):

[0158]

[0159] Where a is the discrete index for time and b is the discrete index for frequency.

[0160] Furthermore, in step 3, the Radon transform is used to ambiguate the signal ambiguity function A using the following method. z The detection is performed on (m,n), and the initial radial angle set Ψ of the signal ambiguity domain is estimated. The specific steps include:

[0161] Step 3.1: Initialize the parameters of the initial radial angle set Ψ of the fuzzy domain of the predicted signal, specifically including the initialization of the following parameters:

[0162] ① The number of discrete radial angles K in the Radon transform is initialized to a positive integer of 21 ≤ K ≤ 181;

[0163] ②The discrete radial angle set of the Radon transform is initialized as follows:

[0164] Θ=[θ1,θ2,…,θ k ,…,θ K ]

[0165] Where k is the discrete index of the radial angle, k = 1, 2, ..., K, and the k-th discrete radial angle θ k Initialize to:

[0166] θ k = -π / 2 + kπ / K;

[0167] ③ Extracting the threshold R from the initial radial angle in the signal ambiguity domain th Initialize to: 0.1≤R th Positive real numbers ≤ 0.5;

[0168] Step 3.2: Calculate the ambiguity function A of the signal to be processed. z The Radon transform of (m,n) at a radial distance of 0 yields the Radon transform set R(Θ) = [R(θ1), R(θ2), ..., R(θ)]. k ),…,R(θ K )], where the k-th discrete radial angle θ k The Radon transform result R(θ) at the corresponding radial distance of 0 k )for:

[0169]

[0170] Where K is the discrete radial angle number of the Radon transform, whose value has been initialized in step 3.1, and δ() is expressed as:

[0171]

[0172] Where x is a real number, when x = 0, δ(x) = 1, and when x ≠ 0, δ(x) = 0;

[0173] Step 3.3: Estimate the initial radial angle set Ψ of the signal ambiguity domain using the Radon transform set R(Θ) at radial distance 0.

[0174]

[0175] Among them, R th The threshold for extracting the initial radial angle in the signal ambiguity domain is given by R(Θ), which was initialized in step 3.1. R(Θ) = [R(θ1), R(θ2), ..., R(θ)].k ),…,R(θ K [] represents the Radon transform set obtained in step 3.2. Let Ψ be the initial set of radial angles in the estimated fuzzy domain, where Ψ represents the Radon transform set R(Θ) containing angles greater than or equal to the extraction threshold R. th The set of angles corresponding to the Radon transform values. It is the estimated initial radial angle of the p-th fuzzy domain term, where p = 1, 2, ..., P, and P is the number of angles contained in the set Ψ of the initial radial angles of the fuzzy domain term.

[0176] Furthermore, in step 4, the time-frequency domain filter kernel is designed using the initial radial angle set Ψ of the signal term, and the time-frequency domain filter result and its energy focusing degree are calculated. Specifically, this includes the following steps:

[0177] Step 4.1: Initialize the parameters for designing the time-frequency domain filter kernel, calculating the time-frequency domain filter results, and their energy focusing degree. Specifically, this includes initializing the following parameters:

[0178] ① The time dimension length parameter v of the time-frequency domain filter kernel t Initialize as: 1≤v t Positive integers ≤ 5;

[0179] ② Frequency dimension length parameter v of the time-frequency domain filter kernel f Initialize as: 1≤v f Positive integers ≤15;

[0180] ③ Time-frequency domain filter kernel length L γ Initialize as: ceil(L / 16)≤L γ A positive odd number ≤ ceil(L / 8), where ceil() is the floor function;

[0181] ④ Time quantity t(a) of the time-frequency domain filter kernel γ Initialize to: t(a) γ )=-1+a γ (2 / L γ ), where a γ For the discrete index of the filter kernel time quantity, a γ =0,1,…,L γ -1;

[0182] ⑤ Time-frequency domain filtering kernel frequency quantity f(b) γ Initialized as: f(b) γ )=-1+b γ (2 / L γ ), where b γ For the discrete index of the filter kernel frequency quantity, bγ =0,1,…,L γ -1;

[0183] Step 4.2, set the initial radial angle of the term. The discrete index p = 1;

[0184] Step 4.3: Utilize the estimated initial radial angle of the self-terminus. Design the time-frequency domain filter kernel γ as follows: p (a γ ,b γ ):

[0185]

[0186] Among them, v t The time dimension length parameter of the time-frequency domain filter kernel has been initialized in step 4.1, v f The frequency dimension length parameter of the time-frequency domain filter kernel has been initialized in step 4.1. p (a γ ) and f p (b γ ) are the initial radial angles of the p-th term. The corresponding time and frequency components of the time-frequency domain filter kernel are expressed as follows:

[0187]

[0188]

[0189] Wherein, t(a γ ) is the time quantity of the time-frequency domain filter kernel, whose value has been initialized in step 4.1, a γ For the discrete index of the filter kernel time quantity, a γ =0,1,…,L γ -1, f(b) γ ) is the time-frequency domain filter kernel frequency, whose value has been initialized in step 4.1, b γ For the discrete index of the filter kernel frequency quantity, b γ =0,1,…,L γ -1,L γ This is the length of the time-frequency domain filter kernel, whose value has been initialized in step 4.1;

