A method for extracting instantaneous frequency of pulse signal based on time-frequency distribution-improved Hough transform

Abstract

The application discloses a kind of based on time-frequency distribution-improved Hough transform combination pulse signal instantaneous frequency extraction method.The method includes the following steps: obtaining the signal sampling data sequence to be processed, the time-frequency distribution of signal sampling data sequence to be processed is calculated;Single-frequency signal is detected based on time-frequency distribution, its frequency parameter is estimated and single-frequency signal instantaneous frequency is extracted based on frequency parameter, to estimate the time range possibly existing of frequency modulation signal;Frequency modulation signal detection is carried out in the time range possibly existing of frequency modulation signal, the signal type detected is judged and its frequency parameter is estimated, frequency modulation signal instantaneous frequency is extracted based on frequency parameter, the detected frequency modulation signal is removed, and frequency modulation signal detection is continued until all frequency modulation signals are detected.The method can extract single-frequency and frequency modulation signal instantaneous frequency under the condition that single-frequency and frequency modulation signal time-frequency are connected, and is also applicable under low signal-to-noise ratio and non-Gaussian white noise conditions.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, specifically relating to a method for extracting the instantaneous frequency of a combined pulse signal based on time-frequency distribution and improved Hough transform. Background Technology

[0002] Interception and detection of underwater acoustic pulse signals, along with parameter estimation, are key technologies in underwater acoustic information countermeasures. Extracting the instantaneous frequency of the underwater acoustic pulse signal is an important method for interception and detection. Since the instantaneous frequency is represented by a ridge in the time-frequency distribution, extracting the ridge can estimate the instantaneous frequency. Therefore, the instantaneous frequency of the underwater acoustic pulse signal can be extracted through time-frequency analysis. A signal composed of a combination of single-frequency and frequency-modulated signals is a type of underwater acoustic pulse signal.

[0003] Currently, scholars both domestically and internationally have conducted extensive research on algorithms for extracting the instantaneous frequency of underwater acoustic pulse signals. However, in practice, there are combined pulse signals where single-frequency and frequency-modulated (FM) signals are intersected in time and frequency. These are signals where the termination frequency (start frequency) and termination time (start time) of the FM signal are very close to the frequency and start time (end time) of the single-frequency signal. If the classic time-frequency distribution peak extraction algorithm is used to estimate the instantaneous frequency of such signals, the following problem arises: after estimating the termination frequency of the FM (single-frequency) signal, due to the continuity of instantaneous frequency, the instantaneous frequency will continue to be estimated, and the instantaneous frequency of the single-frequency (FM) signal will be treated as part of the instantaneous frequency of the FM (single-frequency) signal. This will lead to the single-frequency (FM) signal being undetectable, and the estimation result of the instantaneous frequency of the FM (single-frequency) signal will have a large error. This type of signal can be modeled as a special instantaneous frequency intersection signal: the instantaneous frequency curves of each signal can be approximated as intersecting, except that the intersection point approximately coincides with the end of the curve.

[0004] There are many instantaneous frequency estimation algorithms for signals with intersecting instantaneous frequencies, which can be broadly classified into two categories based on their algorithmic ideas:

[0005] (1) First, multiple time-frequency ridges are extracted using only the continuity of instantaneous frequency. Then, the intersection time of instantaneous frequencies is found. Finally, the ridges are reconstructed based on the rate of change of each ridge at the intersection time. Representative algorithms include ridge path reconstruction and automatic ridge extraction. Although this algorithm can accurately estimate the instantaneous frequency of the intersecting signal when the signal-to-noise ratio is low and the number, type, and duration of the signal are unknown, this algorithm fails for the signal to be processed in this patent. The reason is that the signal to be processed has only one time-frequency ridge within its duration. Therefore, after extracting the time-frequency ridge using only the continuity of instantaneous frequency, the algorithm terminates and does not find the intersection time or reconstruct the ridge.

[0006] (2) If the peak points of two time-frequency distributions have a small difference in time and frequency and are in the same direction, then the two peak points are considered to be on the same signal and can be connected. Otherwise, they are considered not to be on the same signal and are not connected. This indicates that the algorithm has automatic ridgeline tracking prediction and improved component connection algorithm. This algorithm has the following advantages: it can accurately estimate the instantaneous frequency of intersecting signals when the number, type, and duration of signals are unknown. However, it also has the following disadvantages: ① It is difficult to accurately and quickly estimate the direction of the peak points of the time-frequency distribution under low signal-to-noise ratio conditions. ② For the signal to be processed, the direction of the peak points of the time-frequency distribution does not change suddenly with time in the vicinity of the single-frequency modulation time-frequency junction area, but changes gradually. Therefore, the peak points of the time-frequency distributions of different signals in the vicinity of the single-frequency modulation time-frequency junction area may still be connected, which may lead to errors in the instantaneous frequency estimation. Summary of the Invention

[0007] The purpose of this invention is to propose a method for extracting the instantaneous frequency of a combined pulse signal based on time-frequency distribution-improved Hough transform. By using the proposed time-frequency distribution-improved Hough transform algorithm, the instantaneous frequencies of the single-frequency and frequency-modulated signals can still be extracted separately when the time and frequency of the single-frequency and frequency-modulated signals are connected.

[0008] The technical solution to achieve the purpose of this invention is: a method for extracting the instantaneous frequency of a combined pulse signal based on time-frequency distribution and improved Hough transform, comprising the following steps:

[0009] Obtain the sampled data sequence of the signal to be processed, and calculate the time-frequency distribution of the sampled data sequence of the signal to be processed;

[0010] Based on the detection of single-frequency signals by time-frequency distribution, if a single-frequency signal is detected, its frequency parameters are estimated and the instantaneous frequency of the single-frequency signal is extracted based on the frequency parameters, thereby estimating the possible time range of the frequency-modulated signal; otherwise, the possible time range of the frequency-modulated signal is directly estimated.

[0011] If the possible time range of the FM signal is an empty set, directly output the instantaneous frequency extraction result of the single-frequency signal. Otherwise, perform FM signal detection within the possible time range of the FM signal. If no FM signal is detected, directly output the instantaneous frequency extraction result of the single-frequency signal or no signal is detected. Otherwise, determine the type of the detected signal and estimate its frequency parameters. Extract the instantaneous frequency of the FM signal based on the frequency parameters, remove the detected FM signal, and continue FM signal detection until all FM signals are detected. Finally, output the instantaneous frequency extraction results of the single-frequency and FM signals or the instantaneous frequency extraction result of the FM signal.

[0012] Further, the sampled data sequence s(a) of the signal to be processed is obtained, where a is the discrete index of the signal time quantity, specifically including the following steps:

[0013] Receive data and signal sampling frequency f from N sampling points from the active sonar system. s The collected data is used as the sampling data sequence s(a) of the signal to be processed, where a is the discrete index of the signal time quantity, which is a non-negative integer and 0≤a≤N-1, and N is the number of sampling points corresponding to the entire signal duration, which is a positive integer not less than 800.

[0014] Furthermore, the time-frequency distribution S of the sampled data sequence of the signal to be processed is calculated. w (n,k), where n and k are S w The (n,k) time and frequency discrete index includes the following steps:

[0015] (2-1) Initialize the parameters for calculating the time-frequency distribution, specifically including the initialization of the following parameters:

[0016] (1) The length M of the Gaussian window function is initialized to a positive integer of max{ceil(0.1N),200}≤M≤floor(0.25N), where max{·} is the maximum value function, ceil(·) is the floor function, floor(·) is the floor function, and N is the number of sampling points defined in step 1;

[0017] (2) The Gaussian window function factor α0 is initialized to a positive real number of 5 ≤ α0 ≤ 12.5;

[0018] (3) Gaussian window function w g (m) is initialized as: Where m is the discrete index of the time quantity of the window function, and is a non-negative integer;

[0019] (4) Length N of the non-overlapping portion of the window function step Initialize as: 1≤N step A positive integer ≤ floor(0.01N);

[0020] (5) Number of sampling points N on the time axis of the time-frequency distribution t Initialized to: N t =floor(N / N) step );

[0021] (6) Number of sampling points N for time-frequency distribution frequency axis f Initialize to:

[0022] (2-2) Pad the beginning and end of the sampled data sequence s(a) of the signal to be processed with zeros to obtain the zero-padding sampled data sequence s zerofill (a zerofill ):

[0023] szerofill (a zerofill ) = zero start,end {s(a),round(0.5M)}

[0024] Where zero start,end {s(a),round(0.5M)} means padding s(a) with round(0.5M) zeros at the beginning and end, where round(·) is the rounding function. zerofill The zero-padded discrete index of the signal time quantity is an integer that satisfies -round(0.5M)≤a zerofill ≤N-1+round(0.5M);

[0025] (2-3) Calculate the zero-padded signal sampling data sequence s zerofill (a zerofill The time-frequency distribution S w (n,k):

[0026]

[0027] Where |.| is the modulus operator for complex numbers, and j is the imaginary unit, i.e., j 2 =-1, n and k are S w (n,k) are discrete indices for time and frequency quantities, both of which are non-negative integers.