[0190] Step 4.4: Utilize the time-frequency domain filtering kernel γ p (a γ ,b γ ) and the Wigner-Ville distribution ρ of the signal WVD (a,b), calculate the time-frequency domain filtering result ρ as follows: p (i,j):

[0191]

[0192] Where i is the discrete index of time quantity in the time-frequency domain, and j is the discrete index of frequency quantity in the time-frequency domain. This represents the summation of each element in all computable numerical matrices within the parentheses, where a and b are non-negative integer values ​​that satisfy the following condition:

[0193]

[0194] Where L is the number of sampling points covering the entire signal duration, and its value has been initialized in step 1. γ This is the length of the time-frequency domain filter kernel, whose value has been initialized in step 4.1;

[0195] Step 4.5: Calculate the time-frequency domain filtering result ρ p The degree of energy focusing E of (i,j) p :

[0196]

[0197] Among them, the averaged time-frequency domain filtering result ρ avg (i,j) uses the time-frequency domain filtering result ρ p (i,j) is calculated to be:

[0198]

[0199] Step 4.6: Let p = p + 1, and determine whether the following conditions are true:

[0200] p > P

[0201] Where p is the initial radial angle of the term. The discrete index is P, which is the number of initial radial angles of the term estimated in step 3.3. If the above conditions are met, proceed to step 5; if the conditions are not met, return to step 4.3.

[0202] Furthermore, in step 5, the initial radial angle set Ψ of the self-term is expanded based on the degree of energy focusing using the energy focusing criterion, resulting in the expanded radial angle set Φ. after and through Φ after Calculating the optimal time-frequency distribution ρ(i,j) of a signal involves the following steps:

[0203] Step 5.1: Based on the degree of energy focusing, expand the initial radial angle set Ψ of the self-term using the energy focusing criterion to obtain the expanded radial angle set Φ of the self-term. after and through Φ afterThe parameters of the optimal time-frequency distribution ρ(i,j) of the signal are initialized, specifically including the initialization of the following parameters:

[0204] ① Expand the radial angle step of the terminator Initialize to: A positive real number, where C is a positive integer satisfying 1 ≤ C ≤ 20;

[0205] ② The flag flag1, which controls the radial angular direction of the extended term, is initialized to: flag1 = 1;

[0206] ③ The proportional threshold r for the termination angle expansion th Initialize to: 0.2≤r th Positive real numbers ≤ 0.8;

[0207] ④ The set of radial angles Φ before self-expansion before Initialized to: Φ before =Ψ;

[0208] ⑤ Maximum time-frequency distribution ρ max (i,j) is initialized as follows:

[0209] ρ max (i,j)=0,i=0,1,…,L-1,j=0,1,…,L-1

[0210] Where i is the discrete index of time quantity in the time-frequency domain, and j is the discrete index of frequency quantity in the time-frequency domain;

[0211] ⑥ The optimal time-frequency distribution ρ(i,j) is initialized as follows:

[0212] ρ(i,j)=0,i=0,1,…,L-1,j=0,1,…,L-1

[0213] Where i is the discrete index of time quantity in the time-frequency domain, and j is the discrete index of frequency quantity in the time-frequency domain;

[0214] Step 5.2, set the initial radial angle of the term. The discrete index p = 1;

[0215] Step 5.3: Utilize the time-frequency domain filtering result ρ p (i,j), calculate the time-frequency distribution ρ of the maximum value. max (i,j):

[0216] ρ max (i,j)=max(ρ(i,j),ρ p (i,j)),i=0,1,…,L-1,j=0,1,…,L-1

[0217] Where max(ρ(i,j),ρ p(i,j)) represents the comparison between ρ(i,j) and ρp(i,j), taking the element with the largest modulus. ρ(i,j) is the optimal time-frequency distribution, whose value has been initialized in step 5.1. p (i,j) represents the time-frequency domain filtering result calculated in step 4.4, where i is the discrete index of the time quantity in the time-frequency domain and j is the discrete index of the frequency quantity in the time-frequency domain. After completing the above steps, let ρ(i,j) = ρ max (i,j);

[0218] Step 5.4: Calculate the radial angle before self-expansion.

[0219]

[0220] in, The p-th self-term initial radial angle is obtained from step 3.3;

[0221] Step 5.5: Based on the radial angle before self-expansion After obtaining the radial angle of the self-expansion

[0222]

[0223] Here, flag1 is a flag that controls the radial angular direction of the extended term, and its value has been initialized in step 5.1. The angular step of the radial angle of the term has been initialized in step 5.1 to extend the step.

[0224] Step 5.6: Calculate the radial angle after self-expansion. Extended time-frequency domain filter kernel γ after (a γ ,b γ ):

[0225]

[0226] Among them, v t The time dimension length parameter of the time-frequency domain filter kernel has been initialized in step 4.1, v f The frequency dimension length parameter of the time-frequency domain filter kernel has been initialized in step 4.1. after (a γ ) and f after (b γ The radial angles after self-expansion are respectively. The corresponding extended time-frequency domain filter kernel time and frequency quantities are expressed as follows:

[0227]

[0228]

[0229] Wherein, t(a γ ) is the time quantity of the time-frequency domain filter kernel, whose value has been initialized in step 4.1, a γ For the discrete index of the filter kernel time quantity, a γ =0,1,…,L γ -1, f(b) γ ) is the time-frequency domain filter kernel frequency, whose value has been initialized in step 4.1, b γ For the discrete index of the filter kernel frequency quantity, b γ =0,1,…,L γ -1,L γ This is the length of the time-frequency domain filter kernel, whose value has been initialized in step 4.1;

[0230] Step 5.7: Utilize the extended time-frequency domain filter kernel γ after (a γ ,b γ ) and the Wigner-Ville distribution ρ of the signal WVD (a,b), calculate the extended time-frequency domain filtering result ρ as follows: after (i,j):

[0231]

[0232] Where i is the discrete index of time quantity in the time-frequency domain, and j is the discrete index of frequency quantity in the time-frequency domain. Indicates the brackets

[0233] Summing each element in all computable numerical matrices within the matrix, where a and b are non-negative integer values ​​satisfying the following condition:

[0234]

[0235] Where L is the number of sampling points covering the entire signal duration, and its value has been initialized in step 1. γ This is the length of the time-frequency domain filter kernel, whose value has been initialized in step 4.1;

[0236] Step 5.8: Calculate the extended time-frequency domain filtering result ρ after The degree of energy focusing E of (i,j) after :

[0237]

[0238] Among them, the averaged extended time-frequency domain filtering result ρ′ avg (i,j) utilizes the extended time-frequency domain filtering result ρ after (i,j) is calculated to be:

[0239]

[0240] Step 5.9: Determine whether the following conditions are true:

[0241] E after >E p ·r th and and

[0242] Among them, E p For step 4.5, the initial radial angle is obtained using the p-th self-term. The calculated energy focusing degree, r th The proportional threshold for terminating angle expansion, whose value was initialized in step 5.1, Φ before The set of radial angles before self-expansion is initialized in step 5.1. If the above condition is not met, proceed to step 5.10; if the condition is met, calculate the set of radial angles Φ after self-expansion as follows. after With the time-frequency distribution of the maximum value ρ max (i,j):

[0243]

[0244] ρ max (i,j)=max(ρ(i,j),ρ after (i,j)),i=0,1,…,L-1,j=0,1,…,L-1

[0245] Where, Φ before It is the set of radial angles before the self-expansion, and its values ​​have been initialized in step 5.1. Let be the radial angle after self-expansion calculated in step 5.5, and let ∪ denote the union of the sets on both sides of the sign. max(ρ(i,j),ρ after (i,j)) represents the expression for ρ(i,j) and ρ after Compare (i,j) and take the element with the largest modulus value. ρ(i,j) is the optimal time-frequency distribution, and its value has been initialized in step 5.1. after (i,j) represents the extended time-frequency domain filtering result calculated in step 5.7. After completing the above steps, let Φ before =Φ after , ρ(i,j)=ρ max (i,j), and return to step 5.5;

[0246] Step 5.10: Determine whether the following conditions are true:

[0247] flag1>0

[0248] Here, flag1 is a flag that controls the radial angle direction of the extended term. Its value has been initialized in step 5.1. If the condition is true, set flag1 = -1 and return to step 5.5; if the condition is false, set flag1 = 1 and proceed to step 5.11.

[0249] Step 5.11: Let p = p + 1, and determine whether the following conditions are true:

[0250] p > P

[0251] Where p is the initial radial angle of the term. The discrete index is P, which is the number of initial radial angles of the self-term estimated in step 3.3. If the condition is met, step 5 ends and the optimal time-frequency distribution ρ(i,j) of the signal to be detected is obtained; otherwise, return to step 5.3.

[0252] In the embodiments of the present invention, the simulated received signal model x(t) is:

[0253] x(t) = s(t) + w(t)

[0254] Wherein, the background noise of the observed signal w(t) is the noise power P n Gaussian white noise, noise power P n The size depends on the signal-to-noise ratio (SNR): SNR = 10log 10 [P s / P n ], where P s It is the signal power; the multi-component signal s(t) is represented as:

[0255]

[0256] Where N1 is the number of signal components, s q (t) represents the q-th signal component, A q For s q The amplitude of (t) then the signal power Π q (t) is s q The signal duration of (t), For s q The instantaneous phase of (t), where T is the observation time. Π q (t) is represented as:

[0257]

[0258] Among them, t q and τ q and represent the start time and duration of the q-th signal component, respectively.

[0259] For different types of signal components, the instantaneous phase of the q-th signal component It can be represented as:

[0260]

[0261] in, f represents the initial phase. lq k represents the starting frequency of the signal. q For LFM signal frequency modulation, μ q The slope of the HFM signal period.