[0028] Furthermore, based on the time-frequency distribution S w The detection of a single-frequency signal (n,k) specifically includes the following steps:

[0029] (3-1) Initialize the parameters for detecting the single-frequency signal, specifically including the initialization of the following parameters:

[0030] (1) Mean parameter μ of time-frequency distribution TFD Initialize to: Where N t and N f For S initialized in step (2-1) w (n,k) represents the number of sampling points on the time axis and frequency axis, where n and k are Stime and Sfrequency, respectively. w (n,k) Discrete index of time and frequency quantities;

[0031] (2) Time-frequency distribution standard deviation parameter σ TFD Initialize to:

[0032] (3) Threshold of peak point in time-frequency distribution th a Initialized to: th a =μ TFD +σ TFD ;

[0033] (4) The frequency range M0 surrounding the peak point of the time-frequency distribution is initialized as: max{5,ceil(0.015N f )}≤M0≤floor(0.05N f Positive integers;

[0034] (5) Evaluation function for the peak point frequency domain narrowband characteristics of time-frequency distribution: threshold th nb Initialize to: 3 / 2≤th nb Positive real numbers ≤ 5 / 3;

[0035] (6) The time range N0 of the neighborhood of the peak point of the time-frequency distribution is initialized as: max{3,ceil(0.01N) t )}≤N0≤floor(0.03N t Positive integers;

[0036] (7) The maximum allowable value K1 for the peak point jump between adjacent time points is initialized as: max{2,ceil(0.005N f )}≤K1≤floor(0.02N f Positive integers;

[0037] (8) The distance threshold th of other peak points in the neighborhood from the horizontal line passing through the peak point to be evaluated. d1 Initialized to: 0.0025N f ≤th d1 ≤0.01N f Positive real numbers;

[0038] (9) Number of sampling points for the radial distance axis of the Hough transform slice Initialize to: Positive integers;

[0039] (10) The radial distance resolution Δρ of the Hough transform slice is initialized as follows:

[0040] (11) Threshold H for determining the presence of a signal exist Initialized to: 0.02N t ≤H exist ≤0.05N t Positive real numbers;

[0041] (12) The range δρ surrounding the peak point of the Hough transform slice is initialized as follows: Positive integers;

[0042] (3-2) Calculate the binarized time-frequency image B(n,k):

[0043]

[0044] Where diff(·) is the frequency difference operator, diff(S w (n,k))=S w (n,k+1)-S w (n,k);

[0045] (3-3) Calculate the evaluation function ω of the frequency domain narrowband characteristics of the time-frequency distribution peak point. nb (n,k):

[0046]

[0047] in This is the average value of the surrounding time-frequency distribution. i is the discrete index of the frequency surrounding the peak point, which is a positive integer, and min{·} is the function to find the minimum value;

[0048] (3-4) Set the neighborhood Ψ(n,k) of the time-frequency point (n,k):

[0049]

[0050] Where i1 and j1 are discrete indices of time and frequency within the neighborhood, respectively, and are non-zero integers;

[0051] (3-5) Evaluate the continuity of the peak points of the single-frequency signal and generate the characteristic image B of the peak points of the single-frequency signal. char_cw (n,k):

[0052]

[0053] (3-6) Calculate the Hough transform slice SH at a radial angle of π / 2. CW (ρ1):

[0054]

[0055] Where ρ1 is the discrete index of the radial distance of the Hough transform slice, which is a non-negative integer, and δ(·) is the delta function, expressed as:

[0056]

[0057] Where x is a real number;

[0058] (3-7) Initialize the single-frequency signal number p: p = 1;

[0059] (3-8) Calculate the maximum value of the slice in the improved Hough transform. h_max1 :th h_max1 =max{SH CW (ρ1)};

[0060] (3-9) Determine whether a single-frequency signal exists, i.e., determine whether the following conditions are met:

[0061] th h_max1 ≥H exist

[0062] If the condition is met, proceed to step (3-10); otherwise, proceed to step (3-13).

[0063] (3-10) Estimate the frequency parameter f of the p-th single-frequency signal cw (p):

[0064]

[0065] Where f s ρ is the signal sampling frequency defined in step 1. p For the p-th single-frequency signal, the peak point of the Hough transform slice is... in A function to find the maximum value of ρ;

[0066] (3-11) Remove the peak point and surrounding area of ​​the Hough transform slice of the p-th single-frequency signal:

[0067]

[0068] (3-12) Update the value of the single-frequency signal number p to p+1, and return to step (3-8);

[0069] (3-13) Calculate the number P of detected single-frequency signals, taking the value as p-1, and determine whether the following condition is true:

[0070] P > 0

[0071] If the condition is met, a single-frequency signal is considered to exist, and its instantaneous frequency is extracted based on the frequency parameters of the single-frequency signal; otherwise, the possible time range of the frequency modulation signal is directly estimated.

[0072] Furthermore, based on the estimated single-frequency signal frequency parameter f cw (p) Extract its instantaneous frequency, and record the extraction result as . Where Δt is S w (n,k) time resolution specifically includes the following steps:

[0073] (4-1) Initialize the parameters for extracting the instantaneous frequency of the single-frequency signal, specifically including the initialization of the following parameters:

[0074] (1) The time-frequency distribution frequency resolution Δf is initialized as: Δf = 0.5f s / (N f -1), where f sN is the signal sampling frequency defined in step 1. f The number of sampling points for the time-frequency distribution frequency axis initialized in step (2-1);

[0075] (2) The time-frequency distribution narrowband bandwidth δf is initialized as: max{2,ceil(0.0075N f )}≤δf≤floor(0.02N f Positive integers;

[0076] (3) Threshold th, a function for evaluating the peak characteristics of a single-frequency signal ω_cw Initialized as: 0.4≤th ω_cw Positive real numbers ≤ 0.6;

[0077] (4) The time resolution Δt of the time-frequency distribution is initialized as: Δt = N / (f s N t ), where N is the number of sampling points defined in step 1, N t This is the number of time axis sampling points for the time-frequency distribution initialized in step (2-1);

[0078] (4-2) Update the single-frequency signal number p: p = 1;

[0079] (4-3) Using the estimated frequency parameter f of the p-th single-frequency signal cw (p) Setting the time-frequency narrowband Ω cw :

[0080]

[0081] Where n and k are S in step (2-3) respectively. w (n,k) Discrete index of time and frequency quantities;

[0082] (4-4) Finding the time-frequency narrowband Ω cw The peak points of the time-frequency distribution that satisfy the peak point characteristics of a single-frequency signal are found within the range of the single-frequency signal, i.e., the existence function κ of the single-frequency signal is calculated. cw (n):

[0083]

[0084] Among them B char_cw (n,k) is the peak point characteristic image of the single-frequency signal generated in step (3-5);

[0085] (4-5) Let p be the index of the ridge segment number of the single-frequency signal within the time-frequency narrowband. R =1, discrete-time index n1=0;

[0086] (4-6) Determine whether a certain moment is the start time of a ridge segment, that is, determine whether the following conditions are met:

[0087] (κ cw (n1)=0 and κ cw (n1+1)=1) or (κ) cw (n1) = 1 and n1 = 0)

[0088] If true, then let the p-th... R Ridge segment start time Update p R The value of is p R +1, then proceed to step (4-7); otherwise, proceed directly to step (4-7).

[0089] (4-7) Judge n1≥N t If -1 is true, proceed to step (4-8); otherwise, update the value of n1 to n1+1 and return to step (4-6).

[0090] (4-8) Calculate the number of ridge segments of the p-th single-frequency signal.

[0091] (4-9) Update the index p of the ridge segment number of the single-frequency signal within the time-frequency narrowband. R =1;

[0092] (4-10) Update the discrete-time index

[0093] (4-11) Calculate the p-th... R The termination time of a ridge segment is determined by checking whether the following conditions are met:

[0094] (κ cw (n1)=1 and κ cw (n1+1)=0) or (κ) cw (n1) = 1 and n1 = N t -1)

[0095] If this is not true, proceed to step (4-12); otherwise, let the p-th... R Termination time of the ridge line segment Determine p R Is it not less than If true, proceed to step (4-13); otherwise, update p. R The value is p R +1, return to step (4-10);

[0096] (4-12) Update the value of n1 to n1+1, and return to step (4-11);

[0097] (4-13) Extract the instantaneous frequency of the p-th single-frequency signal

[0098]

[0099] Where D cw (p) represents the time range of the p-th single-frequency signal, satisfying:

[0100]

[0101] in For set D i The union of sets i = 1, 2, ..., I, where I is the number of sets;

[0102] (4-14) Determine whether the following conditions are true:

[0103] p = P

[0104] Where P is the number of single-frequency signals detected in step (3-13). If it is true, it is considered that the instantaneous frequency of all single-frequency signals has been extracted and the possible time range of the frequency modulation signal is estimated. Otherwise, the single-frequency signal number p is updated and the value is p+1, and the process returns to step (4-3).

[0105] Furthermore, the possible time range D of the FM signal is estimated. fm_p Specifically, it includes the following steps:

[0106] Calculate the possible time range D of the frequency modulation signal. fm_p If the number of detected single-frequency signals P = 0, then D fm_p The calculation is as follows:

[0107] D fm_p ={n|0≤n≤N t -1},

[0108] Otherwise D fm_p The calculation is as follows:

[0109]

[0110] Where n is the value of S in step (2-3) w (n,k) time-discrete index, D cw (p) represents the time range of the p-th single-frequency signal given in step (4-13). The number of detected frequency modulation signals Q is calculated. If the value is 0, the instantaneous frequency extraction result is directly output. Otherwise, frequency modulation signal detection is performed within the time range in which the frequency modulation signal may exist, the type of the detected signal is determined, and its frequency parameters are estimated.

[0111] Furthermore, frequency modulation (FM) signal detection is performed within the possible time range of the FM signal, the type of the detected signal is determined, and its frequency parameters are estimated. If it is determined to be a linear frequency modulation (LFM) signal, the estimated frequency parameters are denoted as [f]. 1_L,μ], where f 1_L Let f be the starting frequency of the linear frequency modulated signal, and μ be the modulation frequency. If the signal is determined to be a hyperbolic frequency modulated signal, then the estimated frequency parameters are [f]. 1_H ,k c ], where f 1_H k is the starting frequency of the hyperbolic frequency modulated signal. c The periodic slope is based on the estimated frequency modulation signal frequency parameter [f]. 1_L ,μ] or [f 1_H ,k c Extract its instantaneous frequency, and record the result as follows: Where q is the frequency modulation signal number, the detected frequency modulation signal is removed, and frequency modulation signal detection continues until all frequency modulation signals are detected. The specific steps include:

[0112] (6-1) Initialize the parameters of the detected FM signal, specifically including the initialization of the following parameters:

[0113] (1) Number of straight line inclination angles N Θ Initialized to: N Θ Even numbers ≥ 28;

[0114] (2) The distance threshold th from the remaining peak points in the neighborhood to the oblique line passing through the peak point to be evaluated. d2 Initialize to: positive real numbers, where N t and N f These are the number of sampling points for the time axis and frequency axis of the time-frequency distribution initialized in step (2-1), respectively.