[0262] With sampling frequency f s Discrete sampling is performed on the noisy multi-component signal x(t) received in the above simulation to obtain the noisy multi-component signal sampling data sequence x(n):

[0263]

[0264] Example 1:

[0265] The simulation signal parameters are set as follows: number of signal components N1 = 1, observation time T = 1s, the first signal component s1(t) is a hyperbolic frequency modulated signal, signal amplitude A1 = 1, start time t1 = 0.25s, duration τ1 = 0.5s, and initial phase. Starting frequency f l1 =100Hz, period slope μ1=3 / 200Hz -1 ·s -1 Sampling frequency f s =1024Hz, observed data sequence points L=1024, maximum signal-to-noise ratio SNR=5dB;

[0266] According to step 1, the data collected from 1024 sampling points of the sensor is used as the sampling data sequence s(a) of the signal to be processed, where a = 0, 1, ..., L;

[0267] Based on step 2, calculate the ambiguity function A of the signal. z (m,n), such as Figure 2 As shown, and the Wigner-Ville distribution ρ WVD (a,b), such as Figure 3 As shown;

[0268] Based on step 3, initialize the number of discrete radial angles of the Radon transform to K = 181, and the set of discrete radial angles of the Radon transform to Θ = [θ1, θ2, ..., θ]. k ,…,θ K The k-th discrete radial angle θ k = -π / 2 + kπ / K, threshold R for extracting the initial radial angle of the signal ambiguity domain. th=0.2. Using the above parameters, the Radon transform is applied to the signal ambiguity function A. z (m,n) is used for detection, and the initial radial angle set Ψ of the fuzzy domain of the signal is estimated. To facilitate the presentation of the angle expansion process, the initial radial angle set Ψ of the fuzzy domain is expressed in angles, i.e., Ψ=[0°,17°,26°,28°,35°,38°,45°,47°,53°,56°,66°]. It can be obtained that the number of angles contained in the initial radial angle set Ψ of the fuzzy domain is P=11;

[0269] Based on step 4, initialize the time dimension length parameter v of the time-frequency domain filter kernel. t =3, the frequency dimension length parameter v of the time-frequency domain filter kernel f =8, Time-frequency domain filter kernel length L γ =127, time-frequency domain filter kernel time quantity t(a) γ )=-1+a γ (2 / L γ ), a γ =0,1,…,L γ -1, Time-frequency domain filter kernel frequency quantity f(b) γ )=-1+b γ (2 / L γ ), b γ =0,1,…,L γ -1. Using the above parameters, the time-frequency domain filter kernel γ is obtained for p = 1, 2, ..., 11. p (a γ ,b γ The filtering result ρ in the time-frequency domain is calculated. p (i,j) and the corresponding energy focusing degree E p ;

[0270] Based on step 5, initialize the angle step of the extended radial angle. The flag flag1 = 1 controls the expansion of the radial angle direction, and the threshold r for terminating the angular expansion is set to the maximum value. th =0.7, the set of radial angles Φ before self-expansion before =Ψ, the time-frequency distribution of the maximum value ρ max (i,j)=0, the optimal time-frequency distribution ρ(i,j)=0, i=0,1,…,L-1, j=0,1,…,L-1. Using these parameters, the 11 initial radial angles of the self-terms are expanded according to the energy focusing criterion. Similarly, to facilitate observation of the angle expansion process, the radial angle set Φ after the self-term expansion is represented using an angle system and converted to 0°-180°. after Then, after the expansion of the term, the radial angle set Φ after= [0°, 1°, 2°, 3°, 4°, 5°, 6°, 7°, 8°, 9°, 10°, 11°, 12°, 13°, 14°, 15°, 16°, 17°, 18°, 19°, 20°, 21°, 22°, 23°, 24°, 25°, 26°, 27°, 28°, 29°, 30°, 31°, 32°, 33°, 34°, 35°, 36°, 37°, 38°, 39°, 4 [0°, 41°, 42°, 43°, 44°, 45°, 46°, 47°, 48°, 49°, 50°, 51°, 52°, 53°, 54°, 55°, 56°, 57°, 58°, 59°, 60°, 61°, 62°, 63°, 64°, 65°, 66°, 67°, 68°, 69°, 70°, 71°, 72°, 73°, 74°], it can be seen that the radial angle set Φ after the self-term expansion is... after The number of filters is 75. Time-frequency domain filter kernels are designed using these 75 self-defined radial angles, and time-frequency domain filtering is performed to obtain the optimal time-frequency distribution ρ(i,j). Figure 4 As shown. The Wigner-Ville distribution of the simulated signal (…). Figure 3 By comparison, it can be found that the proposed algorithm can effectively suppress the internal cross terms of the hyperbolic frequency modulated signal and obtain a high-resolution time-frequency distribution.

[0271] Example 2:

[0272] The simulation signal parameters are set as follows: number of signal components N1 = 2, observation time T = 1s, the first signal component s1(t) is a linear frequency modulated signal, signal amplitude A1 = 1, initial time t1 = 0.25s, duration τ1 = 0.5s, and initial phase. Starting frequency f l1 =50Hz, modulation rate k1 = 500Hz·s -1 The second signal component s2(t) is a hyperbolic frequency modulated signal with amplitude A2 = 1, initial time t2 = 0.25s, duration τ2 = 0.5s, and initial phase. Starting frequency f l2 =200Hz, period slope μ2 = 1 / 180Hz -1 ·s -1 Sampling frequency f s =1024Hz, observed data sequence points L=1024, maximum signal-to-noise ratio SNR=5dB;

[0273] According to step 1, the data collected from 1024 sampling points of the sensor is used as the sampling data sequence s(a) of the signal to be processed, where a = 0, 1, ..., L;

[0274] Based on step 2, calculate the ambiguity function A of the signal. z(m,n), such as Figure 5 As shown, and the Wigner-Ville distribution ρ WVD (a,b), such as Figure 6 As shown;

[0275] Based on step 3, initialize the number of discrete radial angles of the Radon transform to K = 181, and the set of discrete radial angles of the Radon transform to Θ = [θ1, θ2, ..., θ]. k ,…,θ K The k-th discrete radial angle θ k = -π / 2 + kπ / K, threshold R for extracting the initial radial angle of the signal ambiguity domain. th =0.2. Using the above parameters, the Radon transform is applied to the signal ambiguity function A. z (m,n) is used for detection, and the initial radial angle set Ψ of the fuzzy domain of the signal is estimated. To facilitate the presentation of the angle expansion process, the initial radial angle set Ψ of the fuzzy domain is expressed in degrees, i.e., Ψ=[11°,17°,33°,38°,40°,44°,54°]. It can be obtained that the number of angles contained in the initial radial angle set Ψ of the fuzzy domain is P=7;

[0276] Based on step 4, initialize the time dimension length parameter v of the time-frequency domain filter kernel. t =3, the frequency dimension length parameter v of the time-frequency domain filter kernel f =8, Time-frequency domain filter kernel length L γ =127, time-frequency domain filter kernel time quantity t(a) γ )=-1+a γ (2 / L γ ), a γ =0,1,…,L γ -1, Time-frequency domain filter kernel frequency quantity f(b) γ )=-1+b γ (2 / L γ ), b γ =0,1,…,L γ -1. Using the above parameters, the time-frequency domain filter kernel γ is obtained for p = 1, 2, ..., 7 respectively. p (a γ ,b γ The filtering result ρ in the time-frequency domain is calculated. p (i,j) and the corresponding energy focusing degree E p ;

[0277] Based on step 5, initialize the angle step of the extended radial angle. The flag flag1 = 1 controls the expansion of the radial angle direction, and the threshold r for terminating the angular expansion is set to the maximum value. th =0.7, the set of radial angles Φ before self-expansionbefore =Ψ, the time-frequency distribution of the maximum value ρ max (i,j)=0, the optimal time-frequency distribution ρ(i,j)=0, i=0,1,…,L-1, j=0,1,…,L-1. Using these parameters, the seven initial radial angles of the self-terms are expanded according to the energy focusing criterion. Similarly, to facilitate observation of the angle expansion process, the radial angle set Φ after the self-term expansion is represented using the angle system and converted to 0°-180°. after Then, after the expansion of the term, the radial angle set Φ after = [4°, 5°, 6°, 7°, 8°, 9°, 10°, 11°, 12°, 13°, 14°, 15°, 16°, 17°, 18°, 19°, 20°, 21°, 22°, 23°, 24°, 25°, 26°, 27°, 28°, 29°, 30°, 31°, 32°, 33°, 34°, 35°, 36°, 37°, 38°, 39°, 40°, 41°, 42°, 43°, 44°, 45°, 46°, 47°, 48°, 49°, 50°, 51°, 52°, 53°, 54°, 55°, 56°, 57°, 58°, 59°, 60°], it can be seen that the radial angle set Φ after the self-expansion is... after The number of filters is 57. Time-frequency domain filter kernels are designed using these 57 self-defined radial angles, and time-frequency domain filtering is performed to obtain the optimal time-frequency distribution ρ(i,j). Figure 7 As shown. The Wigner-Ville distribution of the simulated signal (…). Figure 6 By comparison, it can be found that the proposed algorithm can effectively suppress the cross terms of linear frequency modulation (LFM) and hyperbolic frequency modulation (HFM) signals, and can also suppress the internal cross terms of hyperbolic frequency modulation signals, thus obtaining a high-resolution time-frequency distribution.

[0278] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. An adaptive time-frequency analysis method based on parameter prediction and energy focusing criteria, characterized in that, The method includes the following steps: Step 1: Obtain the sampled data sequence s(a) of the signal to be processed, where a is the discrete index of the time quantity; Step 2: Calculate the ambiguity function A of the sampled data sequence s(a) of the signal to be processed. z (m,n) and Wigner-Ville distribution ρ WVD (a,b), where m is the discrete index of frequency shift, n is the discrete index of time delay, a is the discrete index of time, and b is the discrete index of frequency. Step 3: Use Radon transform to blur the signal function A z (m,n) are used for detection, and the initial radial angle set Ψ of the signal ambiguity domain is estimated from the term. Step 4: Design a time-frequency domain filter kernel using the initial radial angle set Ψ, and calculate the time-frequency domain filtering results and their energy focusing degree; Step 5: Based on the energy focusing degree calculated in Step 4, expand the initial radial angle set Ψ of the self-term using the energy focusing criterion to obtain the expanded radial angle set Φ. after and through Φ after Calculate the optimal time-frequency distribution ρ(i,j) of the signal, where i is the discrete index of the time quantity in the time-frequency domain and j is the discrete index of the frequency quantity in the time-frequency domain.