[0115] (3) Instantaneous lower limit of frequency modulation signal Initialized to: 0.01f s ≤f i min ≤0.05f s positive real numbers, where f s The signal sampling frequency defined in step 1;

[0116] (4) Number of sampling points M on the reciprocal frequency axis r Initialize to: A positive integer, where Δf is the time resolution of the time-frequency distribution initialized in step (4-1);

[0117] (5) Frequency reciprocal axis resolution Δf r Initialize to:

[0118] (6) Hough transform of the peak point characteristic image of the frequency modulation signal, number of sampling points N on the radial distance axis ρ Initialize to: Even numbers;

[0119] (7) Hough transform of the peak point characteristic image of the frequency modulation signal, number of sampling points N on the radial angle axis θ Initialized to: N θ Even numbers ≥ 90;

[0120] (8) Hough transform of the peak point characteristic image of the reciprocal time-frequency domain frequency-modulated signal, number of radial distance axis sampling points Initialize to: Even numbers;

[0121] (9) Hough transform of radial angle axis sampling points of the peak point characteristic image of the reciprocal time-frequency domain frequency-modulated signal Initialize to: Even numbers;

[0122] (10) Radial distance resolution Δρ of the peak point characteristic image of frequency modulation signal L Initialize to:

[0123] (11) Radial distance resolution Δρ of peak point characteristic image of reciprocal time-frequency domain frequency-modulated signal H Initialize to:

[0124] (12) Evaluation function threshold th for peak point characteristics of frequency modulation signal ω_fm Initialized as: 0.4≤th ω_fm Positive real numbers ≤ 0.6;

[0125] (6-2) Initialize the frequency modulation signal number q: q = 1;

[0126] (6-3) Evaluate the continuity of the FM signal peak points and generate the FM signal peak point characteristic image B. char_fm (n,k):

[0127]

[0128] d2(i1,j1)=|j1-tan(πb / (N Θ +2))i1||cos(πb / (NΘ+2))|

[0129] Where Num(πb / (N Θ +2)) To determine if there exists a neighboring region Ψ(n,k) that is more than or equal to the peak point (n,k) to be evaluated and has a tilt angle of πb / (N) Θ The distance d2(i1,j1) of the straight line +2) does not exceed th d2 The number of peak points, b is the tilt angle, the discrete index, is a positive integer, 1≤b≤N. Θ+1 and b≠0.5N Θ +1, N0 is the time range of the neighborhood of the peak point of the time-frequency distribution, i1 and j1 are the discrete indices of the neighborhood time and frequency, respectively, the neighborhood Ψ(n,k) and N0, i1 and j1 have been set in step (3-4), ω nb (n,k) is the frequency domain narrowband characteristic evaluation function of the time-frequency distribution peak point calculated in step (3-3), where n and k are the values ​​of S in step (2-3). w (n,k) Discrete index of time and frequency quantities, D fm_p The possible time range of the frequency modulation signal calculated in step 5; (6-4) Based on the peak point characteristic image B of the frequency modulation signal. char_fm (n,k) Generates peak point characteristic image of time-frequency reciprocal domain frequency modulated signal. Where round(f i min / Δf)≤k≤N f -1, 0≤k1≤M r -1:

[0130]

[0131] Where k1 is the discrete index of the reciprocal of the frequency, and is a non-negative integer;

[0132] (6-5) Image B of the peak point characteristic of the frequency modulation signal char_fm Image of peak point characteristics of (n,k) and reciprocal time-frequency domain frequency-modulated signal Perform improved Hough transforms (SH) separately LFM (ρ,θ) and SH HFM (ρ,θ):

[0133]

[0134] -0.5N ρ +1≤ρ≤0.5N ρ -0.5N θ +1≤θ≤0.5N θ

[0135]

[0136] Where ρ and θ are discrete indices for radial distance and angle in the improved Hough transform, and are both integers;

[0137] (6-6) Determine whether all FM signals have been detected, i.e., determine whether the following condition is met:

[0138] max{max{SH LFM (ρ,θ)},max{SH HFM (ρ,θ)}}≥Hexist

[0139] Where H exist The threshold for determining the presence of the signal initialized in step (3-1) is used. If the threshold is met, proceed to step (6-7); otherwise, calculate the number of detected frequency modulation signals Q, with a value of q-1, and output the instantaneous frequency extraction results of the single-frequency signal and the frequency modulation signal.

[0140] (6-7) Determine whether the detected signal is a linear frequency modulated signal, that is, determine whether the following conditions are met:

[0141] max{SH LFM (ρ,θ)}>max{SH HFM (ρ,θ)}

[0142] If true, then the signal is a linear frequency modulated signal. Calculate SH. LFM The maximum value of (ρ,θ) corresponds to the peak point (ρ). 0L ,θ 0L ): The frequency parameters, namely the starting frequency and modulation frequency of the linear frequency modulated signal, are estimated as follows:

[0143]

[0144] Where Δt is the time resolution of the time-frequency distribution initialized in step (4-1);

[0145] If this condition is not met, then the signal is determined to be a hyperbolic frequency modulated signal. Calculate SH. HFM The maximum value of (ρ,θ) corresponds to the peak point (ρ). 0H ,θ 0H ): The frequency parameters, namely the starting frequency and period slope of the hyperbolic FM signal, are estimated as follows:

[0146]

[0147] (6-8) Use the frequency parameter of the qth frequency modulation signal to set the time-frequency narrowband Ω fm :

[0148]

[0149] Where n and k are S in step (2-3) respectively. w (n,k) Discrete index of time and frequency quantities, D fm_p The time range within which the frequency-modulated signal might exist, as calculated in step 5. Let n be the estimated instantaneous frequency of the assumed signal at time n, satisfying:

[0150]

[0151] Where Δf, Δt, and δf are the frequency resolution, time resolution, and narrowband bandwidth of the time-frequency distribution initialized in step (4-1), respectively;

[0152] (6-9) Find the time-frequency distribution peak points within the time-frequency narrow band that satisfy the peak point characteristics of the frequency-modulated signal, i.e., calculate the existence function κ of the frequency-modulated signal. fm (n):

[0153]

[0154] (6-10) Let the index of the ridge segment number of the frequency modulation signal in the time-frequency narrowband be q. R =1, discrete-time index n1=0;

[0155] (6-11) Determine whether a certain moment is the start time of a ridge segment, that is, determine whether the following conditions are met:

[0156] (κ fm (n1)=0 and κ fm (n1+1)=1) or (κ) fm (n1) = 1 and n1 = 0)

[0157] If true, then let the q-th... R Ridge segment start time Update q R The value of q R +1, then proceed to step (6-12); otherwise, proceed directly to step (6-12).

[0158] (6-12) Judge n1≥N t If -1 is true, proceed to step (6-13); otherwise, update the value of n1 to n1+1 and return to step (6-11).

[0159] (6-13) Calculate the number of ridge segments of the q-th frequency modulated signal.

[0160] (6-14) Update the index q of the ridge segment number of the frequency modulation signal within the narrow band. R =1;

[0161] (6-15) Update the discrete-time index

[0162] (6-16) Calculate the q-th... R The termination time of a ridge segment is determined by checking whether the following conditions are met:

[0163] (κ fm (n1)=1 and κ fm (n1+1)=0) or (κ) fm(n1) = 1 and n1 = N t -1)

[0164] If not, proceed to step (6-17); otherwise, let the q-th... R Termination time of the ridge line segment Determine q R Is it not less than If true, proceed to step (6-18); otherwise, update q. R The value of q R +1, return to step (6-15);

[0165] (6-17) Update the value of n1 to n1+1, and return to step (6-16);

[0166] (6-18) Extract the instantaneous frequency of the q-th frequency-modulated signal.

[0167]

[0168] Where D fm (q) represents the time range in which the q-th frequency-modulated signal exists, satisfying:

[0169]

[0170] (6-19) Characteristic image B at the peak point of the frequency modulation signal char_fm Remove the q-th frequency modulation signal from (n,k), i.e., B char_fm (n,k)=0, where n and k satisfy:

[0171]

[0172] Update the value of the FM signal number q to q+1, and return to step (6-4) to continue the FM signal detection.

[0173] Furthermore, the instantaneous frequency extraction results of the output single-frequency and frequency-modulated signals specifically include:

[0174] If P=0 and Q=0, then output "No signal detected";

[0175] If P > 0 and Q = 0, then the instantaneous frequency of the output single-frequency signal is...

[0176] If P = 0 and Q > 0, then the instantaneous frequency of the output frequency modulation signal is...

[0177] If P > 0 and Q > 0, then the instantaneous frequencies of the output single-frequency signal and frequency-modulated signal are... and

[0178] Where Δt is the time resolution of the time-frequency distribution initialized in step (4-1), p is the single-frequency signal number, 1≤p≤P, P is the number of single-frequency signals detected in step (3-13), q is the frequency modulation signal number, 1≤q≤Q, and Q is the number of frequency modulation signals detected in step (6-6).

[0179] A system for extracting the instantaneous frequency of a combined pulse signal based on time-frequency distribution-improved Hough transform is provided. The system implements the aforementioned method for extracting the instantaneous frequency of a combined pulse signal based on time-frequency distribution-improved Hough transform, achieving the extraction of the instantaneous frequency of the combined pulse signal based on time-frequency distribution-improved Hough transform, including:

[0180] Module 1: Acquire the sampled data sequence of the signal to be processed and calculate the time-frequency distribution of the sampled data sequence of the signal to be processed;

[0181] Module 2: Detect single-frequency signals based on time-frequency distribution. If a single-frequency signal is detected, estimate its frequency parameters and extract the instantaneous frequency of the single-frequency signal based on the frequency parameters, thereby estimating the possible time range of the frequency-modulated signal. Otherwise, directly estimate the possible time range of the frequency-modulated signal.