2. The adaptive time-frequency analysis method based on parameter prediction and energy focusing criteria according to claim 1, characterized in that, In step 1, the sampling data sequence s(a) of the signal to be processed is obtained using the following method, specifically including the following steps: receiving data from L sampling points from the sensor as the sampling data sequence s(a) of the signal to be processed, a = 0, 1, ..., L-1, where a is the discrete index of the time quantity, and L is the number of sampling points corresponding to the entire duration of the signal, L = 2. r r is an integer greater than or equal to 10.

3. The adaptive time-frequency analysis method based on parameter prediction and energy focusing criteria according to claim 1, characterized in that, In step 2, the ambiguity function A of the sampled data sequence s(a) of the signal to be processed is calculated using the following method. z (m,n) and Wigner-Ville distribution ρ WVD (a,b), specifically including the following steps: Step 2.1: Calculate the discrete Fourier transform S(α) of the sampled data sequence s(a) of the signal to be processed: Where α is the discrete index of the frequency of S(α), and j is the imaginary unit, i.e. Step 2.2: Generate the Fourier transform Z(β) of the discrete analytic signal z(a) of s(a) using the discrete Fourier transform S(α) of the signal to be processed: Where β is the frequency discrete index of Z(β); Step 2.3: Perform a discrete inverse Fourier transform on Z(β) to obtain the discrete analytic signal z(a) of the signal to be processed: Where 'a' is the time-based discrete index; Step 2.4: Calculate the autocorrelation function K of the discrete analytic signal z(a). z (a,n): in, express The conjugate form of the time delay is n, where n = 0, 1, ..., L-1, and a = 0, 1, ..., L-1. Step 2.5: Based on the autocorrelation function K of the discrete analytic signal z(a) z (a,n), calculate the ambiguity function A of the signal to be processed. z (m,n): Where m is the discrete index of frequency shift and n is the discrete index of time delay; Step 2.6: Based on the autocorrelation function K of the discrete analytic signal z(a) z Calculate the Wigner-Ville distribution ρ of the signal to be processed (a,n). WVD (a,b): Where a is the discrete index for time and b is the discrete index for frequency.

4. The adaptive time-frequency analysis method based on parameter prediction and energy focusing criteria according to claim 3, characterized in that, In step 3, the Radon transform is used to ambiguate the signal function A using the following method. z The detection is performed on (m,n), and the initial radial angle set Ψ of the signal ambiguity domain is estimated. The specific steps include: Step 3.1: Initialize the parameters of the initial radial angle set Ψ of the fuzzy domain of the predicted signal, specifically including the initialization of the following parameters: ① The number of discrete radial angles K in the Radon transform is initialized to a positive integer of 21 ≤ K ≤ 181; ②The discrete radial angle set of the Radon transform is initialized as follows: Θ=[θ1,θ2,...,θ k ,...,θ K ] Where k is the discrete index of the radial angle, k = 1, 2, ..., K, and the k-th discrete radial angle θ k Initialize to: i k =-π / 2+kπ / K; ③ Extracting the threshold R from the initial radial angle in the signal ambiguity domain th Initialize to: 0.1≤R th Positive real numbers ≤ 0.5; Step 3.2: Calculate the ambiguity function A of the signal to be processed. z The Radon transform of (m,n) at a radial distance of 0 yields the Radon transform set R(Θ) = [R(θ1), R(θ2), ..., R(θ)]. k ),…,R(θ K )], where the k-th discrete radial angle θ k The Radon transform result R(θ) at the corresponding radial distance of 0 k )for: Where K is the discrete radial angle number of the Radon transform, whose value has been initialized in step 3.1, and δ() is expressed as: Where x is a real number, when x = 0, δ(x) = 1, and when x ≠ 0, δ(x) = 0; Step 3.3: Estimate the initial radial angle set Ψ of the signal ambiguity domain using the Radon transform set R(Θ) at radial distance 0. Ψ={Θ:R(Θ)≥R th } Among them, R th The threshold for extracting the initial radial angle in the signal ambiguity domain is given by R(Θ), which was initialized in step 3.

1. R(Θ) = [R(θ1), R(θ2), ..., R(θ)]. k ),…,R(θ K [] represents the Radon transform set obtained in step 3.

2. Let Ψ be the initial set of radial angles in the estimated fuzzy domain, where Ψ represents the Radon transform set R(Θ) containing angles greater than or equal to the extraction threshold R. th The set of angles corresponding to the Radon transform values. It is the estimated initial radial angle of the p-th fuzzy domain term, where p = 1, 2, ..., P, and P is the number of angles contained in the set Ψ of the initial radial angles of the fuzzy domain term.

5. The adaptive time-frequency analysis method based on parameter prediction and energy focusing criteria according to claim 4, characterized in that, In step 4, the following method is used to design a time-frequency domain filter kernel using the initial radial angle set Ψ of the signal term, and to calculate the time-frequency domain filter result and its energy focusing degree. Specifically, the steps include: Step 4.1: Initialize the parameters for designing the time-frequency domain filter kernel, calculating the time-frequency domain filter results, and their energy focusing degree. Specifically, this includes initializing the following parameters: ① The time dimension length parameter v of the time-frequency domain filter kernel t Initialize as: 1≤v t Positive integers ≤ 5; ② Frequency dimension length parameter v of the time-frequency domain filter kernel f Initialize as: 1≤v f Positive integers ≤15; ③ Time-frequency domain filter kernel length L γ Initialize as: ceil(L / 16)≤L γ A positive odd number ≤ ceil(L / 8), where ceil() is the floor function; ④ Time quantity t(a) of the time-frequency domain filter kernel γ Initialize to: t(a) γ )=-1+a γ (2 / L γ ), where a γ For the discrete index of the filter kernel time quantity, a γ =0,1,…,L γ -1; ⑤ Time-frequency domain filtering kernel frequency quantity f(b) γ Initialized as: f(b) γ )=-1+b γ (2 / L γ ), where b γ For the discrete index of the filter kernel frequency quantity, b γ =0,1,…,L γ -1; Step 4.2, set the initial radial angle of the term. The discrete index p = 1; Step 4.3: Utilize the estimated initial radial angle of the self-terminus. Design the time-frequency domain filter kernel γ as follows: p (a γ ,b γ ): Among them, v t The time dimension length parameter of the time-frequency domain filter kernel has been initialized in step 4.1, v f The frequency dimension length parameter of the time-frequency domain filter kernel has been initialized in step 4.

1. p (a γ ) and f p (b γ ) are the initial radial angles of the p-th term. The corresponding time and frequency components of the time-frequency domain filter kernel are expressed as follows: Wherein, t(a γ ) is the time quantity of the time-frequency domain filter kernel, whose value has been initialized in step 4.1, a γ For the discrete index of the filter kernel time quantity, a γ =0,1,…,L γ -1, f(b) γ ) is the time-frequency domain filter kernel frequency, whose value has been initialized in step 4.1, b γ For the discrete index of the filter kernel frequency quantity, b γ =0,1,…,L γ -1,L γ This is the length of the time-frequency domain filter kernel, whose value has been initialized in step 4.1; Step 4.4: Utilize the time-frequency domain filtering kernel γ p (a γ ,b γ ) and the Wigner-Ville distribution ρ of the signal WVD (a,b), calculate the time-frequency domain filtering result ρ as follows: p (i,j): Where i is the discrete index of time quantity in the time-frequency domain, and j is the discrete index of frequency quantity in the time-frequency domain. This represents the summation of each element in all computable numerical matrices within the parentheses, where a and b are non-negative integer values ​​that satisfy the following condition: Where L is the number of sampling points covering the entire signal duration, and its value has been initialized in step 1. γ This is the length of the time-frequency domain filter kernel, whose value has been initialized in step 4.1; Step 4.5: Calculate the time-frequency domain filtering result ρ p The degree of energy focusing E of (i,j) p : Among them, the averaged time-frequency domain filtering result ρ avg (i,j) uses the time-frequency domain filtering result ρ p (i,j) is calculated to be: Step 4.6: Let p = p + 1, and determine whether the following conditions are true: p > P Where p is the initial radial angle of the term. The discrete index is P, which is the number of initial radial angles of the term estimated in step 3.

3. If the above conditions are met, proceed to step 5; otherwise, return to step 4.

3.

6. The adaptive time-frequency analysis method based on parameter prediction and energy focusing criteria according to claim 5, characterized in that, In step 5, the initial radial angle set Ψ of the self-term is expanded based on the degree of energy focusing using the energy focusing criterion, resulting in the expanded radial angle set Φ. after and through Φ after Calculating the optimal time-frequency distribution ρ(i,j) of a signal involves the following steps: Step 5.1: Based on the degree of energy focusing, expand the initial radial angle set Ψ of the self-term using the energy focusing criterion to obtain the expanded radial angle set Φ of the self-term. after and through Φ after The parameters of the optimal time-frequency distribution ρ(i,j) of the signal are initialized, specifically including the initialization of the following parameters: ① Expand the radial angle step of the terminator Initialize to: A positive real number, where C is a positive integer satisfying 1 ≤ C ≤ 20; ② The flag flag1, which controls the radial angular direction of the extended term, is initialized to: flag1 = 1; ③ The proportional threshold r for the termination angle expansion th Initialize to: 0.2≤r th Positive real numbers ≤ 0.8; ④ The set of radial angles Φ before self-expansion before Initialized to: Φ before =Ψ; ⑤ Maximum time-frequency distribution ρ max (i,j) is initialized as follows: ρ max (i,j)=0,i=0,1,...,L-1,j=0,1,...,L-1 Where i is the discrete index of time quantity in the time-frequency domain, and j is the discrete index of frequency quantity in the time-frequency domain; ⑥ The optimal time-frequency distribution ρ(i,j) is initialized as follows: ρ(i,j)=0,i=0,1,...,L-1,j=0,1,...,L-1 Where i is the discrete index of time quantity in the time-frequency domain, and j is the discrete index of frequency quantity in the time-frequency domain; Step 5.2, set the initial radial angle of the term. The discrete index p = 1; Step 5.3: Utilize the time-frequency domain filtering result ρ p (i,j), calculate the time-frequency distribution ρ of the maximum value. max (i,j): r max (i,j)=max(ρ(i,j),ρ p (i,j)),i=0,1,...,L-1,j=0,1,...,L-1 Where max(ρ(i,j),ρ p (i,j)) represents the comparison between ρ(i,j) and ρp(i,j), taking the element with the largest modulus. ρ(i,j) is the optimal time-frequency distribution, whose value has been initialized in step 5.