[0182] Module 3: If the time range in which the FM signal may exist is an empty set, directly output the instantaneous frequency extraction result of the single-frequency signal. Otherwise, perform FM signal detection within the time range in which the FM signal may exist. If no FM signal is detected, directly output the instantaneous frequency extraction result of the single-frequency signal or no signal is detected. Otherwise, determine the type of the detected signal and estimate its frequency parameters. Extract the instantaneous frequency of the FM signal based on the frequency parameters, remove the detected FM signal, and continue to perform FM signal detection until all FM signals are detected. Finally, output the instantaneous frequency extraction results of the single-frequency and FM signals or the instantaneous frequency extraction result of the FM signal.

[0183] Compared with the prior art, the significant advantages of this invention are:

[0184] 1. The instantaneous frequency extraction algorithm of this invention achieves the separation of single-frequency and frequency-modulated (FM) signals. It utilizes Hough transform to first detect the single-frequency signal and then the FM signal, thereby achieving separation. This signal separation method leverages the different characteristics of single-frequency and FM signals in the Hough domain. Specifically, the Hough transform of the time-frequency image of a single-frequency signal has an energy focusing region only around a radial angle of π / 2, while the Hough transform of the time-frequency image of an FM signal has energy focusing regions at other radial angles. This avoids complex ridge reconstruction and estimation of the peak point direction of the time-frequency distribution, thus accurately separating single-frequency and FM signals even when they are contiguous.

[0185] 2. The instantaneous frequency extraction algorithm of this invention can improve the accuracy of instantaneous frequency estimation. Because the characteristics of signal peak points are evaluated, pseudo-time-frequency distribution peak points caused by noise are removed, and signal peak points are retained. Therefore, this instantaneous frequency extraction method can guarantee estimation accuracy even under low signal-to-noise ratio and non-Gaussian white noise conditions. Attached Figure Description

[0186] Figure 1 This is a schematic diagram of the instantaneous frequency extraction method for combined pulse signals based on time-frequency distribution and improved Hough transform proposed in this invention;

[0187] Figure 2 The time-frequency distribution of the signal in Example 1;

[0188] Figure 3 This is an improved Hough transform slice from Example 1;

[0189] Figure 4 The instantaneous frequency curve of the single-frequency signal in Example 1;

[0190] Figure 5 An improved Hough transform for the time-frequency domain image of Example 1;

[0191] Figure 6 An improved Hough transform for the t-1 / f domain image of Example 1;

[0192] Figure 7 The instantaneous frequency curve of the frequency-modulated signal from 0 to 1.17s in Example 1;

[0193] Figure 8 The instantaneous frequency curve of the combined pulse signal in Example 1 is shown. Detailed Implementation

[0194] To better understand the purpose, structure, and function of this invention, the invention will be further described below with reference to the accompanying drawings.

[0195] like Figure 1 As shown, the present invention provides a method for extracting the instantaneous frequency of a combined pulse signal based on time-frequency distribution and improved Hough transform, comprising the following steps:

[0196] Obtain the sampled data sequence of the signal to be processed, and calculate the time-frequency distribution of the sampled data sequence of the signal to be processed;

[0197] Based on the detection of single-frequency signals by time-frequency distribution, if a single-frequency signal is detected, its frequency parameters are estimated and the instantaneous frequency of the single-frequency signal is extracted based on the frequency parameters, thereby estimating the possible time range of the frequency-modulated signal; otherwise, the possible time range of the frequency-modulated signal is directly estimated.

[0198] If the possible time range of the FM signal is an empty set, directly output the instantaneous frequency extraction result of the single-frequency signal. Otherwise, perform FM signal detection within the possible time range of the FM signal. If no FM signal is detected, directly output the instantaneous frequency extraction result of the single-frequency signal or no signal is detected. Otherwise, determine the type of the detected signal and estimate its frequency parameters. Extract the instantaneous frequency of the FM signal based on the frequency parameters, remove the detected FM signal, and continue FM signal detection until all FM signals are detected. Finally, output the instantaneous frequency extraction results of the single-frequency and FM signals or the instantaneous frequency extraction result of the FM signal.

[0199] Further, the sampled data sequence s(a) of the signal to be processed is obtained, where a is the discrete index of the signal time quantity, specifically including the following steps:

[0200] Receive data and signal sampling frequency f from N sampling points from the active sonar system. s The collected data is used as the sampling data sequence s(a) of the signal to be processed, where a is the discrete index of the signal time quantity, which is a non-negative integer and 0≤a≤N-1, and N is the number of sampling points corresponding to the entire signal duration, which is a positive integer not less than 800.

[0201] Furthermore, the time-frequency distribution S of the sampled data sequence of the signal to be processed is calculated. w (n,k), where n and k are S w The (n,k) time and frequency discrete index includes the following steps:

[0202] (2-1) Initialize the parameters for calculating the time-frequency distribution, specifically including the initialization of the following parameters:

[0203] (1) The length M of the Gaussian window function is initialized to a positive integer of max{ceil(0.1N),200}≤M≤floor(0.25N), where max{·} is the maximum value function, ceil(·) is the floor function, floor(·) is the floor function, and N is the number of sampling points defined in step 1;

[0204] (2) The Gaussian window function factor α0 is initialized to a positive real number of 5 ≤ α0 ≤ 12.5;

[0205] (3) Gaussian window function w g (m) is initialized as: 0 ≤ m ≤ M-1, where m is the discrete index of the time quantity of the window function, and is a non-negative integer;

[0206] (4) Length N of the non-overlapping portion of the window function step Initialize as: 1≤N step A positive integer ≤ floor(0.01N);

[0207] (5) Number of sampling points N on the time axis of the time-frequency distribution t Initialized to: N t =floor(N / N) step );

[0208] (6) Number of sampling points N for time-frequency distribution frequency axis f Initialize to:

[0209] (2-2) Pad the beginning and end of the sampled data sequence s(a) of the signal to be processed with zeros to obtain the zero-padding sampled data sequence s zerofill (a zerofill ):

[0210] s zerofill (a zerofill ) = zero start,end {s(a),round(0.5M)}

[0211] Where zero start,end {s(a),round(0.5M)} means padding s(a) with round(0.5M) zeros at the beginning and end, where round(·) is the rounding function. zerofill The zero-padded discrete index of the signal time quantity is an integer that satisfies -round(0.5M)≤a zerofill ≤N-1+round(0.5M);

[0212] (2-3) Calculate the zero-padded signal sampling data sequence s zerofill (a zerofill The time-frequency distribution S w (n,k):

[0213]

[0214] Where |.| is the modulus operator for complex numbers, and j is the imaginary unit, i.e., j 2 =-1, n and k are S w (n,k) are discrete indices for time and frequency quantities, both of which are non-negative integers.

[0215] Furthermore, based on the time-frequency distribution S w The detection of a single-frequency signal (n,k) specifically includes the following steps:

[0216] (3-1) Initialize the parameters for detecting the single-frequency signal, specifically including the initialization of the following parameters:

[0217] (1) Mean parameter μ of time-frequency distribution TFD Initialize to: Where Nt and N f For S initialized in step (2-1) w (n,k) represents the number of sampling points on the time axis and frequency axis, where n and k are Stime and Sfrequency, respectively. w (n,k) Discrete index of time and frequency quantities;

[0218] (2) Time-frequency distribution standard deviation parameter σ TFD Initialize to:

[0219] (3) Threshold of peak point in time-frequency distribution th a Initialized to: th a =μ TFD +σ TFD ;

[0220] (4) The frequency range M0 surrounding the peak point of the time-frequency distribution is initialized as: max{5,ceil(0.015N f )}≤M0≤floor(0.05N f Positive integers;

[0221] (5) Evaluation function for the peak point frequency domain narrowband characteristics of time-frequency distribution: threshold th nb Initialize to: 3 / 2≤th nb Positive real numbers ≤ 5 / 3;

[0222] (6) The time range N0 of the neighborhood of the peak point of the time-frequency distribution is initialized as: max{3,ceil(0.01N) t )}≤N0≤floor(0.03N t Positive integers;

[0223] (7) The maximum allowable value K1 for the peak point jump between adjacent time points is initialized as: max{2,ceil(0.005N f )}≤K1≤floor(0.02N f Positive integers;

[0224] (8) The distance threshold th of other peak points in the neighborhood from the horizontal line passing through the peak point to be evaluated. d1 Initialized to: 0.0025N f ≤th d1 ≤0.01N f Positive real numbers;

[0225] (9) Number of sampling points for the radial distance axis of the Hough transform slice Initialize to: Positive integers;

[0226] (10) The radial distance resolution Δρ of the Hough transform slice is initialized as follows:

[0227] (11) Threshold H for determining the presence of a signal exist Initialized to: 0.02N t ≤H exist ≤0.05N t Positive real numbers;

[0228] (12) The range δρ surrounding the peak point of the Hough transform slice is initialized as follows: Positive integers;

[0229] (3-2) Calculate the binarized time-frequency image B(n,k):

[0230]

[0231] Where diff(·) is the frequency difference operator, diff(S w (n,k))=S w (n,k+1)-S w (n,k);

[0232] (3-3) Calculate the evaluation function ω of the frequency domain narrowband characteristics of the time-frequency distribution peak point. nb (n,k):

[0233]

[0234] in This is the average value of the surrounding time-frequency distribution. i is the discrete index of the frequency surrounding the peak point, which is a positive integer, and min{·} is the function to find the minimum value;

[0235] (3-4) Set the neighborhood Ψ(n,k) of the time-frequency point (n,k):

[0236]

[0237] Where i1 and j1 are discrete indices of time and frequency within the neighborhood, respectively, and are non-zero integers;

[0238] (3-5) Evaluate the continuity of the peak points of the single-frequency signal and generate the characteristic image B of the peak points of the single-frequency signal. char_cw (n,k):

[0239]

[0240] (3-6) Calculate the Hough transform slice SH at a radial angle of π / 2. CW (ρ1):

[0241]

[0242] Where ρ1 is the discrete index of the radial distance of the Hough transform slice, which is a non-negative integer, and δ(·) is the delta function, expressed as:

[0243]

[0244] Where x is a real number;

[0245] (3-7) Initialize the single-frequency signal number p: p = 1;

[0246] (3-8) Calculate the maximum value of the slice in the improved Hough transform. h_max1 :th h_max1 =max{SH CW (ρ1)};

[0247] (3-9) Determine whether a single-frequency signal exists, i.e., determine whether the following conditions are met:

[0248] th h_max1 ≥H exist

[0249] If the condition is met, proceed to step (3-10); otherwise, proceed to step (3-13).

[0250] (3-10) Estimate the frequency parameter f of the p-th single-frequency signal cw (p):

[0251]

[0252] Where f s ρ is the signal sampling frequency defined in step 1. p For the p-th single-frequency signal, the peak point of the Hough transform slice is... in A function to find the maximum value of ρ;

[0253] (3-11) Remove the peak point and surrounding area of ​​the Hough transform slice of the p-th single-frequency signal:

[0254]

[0255] (3-12) Update the value of the single-frequency signal number p to p+1, and return to step (3-8);

[0256] (3-13) Calculate the number P of detected single-frequency signals, taking the value as p-1, and determine whether the following condition is true:

[0257] P > 0

[0258] If the condition is met, a single-frequency signal is considered to exist, and its instantaneous frequency is extracted based on the frequency parameters of the single-frequency signal; otherwise, the possible time range of the frequency modulation signal is directly estimated.

[0259] Furthermore, based on the estimated single-frequency signal frequency parameter f cw (p) Extract its instantaneous frequency, and record the extraction result as . Where Δt is S w (n,k) time resolution specifically includes the following steps:

[0260] (4-1) Initialize the parameters for extracting the instantaneous frequency of the single-frequency signal, specifically including the initialization of the following parameters:

[0261] (1) The time-frequency distribution frequency resolution Δf is initialized as: Δf = 0.5f s / (N f -1), where f s N is the signal sampling frequency defined in step 1. f The number of sampling points for the time-frequency distribution frequency axis initialized in step (2-1);

[0262] (2) The time-frequency distribution narrowband bandwidth δf is initialized as: max{2,ceil(0.0075N f )}≤δf≤floor(0.02N f Positive integers;

[0263] (3) Threshold th, a function for evaluating the peak characteristics of a single-frequency signal ω_cw Initialized as: 0.4≤th ω_cw Positive real numbers ≤ 0.6;

[0264] (4) The time resolution Δt of the time-frequency distribution is initialized as: Δt = N / (f s N t ), where N is the number of sampling points defined in step 1, N t This is the number of time axis sampling points for the time-frequency distribution initialized in step (2-1);

[0265] (4-2) Update the single-frequency signal number p: p = 1;

[0266] (4-3) Using the estimated frequency parameter f of the p-th single-frequency signal cw (p) Setting the time-frequency narrowband Ω cw :

[0267]

[0268] Where n and k are S in step (2-3) respectively. w (n,k) Discrete index of time and frequency quantities;

[0269] (4-4) Finding the time-frequency narrowband Ω cw The peak points of the time-frequency distribution that satisfy the peak point characteristics of a single-frequency signal are found within the range of the single-frequency signal, i.e., the existence function κ of the single-frequency signal is calculated. cw (n):

[0270]

[0271] Among them B char_cw (n,k) is the peak point characteristic image of the single-frequency signal generated in step (3-5);

[0272] (4-5) Let p be the index of the ridge segment number of the single-frequency signal within the time-frequency narrowband. R =1, discrete-time index n1=0;

[0273] (4-6) Determine whether a certain moment is the start time of a ridge segment, that is, determine whether the following conditions are met:

[0274] (κ cw (n1)=0 and κ cw (n1+1)=1) or (κ) cw (n1) = 1 and n1 = 0)

[0275] If true, then let the p-th... R Ridge segment start time Update p R The value of is p R +1, then proceed to step (4-7); otherwise, proceed directly to step (4-7).

[0276] (4-7) Judge n1≥N t If -1 is true, proceed to step (4-8); otherwise, update the value of n1 to n1+1 and return to step (4-6).

[0277] (4-8) Calculate the number of ridge segments of the p-th single-frequency signal.

[0278] (4-9) Update the index p of the ridge segment number of the single-frequency signal within the time-frequency narrowband. R =1;

[0279] (4-10) Update the discrete-time index

[0280] (4-11) Calculate the p-th... R The termination time of a ridge segment is determined by checking whether the following conditions are met:

[0281] (κ cw (n1)=1 and κ cw (n1+1)=0) or (κ) cw(n1) = 1 and n1 = N t -1)

[0282] If this is not true, proceed to step (4-12); otherwise, let the p-th... R Termination time of the ridge line segment Determine p R Is it not less than If true, proceed to step (4-13); otherwise, update p. R The value is p R +1, return to step (4-10);

[0283] (4-12) Update the value of n1 to n1+1, and return to step (4-11);

[0284] (4-13) Extract the instantaneous frequency of the p-th single-frequency signal

[0285]

[0286] Where D cw (p) represents the time range of the p-th single-frequency signal, satisfying:

[0287]

[0288] in For set D i The union of sets i = 1, 2, ..., I, where I is the number of sets;

[0289] (4-14) Determine whether the following conditions are true:

[0290] p = P

[0291] Where P is the number of single-frequency signals detected in step (3-13). If it is true, it is considered that the instantaneous frequency of all single-frequency signals has been extracted and the possible time range of the frequency modulation signal is estimated. Otherwise, the single-frequency signal number p is updated and the value is p+1, and the process returns to step (4-3).

[0292] Furthermore, the possible time range D of the FM signal is estimated. fm_p Specifically, it includes the following steps:

[0293] Calculate the possible time range D of the frequency modulation signal. fm_p If the number of detected single-frequency signals P = 0, then D fm_p The calculation is as follows:

[0294] D fm_p ={n|0≤n≤N t -1},

[0295] Otherwise D fm_pThe calculation is as follows:

[0296]

[0297] Where n is the value of S in step (2-3) w (n,k) time-discrete index, D cw (p) represents the time range of the p-th single-frequency signal given in step (4-13). The number of detected frequency modulation signals Q is calculated. If the value is 0, the instantaneous frequency extraction result is directly output. Otherwise, frequency modulation signal detection is performed within the time range in which the frequency modulation signal may exist, the type of the detected signal is determined, and its frequency parameters are estimated.

[0298] Furthermore, frequency modulation (FM) signal detection is performed within the possible time range of the FM signal, the type of the detected signal is determined, and its frequency parameters are estimated. If it is determined to be a linear frequency modulation (LFM) signal, the estimated frequency parameters are denoted as [f]. 1_L ,μ], where f 1_L Let f be the starting frequency of the linear frequency modulated signal, and μ be the modulation frequency. If the signal is determined to be a hyperbolic frequency modulated signal, then the estimated frequency parameters are [f]. 1_H ,k c ], where f 1_H k is the starting frequency of the hyperbolic frequency modulated signal. c The periodic slope is based on the estimated frequency modulation signal frequency parameter [f]. 1_L ,μ] or [f 1_H ,k c Extract its instantaneous frequency, and record the result as follows: Where q is the frequency modulation signal number, the detected frequency modulation signal is removed, and frequency modulation signal detection continues until all frequency modulation signals are detected. The specific steps include:

[0299] (6-1) Initialize the parameters of the detected FM signal, specifically including the initialization of the following parameters:

[0300] (1) Number of straight line inclination angles N Θ Initialized to: N Θ Even numbers ≥ 28;

[0301] (2) The distance threshold th from the remaining peak points in the neighborhood to the oblique line passing through the peak point to be evaluated. d2 Initialize to: positive real numbers, where N t and N f These are the number of sampling points for the time axis and frequency axis of the time-frequency distribution initialized in step (2-1), respectively.

[0302] (3) Lower limit of instantaneous frequency f of frequency modulation signal i minInitialized to: 0.01f s ≤f i min ≤0.05f s positive real numbers, where f s The signal sampling frequency defined in step 1;

[0303] (4) Number of sampling points M on the reciprocal frequency axis r Initialized to: M r ≥3(N f -round(f i min / Δf)) is a positive integer, where Δf is the time resolution of the time-frequency distribution initialized in step (4-1);

[0304] (5) Frequency reciprocal axis resolution Δf r Initialize to:

[0305] (6) Hough transform of the peak point characteristic image of the frequency modulation signal, number of sampling points N on the radial distance axis ρ Initialize to: Even numbers;

[0306] (7) Hough transform of the peak point characteristic image of the frequency modulation signal, number of sampling points N on the radial angle axis θ Initialized to: N θ Even numbers ≥ 90;

[0307] (8) Hough transform of the peak point characteristic image of the reciprocal time-frequency domain frequency-modulated signal, number of radial distance axis sampling points Initialize to: Even numbers;

[0308] (9) Hough transform of radial angle axis sampling points of the peak point characteristic image of the reciprocal time-frequency domain frequency-modulated signal Initialize to: Even numbers;

[0309] (10) Radial distance resolution Δρ of the peak point characteristic image of frequency modulation signal L Initialize to:

[0310] (11) Radial distance resolution Δρ of peak point characteristic image of reciprocal time-frequency domain frequency-modulated signal H Initialize to:

[0311] (12) Evaluation function threshold th for peak point characteristics of frequency modulation signal ω_fm Initialized as: 0.4≤th ω_fm Positive real numbers ≤ 0.6;

[0312] (6-2) Initialize the frequency modulation signal number q: q = 1;

[0313] (6-3) Evaluate the continuity of the FM signal peak points and generate the FM signal peak point characteristic image B. char_fm (n,k):

[0314]