1. p (i,j) represents the time-frequency domain filtering result calculated in step 4.4, where i is the discrete index of the time quantity in the time-frequency domain and j is the discrete index of the frequency quantity in the time-frequency domain. After completing the above steps, let ρ(i,j) = ρ max (i,j); Step 5.4: Calculate the radial angle before self-expansion. in, The p-th self-term initial radial angle is obtained from step 3.3; Step 5.5: Based on the radial angle before self-expansion After obtaining the radial angle of the self-expansion Here, flag1 is a flag that controls the radial angular direction of the extended term, and its value has been initialized in step 5.

1. The angular step of the radial angle of the term has been initialized in step 5.1 to extend the step. Step 5.6: Calculate the radial angle after self-expansion. Extended time-frequency domain filter kernel γ after (a γ ,b γ ): Among them, v t The time dimension length parameter of the time-frequency domain filter kernel has been initialized in step 4.1, v f The frequency dimension length parameter of the time-frequency domain filter kernel has been initialized in step 4.

1. after (a γ ) and f after (b γ The radial angles after self-expansion are respectively. The corresponding extended time-frequency domain filter kernel time and frequency quantities are expressed as follows: Wherein, t(a γ ) is the time quantity of the time-frequency domain filter kernel, whose value has been initialized in step 4.1, a γ For the discrete index of the filter kernel time quantity, a γ =0,1,…,L γ -1, f(b) γ ) is the time-frequency domain filter kernel frequency, whose value has been initialized in step 4.1, b γ For the discrete index of the filter kernel frequency quantity, b γ =0,1,…,L γ -1,L γ This is the length of the time-frequency domain filter kernel, whose value has been initialized in step 4.1; Step 5.7: Utilize the extended time-frequency domain filter kernel γ after (a γ ,b γ ) and the Wigner-Ville distribution ρ of the signal WVD (a,b), calculate the extended time-frequency domain filtering result ρ as follows: after (i,j): Where i is the discrete index of time quantity in the time-frequency domain, and j is the discrete index of frequency quantity in the time-frequency domain. This represents the summation of each element in all computable numerical matrices within the parentheses, where a and b are non-negative integer values ​​that satisfy the following condition: Where L is the number of sampling points covering the entire signal duration, and its value has been initialized in step 1. γ This is the length of the time-frequency domain filter kernel, whose value has been initialized in step 4.1; Step 5.8: Calculate the extended time-frequency domain filtering result ρ after The degree of energy focusing E of (i,j) after : Among them, the averaged extended time-frequency domain filtering result ρ′ avg (i,j) utilizes the extended time-frequency domain filtering result ρ after (i,j) is calculated to be: Step 5.9: Determine whether the following conditions are true: E after >E p ·r th and and Among them, E p For step 4.5, the initial radial angle is obtained using the p-th self-term. The calculated energy focusing degree, r th The proportional threshold for terminating angle expansion, whose value was initialized in step 5.1, Φ before The set of radial angles before self-expansion is initialized in step 5.

1. If the above condition is not met, proceed to step 5.10; if the condition is met, calculate the set of radial angles Φ after self-expansion as follows. after With the time-frequency distribution of the maximum value ρ max (i,j): r max (i,j)=max(ρ(i,j),ρ after (i,j)),i=0,1,…,L-1,j=0,1,…,L-1 Where, Φ before It is the set of radial angles before the self-expansion, and its values ​​have been initialized in step 5.

1. The radial angle calculated in step 5.5 after the self-expansion is given by the symbol ∪, which represents the union of the sets on both sides of the symbol, and max(ρ(i,j),ρ after (i,j)) represents the expression for ρ(i,j) and ρ after Compare (i,j) and take the element with the largest modulus value. ρ(i,j) is the optimal time-frequency distribution, and its value has been initialized in step 5.

1. after (i,j) represents the extended time-frequency domain filtering result calculated in step 5.

7. After completing the above steps, let Φ before =Φ after , ρ(i,j)=ρ max (i,j), and return to step 5.5; Step 5.10: Determine whether the following conditions are true: flag1>0 Here, flag1 is a flag that controls the radial angle direction of the extended term. Its value has been initialized in step 5.

1. If the condition is true, set flag1 = -1 and return to step 5.5; if the condition is false, set flag1 = 1 and proceed to step 5.

11. Step 5.11: Let p = p + 1, and determine whether the following conditions are true: p > P Where p is the initial radial angle of the term. The discrete index is P, which is the number of initial radial angles of the self-term estimated in step 3.

3. If the condition is met, step 5 ends and the optimal time-frequency distribution ρ(i,j) of the signal to be detected is obtained. If the condition is not met, return to step 5.3.

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