[0315] d2(i1,j1)=|j1-tan(πb / (N Θ +2))i1||cos(πb / (N Θ +2))|

[0316] Where Num(πb / (N Θ +2)) To determine if there exists a neighboring region Ψ(n,k) that is more than or equal to the peak point (n,k) to be evaluated and has a tilt angle of πb / (N) Θ The distance d2(i1,j1) of the straight line +2) does not exceed th d2 The number of peak points, b is the tilt angle, the discrete index, is a positive integer, 1≤b≤N. Θ +1 and b≠0.5N Θ +1, N0 is the time range of the neighborhood of the peak point of the time-frequency distribution, i1 and j1 are the discrete indices of the neighborhood time and frequency, respectively, the neighborhood Ψ(n,k) and N0, i1 and j1 have been set in step (3-4), ω nb (n,k) is the frequency domain narrowband characteristic evaluation function of the time-frequency distribution peak point calculated in step (3-3), where n and k are the values ​​of S in step (2-3). w (n,k) Discrete index of time and frequency quantities, D fm_p The possible time range of the frequency modulation signal calculated in step 5; (6-4) Based on the peak point characteristic image B of the frequency modulation signal. char_fm (n,k) Generates peak point characteristic image of time-frequency reciprocal domain frequency modulated signal. Where round(f i min / Δf)≤k≤N f -1, 0≤k1≤M r -1:

[0317]

[0318] Where k1 is the discrete index of the reciprocal of the frequency, and is a non-negative integer;

[0319] (6-5) Image B of the peak point characteristic of the frequency modulation signal char_fm Image of peak point characteristics of (n,k) and reciprocal time-frequency domain frequency-modulated signal Perform improved Hough transforms (SH) separatelyLFM (ρ,θ) and SH HFM (ρ,θ):

[0320]

[0321] -0.5N ρ +1≤ρ≤0.5N ρ -0.5N θ +1≤θ≤0.5N θ

[0322]

[0323] Where ρ and θ are discrete indices for radial distance and angle in the improved Hough transform, and are both integers;

[0324] (6-6) Determine whether all FM signals have been detected, i.e., determine whether the following condition is met:

[0325] max{max{SH LFM (ρ,θ)},max{SH HFM (ρ,θ)}}≥H exist

[0326] Where H exist The threshold for determining the presence of the signal initialized in step (3-1) is used. If the threshold is met, proceed to step (6-7); otherwise, calculate the number of detected frequency modulation signals Q: the value is q-1, and output the instantaneous frequency extraction result of the single-frequency signal and the frequency modulation signal.

[0327] (6-7) Determine whether the detected signal is a linear frequency modulated signal, that is, determine whether the following conditions are met:

[0328] max{SH LFM (ρ,θ)}>max{SH HFM (ρ,θ)}

[0329] If true, then the signal is a linear frequency modulated signal. Calculate SH. LFM The maximum value of (ρ,θ) corresponds to the peak point (ρ). 0L ,θ 0L ): The frequency parameters, namely the starting frequency and modulation frequency of the linear frequency modulated signal, are estimated as follows:

[0330]

[0331] Where Δt is the time resolution of the time-frequency distribution initialized in step (4-1);

[0332] If this condition is not met, then the signal is determined to be a hyperbolic frequency modulated signal. Calculate SH. HFMThe maximum value of (ρ,θ) corresponds to the peak point (ρ). 0H ,θ 0H ): The frequency parameters, namely the starting frequency and period slope of the hyperbolic FM signal, are estimated as follows:

[0333]

[0334] (6-8) Use the frequency parameter of the qth frequency modulation signal to set the time-frequency narrowband Ω fm :

[0335]

[0336] Where n and k are S in step (2-3) respectively. w (n,k) Discrete index of time and frequency quantities, D fm_p The time range within which the frequency-modulated signal might exist, as calculated in step 5. Let n be the estimated instantaneous frequency of the assumed signal at time n, satisfying:

[0337]

[0338] Where Δf, Δt, and δf are the frequency resolution, time resolution, and narrowband bandwidth of the time-frequency distribution initialized in step (4-1), respectively;

[0339] (6-9) Find the time-frequency distribution peak points within the time-frequency narrow band that satisfy the peak point characteristics of the frequency-modulated signal, i.e., calculate the existence function κ of the frequency-modulated signal. fm (n):

[0340]

[0341] (6-10) Let the index of the ridge segment number of the frequency modulation signal in the time-frequency narrowband be q. R =1, discrete-time index n1=0;

[0342] (6-11) Determine whether a certain moment is the start time of a ridge segment, that is, determine whether the following conditions are met:

[0343] (κ fm (n1)=0 and κ fm (n1+1)=1) or (κ) fm (n1) = 1 and n1 = 0)

[0344] If true, then let the q-th... R Ridge segment start time Update q R The value of q R +1, then proceed to step (6-12); otherwise, proceed directly to step (6-12).

[0345] (6-12) Judge n1≥N t If -1 is true, proceed to step (6-13); otherwise, update the value of n1 to n1+1 and return to step (6-11).

[0346] (6-13) Calculate the number of ridge segments of the q-th frequency modulated signal.

[0347] (6-14) Update the index q of the ridge segment number of the frequency modulation signal within the narrow band. R =1;

[0348] (6-15) Update the discrete-time index

[0349] (6-16) Calculate the q-th... R The termination time of a ridge segment is determined by checking whether the following conditions are met:

[0350] (κ fm (n1)=1 and κ fm (n1+1)=0) or (κ) fm (n1) = 1 and n1 = N t -1)

[0351] If not, proceed to step (6-17); otherwise, let the q-th... R Termination time of the ridge line segment Determine q R Is it not less than If true, proceed to step (6-18); otherwise, update q. R The value of q R +1, return to step (6-15);

[0352] (6-17) Update the value of n1 to n1+1, and return to step (6-16);

[0353] (6-18) Extract the instantaneous frequency of the q-th frequency-modulated signal.

[0354]

[0355] Where D fm (q) represents the time range in which the q-th frequency-modulated signal exists, satisfying:

[0356]

[0357] (6-19) Characteristic image B at the peak point of the frequency modulation signal char_fm Remove the q-th frequency modulation signal from (n,k), i.e., B char_fm (n,k)=0, where n and k satisfy:

[0358]

[0359] Update the value of the FM signal number q to q+1, and return to step (6-4) to continue the FM signal detection.

[0360] Furthermore, the instantaneous frequency extraction results of the output single-frequency and frequency-modulated signals specifically include:

[0361] If P=0 and Q=0, then output "No signal detected";

[0362] If P > 0 and Q = 0, then the instantaneous frequency of the output single-frequency signal is...

[0363] If P = 0 and Q > 0, then the instantaneous frequency of the output frequency modulation signal is...

[0364] If P > 0 and Q > 0, then the instantaneous frequencies of the output single-frequency signal and frequency-modulated signal are... and

[0365] Where Δt is the time resolution of the time-frequency distribution initialized in step (4-1), p is the single-frequency signal number, 1≤p≤P, P is the number of single-frequency signals detected in step (3-13), q is the frequency modulation signal number, 1≤q≤Q, and Q is the number of frequency modulation signals detected in step (6-6).

[0366] This invention also proposes a system for extracting the instantaneous frequency of a combined pulse signal based on time-frequency distribution-improved Hough transform. Implementing the aforementioned method for extracting the instantaneous frequency of a combined pulse signal based on time-frequency distribution-improved Hough transform, the system achieves instantaneous frequency extraction of the combined pulse signal based on time-frequency distribution-improved Hough transform, including:

[0367] Module 1: Acquire the sampled data sequence of the signal to be processed and calculate the time-frequency distribution of the sampled data sequence of the signal to be processed;

[0368] Module 2: Detect single-frequency signals based on time-frequency distribution. If a single-frequency signal is detected, estimate its frequency parameters and extract the instantaneous frequency of the single-frequency signal based on the frequency parameters, thereby estimating the possible time range of the frequency-modulated signal. Otherwise, directly estimate the possible time range of the frequency-modulated signal.

[0369] Module 3: If the time range in which the FM signal may exist is an empty set, directly output the instantaneous frequency extraction result of the single-frequency signal. Otherwise, perform FM signal detection within the time range in which the FM signal may exist. If no FM signal is detected, directly output the instantaneous frequency extraction result of the single-frequency signal or no signal is detected. Otherwise, determine the type of the detected signal and estimate its frequency parameters. Extract the instantaneous frequency of the FM signal based on the frequency parameters, remove the detected FM signal, and continue to perform FM signal detection until all FM signals are detected. Finally, output the instantaneous frequency extraction results of the single-frequency and FM signals or the instantaneous frequency extraction result of the FM signal.

[0370] Example

[0371] To verify the effectiveness of the present invention, the following experiment was conducted.

[0372] In this implementation, the simulated received signal model x(t) is:

[0373] x(t)=s(t)+w noise (t)

[0374] Among them, the background noise of the observed signal w noise (t) Noise power is P n 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, which satisfies:

[0375]

[0376] Where T is the observation time, the combined pulse signal s(t) is expressed as:

[0377]

[0378] Where R1 is the number of signal components, s r (t) represents the r-th signal component, A r For s r The amplitude of (t), For s r The instantaneous phase of (t), Π r (t) is s r The duration of the signal (t) is denoted as:

[0379]

[0380] Where t r and τ r Let be the start time and duration of the r-th signal component.

[0381] For different types of signal components, the instantaneous phase of the r-th signal component It can be represented as:

[0382]

[0383] in For the initial phase, f 0r f is the frequency of a single-frequency signal. lr FM signal start frequency, μ r For the frequency modulation of a linear frequency modulation signal, k r The slope of the hyperbolic frequency modulated signal period.

[0384] 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):

[0385] x(n)=s(n / f s )+w noise (n / f s )

[0386] The simulation signal parameters are set as follows: number of signal components R1 = 4, observation time T = 4s; the first signal component s1(t) is a linear frequency modulated signal with amplitude A1 = 0.6, initial time t1 = 0.25s, duration τ1 = 0.9s, and initial phase. Starting frequency f l1 =160Hz, modulation frequency μ1 = 400 / 3Hz·s -1 The second signal component s2(t) is a single-frequency signal with an amplitude A2 = 0.7, an initial time t2 = 1.15s, a duration τ2 = 0.5s, and an initial phase. Frequency f 02 =285Hz; the third signal component s3(t) is a hyperbolic frequency modulated signal with amplitude A3 = 0.65, start time t3 = 1.65s, duration τ3 = 1s, and initial phase. Starting frequency f l3 =290Hz, modulation frequency k3=1 / 870Hz -1 ·s -1 The fourth signal component s4(t) is a single-frequency signal with amplitude A4 = 1, initial time t4 = 2.65s, duration τ4 = 0.5s, and initial phase. Frequency f 04 =430Hz; sampling frequency f s=1024Hz, observed data sequence points N=4096, background noise consists of Gaussian white noise, colored noise, and impulse interference at 0.75s and 3s, global signal-to-noise ratio SNR=-4dB;

[0387] According to step 1, the data collected from 4096 sampling points received from the sensor is used as the sampling data sequence s(a0, 0≤a≤4095) of the signal to be processed;

[0388] Based on step 2, initialize the Gaussian window function length M = 614, the Gaussian window function factor α0 = 10.5, and the length N of the non-overlapping portion of the window function. step =10, N is the number of sampling points on the time axis of the time-frequency distribution. t =409, N is the number of sampling points on the frequency axis of the time-frequency distribution. f =308, calculate the time-frequency distribution S of the signal using the above parameters. w (n,k), such as Figure 2 As shown;

[0389] Based on step 3, initialize the frequency range M0 around the peak point of the time-frequency distribution to 6, and set the threshold th for the narrowband characteristic evaluation function of the peak point of the time-frequency distribution in the frequency domain. nb =20 / 13, the time range of the neighborhood of the peak point in the time-frequency distribution is N0=5, the maximum allowable value for the jump between adjacent peak points is K1=3, and the distance threshold th of the other peak points in the neighborhood from the horizontal line passing through the peak point to be evaluated. d1 =1, number of sampling points for the radial distance axis of the Hough transform slice The radial distance resolution of the Hough transform slice is Δρ = 0.666, and the threshold H for determining the presence of a signal is... exist =16.36, the range of the region surrounding the peak point of the Hough transform slice is δρ=9. Using the above parameters, the Hough transform slice SH at the radial angle π / 2 is obtained. CW (ρ1), such as Figure 3 As shown, P = 2 single-frequency signal components were detected, with frequency parameters f0 and f1 respectively. cw (1) = 285.4 Hz, f cw (2) = 429.8 Hz;

[0390] Based on step 4, initialize the time-frequency distribution frequency resolution Δf = 1.668Hz, the time-frequency distribution narrowband bandwidth δf = 5, and the threshold th for the single-frequency signal peak point characteristic evaluation function. ω_cw =0.5, time resolution of time-frequency distribution Δt = 0.00977s, instantaneous frequency is extracted using the above parameters. Instantaneous frequency curve as shown Figure 4 As shown;

[0391] Based on step 5, estimate the possible time range D of the FM signal.fm_p ={n|0≤n≤120}∪{n|170≤n≤268}∪{n|323≤n≤408};

[0392] Based on step 6, initialize the number of straight line tilt angles N. Θ =46, the threshold distance th from the remaining peak points in the neighborhood to the slope passing through the peak point to be evaluated. d2 =1.2, lower limit of instantaneous frequency of FM signal Number of sampling points M on the reciprocal frequency axis r =1136, frequency reciprocal axis resolution Δf r =1.98e-5Hz -1 The number of sampling points N on the radial distance axis of the Hough transform of the peak point characteristic image of the frequency modulation signal. ρ =386, N is the number of sampling points on the radial angle axis. θ =180, the number of sampling points on the radial distance axis of the Hough transform of the peak point characteristic image of the reciprocal time-frequency domain frequency-modulated signal. Radial angle axis sampling points FM signal peak point characteristic evaluation function threshold th ω_fm =0.5, using the above parameters, the Hough transform (SH) of the peak point characteristic image of the frequency modulation signal and the peak point characteristic image of the time-frequency reciprocal domain frequency modulation signal are obtained. LFM (ρ,θ) and SH HFM (ρ,θ), such as Figure 5 and Figure 6 As shown, a linear frequency modulated signal component was detected, with a starting frequency f. 1_L =157.9Hz, modulation frequency μ =133.4Hz / s, then the instantaneous frequency of the linear frequency modulated signal is extracted through the estimated frequency parameters. Instantaneous frequency curve as shown Figure 7 As shown, since the frequency modulation signal component is detected, step 6 needs to be repeated until all frequency modulation signals have been detected and it is found that there is one linear frequency modulation signal component in 0-1.17s, one hyperbolic frequency modulation signal component in 1.66-2.62s, and no frequency modulation signal component in 3.15-4s.

[0393] After the loop ends, according to step 7, the instantaneous frequency estimation result of the combined pulse signal is output. and Instantaneous frequency curve as shown Figure 8 As shown.

[0394] 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. A method for extracting the instantaneous frequency of a combined pulse signal based on time-frequency distribution and improved Hough transform, characterized in that, Includes the following steps: Obtain the sampled data sequence of the signal to be processed, and calculate the time-frequency distribution of the sampled data sequence of the signal to be processed; Based on the detection of single-frequency signals by time-frequency distribution, if a single-frequency signal is detected, its frequency parameters are estimated and the instantaneous frequency of the single-frequency signal is extracted based on the frequency parameters, thereby estimating the possible time range of the frequency-modulated signal; otherwise, the possible time range of the frequency-modulated signal is directly estimated. If the possible time range of the FM signal is an empty set, directly output the instantaneous frequency extraction result of the single-frequency signal; otherwise, perform FM signal detection within the possible time range of the FM signal. If no FM signal is detected, directly output the instantaneous frequency extraction result of the single-frequency signal or no signal detected; otherwise, determine the type of the detected signal and estimate its frequency parameters, extract the instantaneous frequency of the FM signal based on the frequency parameters, remove the detected FM signal, and continue FM signal detection until all FM signals are detected. Finally, output the instantaneous frequency extraction results of the single-frequency and FM signals or the instantaneous frequency extraction result of the FM signal. Where: Frequency modulation (FM) signal detection is performed within the possible time range of the FM signal. The type of the detected signal is determined and its frequency parameters are estimated. If it is determined to be a linear frequency modulation (LFM) signal, the estimated frequency parameters are denoted as [f]. 1_L , μ], where f 1_L Let f be the starting frequency of the linear frequency modulated signal, and μ be the modulation frequency. If the signal is determined to be a hyperbolic frequency modulated signal, then the estimated frequency parameters are [f]. 1_H , k c ], where f 1_H k is the starting frequency of the hyperbolic frequency modulated signal. c The periodic slope is based on the estimated frequency modulation signal frequency parameter [f]. 1_L , μ] or [f 1_H , k c Extract its instantaneous frequency, and record the result as follows: Where q is the frequency modulation signal number, the detected frequency modulation signal is removed, and frequency modulation signal detection continues until all frequency modulation signals are detected. The specific steps include: (6-1) Initialize the parameters of the detected FM signal, specifically including the initialization of the following parameters: (1) Number of straight line inclination angles N Θ Initialize to: Even numbers; (2) The distance threshold th from the remaining peak points in the neighborhood to the oblique line passing through the peak point to be evaluated. d2 Initialize to: positive real numbers, where N t and N f These are the number of sampling points for the time axis and frequency axis of the time-frequency distribution initialized in step (2-1), respectively. (3) Lower limit of instantaneous frequency of FM signal Initialize to: positive real numbers, where f s The signal sampling frequency defined in step 1; (4) Number of sampling points M on the reciprocal frequency axis r Initialize to: A positive integer, where ∆f is the time resolution of the time-frequency distribution initialized in step (4-1); (5) Frequency reciprocal axis resolution ∆f r Initialize to: ; (6) The number of sampling points N of the radial distance axis of the Hough transform of the peak point characteristic image of the frequency modulation signal ρ Initialize to: Even numbers; (7) Number of sampling points N on the radial angle axis of the Hough transform of the peak point characteristic image of the frequency modulation signal θ Initialize to: Even numbers; (8) Number of sampling points on the radial distance axis of the Hough transform of the peak point characteristic image of the reciprocal time-frequency domain frequency-modulated signal Initialize to: Even numbers; (9) Hough transform radial angle axis sampling points of the peak point characteristic image of the time-frequency reciprocal domain frequency-modulated signal Initialize to: Even numbers; (10) Radial distance resolution ∆ρ of the peak point characteristic image of the frequency modulation signal L Initialize to: ; (11) Radial distance resolution ∆ρ of peak point characteristic image of time-frequency reciprocal domain frequency-modulated signal H Initialize to: ; (12) Threshold th, a function for evaluating the peak characteristics of frequency-modulated signals ω_fm Initialize to: Positive real numbers; (6-2) Initialize the frequency modulation signal number q: ; (6-3) Evaluate the continuity of the peak points of the FM signal and generate the peak point characteristic image B of the FM signal. char_fm (n, k): ； in To determine if there exists a neighboring region Ψ(n, k) that is far from the peak point (n, k) to be evaluated and has a tilt angle of 0. straight-line distance No more than th d2 The number of peak points, b is the tilt angle index, and is a positive integer. and N0 represents the time range of the neighborhood of the peak point in the time-frequency distribution, i1 and j1 are the discrete indices of the neighborhood time and frequency, respectively, and the neighborhood Ψ(n, k) and N0, i1 and j1 have been set in step (3-4), ω nb (n, k) is the frequency domain narrowband characteristic evaluation function of the time-frequency distribution peak point calculated in step (3-3), where n and k are the values ​​of S in step (2-3). w (n, k) Discrete index of time and frequency quantities, D fm_p The possible time range of the frequency modulation signal calculated in step 5; (6-4) Based on the peak point characteristic image of the frequency modulation signal. Generate peak point characteristic image of time-frequency reciprocal domain frequency-modulated signal ,in , : ； Where k1 is the discrete index of the reciprocal of the frequency, and is a non-negative integer; (6-5) Peak point characteristic image of frequency modulation signal Peak point characteristic image of time-frequency reciprocal domain frequency-modulated signal Perform improved Hough transforms respectively and : ； ； Where ρ and θ are discrete indices for radial distance and angle in the improved Hough transform, and are both integers; (6-6) Determine whether all FM signals have been detected, i.e., determine whether the following conditions are met: ； Where H exist The threshold for determining the presence of the signal initialized in step (3-1) is used. If the threshold is met, proceed to step (6-7). Otherwise, calculate the number of detected frequency modulation signals Q, with a value of q-1, and output the instantaneous frequency extraction results of the single-frequency signal and the frequency modulation signal. (6-7) Determine whether the detected signal is a linear frequency modulated signal, that is, determine whether the following conditions are met: ； If true, then the signal is determined to be a linear frequency modulated signal. The maximum value corresponds to the peak point : The frequency parameters, namely the starting frequency and modulation frequency of the linear frequency modulated signal, are estimated as follows: ； Where ∆t is the time resolution of the time-frequency distribution initialized in step (4-1); If this condition is not met, then the signal is determined to be a hyperbolic frequency modulated signal. The maximum value corresponds to the peak point : The frequency parameters, namely the starting frequency and period slope of the hyperbolic FM signal, are estimated as follows: ； (6-8) Use the frequency parameter of the qth frequency-modulated signal to set the time-frequency narrowband Ω fm : ； Where n and k are S in step (2-3) respectively. w (n, k) Discrete index of time and frequency quantities, D fm_p The possible time range of the frequency modulation signal calculated in step 5. Let n be the estimated instantaneous frequency of the assumed signal at time n, satisfying: ； Where ∆f, ∆t, and δf are the frequency resolution, time resolution, and narrowband bandwidth of the time-frequency distribution initialized in step (4-1), respectively; (6-9) Find the time-frequency distribution peak points within the time-frequency narrow band that satisfy the peak point characteristics of the frequency-modulated signal, i.e., calculate the existence function κ of the frequency-modulated signal. fm (n): ; (6-10) Index the ridge segment number of the frequency-modulated signal within the time-frequency narrowband. Discrete-time index ; (6-11) Determine whether a certain moment is the start time of a ridge segment, that is, determine whether the following conditions are met: ； If true, then let the q-th... R The start time of the ridge line segment Update q R The value of q R +1, then proceed to step (6-12); otherwise proceed directly to step (6-12). (6-12) Judgment If the condition is met, proceed to step (6-13); otherwise, update the value of n1 to n1+1 and return to step (6-11). (6-13) Calculate the number of ridge segments of the q-th frequency modulated signal. ; (6-14) Update the index of ridge segment numbers for frequency-modulated signals within the time-frequency narrowband. ; (6-15) Update the discrete-time index ; (6-16) Calculate the q-th... R The termination time of a ridge line segment is determined by checking whether the following conditions are met: ； If not, proceed to step (6-17); otherwise, let the q-th... R Termination time of the ridge line segment Determine q R Is it not less than If true, proceed to step (6-18); otherwise, update q. R The value of q R +1, return to step (6-15); (6-17) Update the value of n1 to n1+1 and return to step (6-16). (6-18) Extract the instantaneous frequency of the q-th frequency-modulated signal : ； Where D fm (q) represents the time range in which the q-th frequency-modulated signal exists, satisfying: ； (6-19) Characteristic image at the peak point of the frequency modulation signal Remove the q-th frequency modulation signal from the top, i.e. where n and k satisfy: ， Update the value of the FM signal number q to q+1, and return to step (6-4) to continue the FM signal detection.

2. The method for extracting the instantaneous frequency of a combined pulse signal based on time-frequency distribution-improved Hough transform according to claim 1, characterized in that, Obtain the sampled data sequence s(a) of the signal to be processed, where a is the discrete index of the signal time quantity, specifically including the following steps: Receive data and signal sampling frequency f from N sampling points from the active sonar system. s The collected data is used as the sampled data sequence s(a) of the signal to be processed, where a is the discrete index of the signal time quantity, which is a non-negative integer, and N is the number of sampling points covering the entire signal duration, and is a positive integer not less than 800.

3. The method for extracting the instantaneous frequency of a combined pulse signal based on time-frequency distribution-improved Hough transform according to claim 1, characterized in that, Calculate the time-frequency distribution S of the sampled data sequence of the signal to be processed. w (n, k), where n and k are S w The (n, k) time and frequency discrete index includes the following steps: (2-1) Initialize the parameters for calculating the time-frequency distribution, specifically including the initialization of the following parameters: (1) The length M of the Gaussian window function is initialized as follows: The positive integers, where max{•} is the maximum value function, ceil(•) is the floor function, floor(•) is the floor function, and N is the number of sampling points defined in step 1; (2) The Gaussian window function factor α0 is initialized as follows: Positive real numbers; (3) Gaussian window function w g (m) is initialized as: , where m is the discrete index of the time quantity of the window function, and is a non-negative integer; (4) Length N of the non-overlapping portion of the window function step Initialize to: Positive integers; (5) Number of sampling points N on the time axis of the time-frequency distribution t Initialize to: ; (6) Number of sampling points N on the frequency axis of the time-frequency distribution f Initialize to: ; (2-2) Pad the beginning and end of the sampled data sequence s(a) of the signal to be processed with zeros to obtain the zero-padding sampled data sequence s. zerofill (a zerofill ): ； in This means adding round(0.5M) zeros to the beginning and end of s(a), where round(•) is the rounding function. zerofill The zero-padded discrete index of the signal time quantity is an integer and satisfies ; (2-3) Calculate the zero-padded signal sampled data sequence s zerofill (a zerofill The time-frequency distribution S w (n, k): ； Where |.| is the modulus operator for complex numbers, and j is the imaginary unit, i.e., j 2 =-1, n and k are respectively S w (n, k) are discrete indices for time and frequency quantities, both of which are non-negative integers.

4. The method for extracting the instantaneous frequency of a combined pulse signal based on time-frequency distribution-improved Hough transform according to claim 1, characterized in that, Based on time-frequency distribution S w The detection of a single-frequency signal (n, k) specifically includes the following steps: (3-1) Initialize the parameters of the single-frequency signal detection, specifically including the initialization of the following parameters: (1) Mean parameter μ of time-frequency distribution TFD Initialize to: , where N t and N f For S initialized in step (2-1) w (n, k) represents the number of sampling points on the time axis and frequency axis, where n and k are Stime and Sfrequency, respectively. w (n, k) Discrete index of time and frequency quantities; (2) Time-frequency distribution standard deviation parameter σ TFD Initialize to: ; (3) Threshold of peak point in time-frequency distribution th a Initialize to: ; (4) The frequency range M0 surrounding the peak point of the time-frequency distribution is initialized as follows: Positive integers; (5) Evaluation function for the peak point frequency domain narrowband characteristics of time-frequency distribution: threshold th nb Initialize to: Positive real numbers; (6) The time range N0 of the neighborhood of the peak point of the time-frequency distribution is initialized as follows: Positive integers; (7) The maximum allowable value K1 for the peak point jump between adjacent time points is initialized as follows: Positive integers; (8) The distance threshold th of other peak points in the neighborhood from the horizontal line passing through the peak point to be evaluated. d1 Initialize to: Positive real numbers; (9) Number of sampling points for the radial distance axis of the Hough transform slice Initialize to: Positive integers; (10) The radial distance resolution ∆ρ of the Hough transform slice is initialized as follows: ; (11) Threshold H for determining the presence of a signal exist Initialize to: Positive real numbers; (12) The range δρ surrounding the peak point of the Hough transform slice is initialized as follows: Positive integers; (3-2) Calculate the binarized time-frequency image B(n, k): ； Where diff(•) is the frequency difference operator. ; (3-3) Calculate the evaluation function ω of the frequency domain narrowband characteristics of the time-frequency distribution peak point. nb (n, k): ； in It is the average value of the surrounding time-frequency distribution. , where i is the discrete index of the frequency surrounding the peak point, which is a positive integer, and min{•} is the function for finding the minimum value; (3-4) Set the neighborhood Ψ(n, k) of the time-frequency point (n, k): ； Where i1 and j1 are discrete indices of time and frequency within the neighborhood, respectively, and are non-zero integers; (3-5) Evaluate the continuity of the peak points of the single-frequency signal and generate the characteristic image B of the peak points of the single-frequency signal. char_cw (n, k): ； (3-6) Calculate the Hough transform slice SH at a radial angle of π / 2. CW (ρ1): ； Where ρ1 is the discrete index of the radial distance of the Hough transform slice, which is a non-negative integer, and δ(•) is the delta function, expressed as: ； Where x is a real number; (3-7) Initialize the single-frequency signal number p: ; (3-8) Calculate the maximum value th of the slice in the improved Hough transform. h_max1 : ; (3-9) Determine whether a single-frequency signal exists, i.e., determine whether the following conditions are met: ； If the condition is met, proceed to step (3-10); otherwise, proceed to step (3-13). (3-10) Estimate the frequency parameter f of the p-th single-frequency signal cw (p): ； Where f s ρ is the signal sampling frequency defined in step 1. p For the p-th single-frequency signal, the peak point of the Hough transform slice is... ,in A function to find the maximum value of ρ; (3-11) Remove the peak point and surrounding region of the Hough transform slice of the p-th single-frequency signal: ； (3-12) Update the value of the single-frequency signal number p to p+1 and return to step (3-8). (3-13) Calculate the number P of detected single-frequency signals, taking the value as p-1, and determine whether the following condition is true: ； If the condition is met, a single-frequency signal is considered to exist, and its instantaneous frequency is extracted based on the frequency parameters of the single-frequency signal; otherwise, the possible time range of the frequency modulation signal is directly estimated.

5. The method for extracting the instantaneous frequency of a combined pulse signal based on time-frequency distribution-improved Hough transform according to claim 1, characterized in that, Based on the estimated single-frequency signal frequency parameter f cw (p) Extract its instantaneous frequency, and record the extraction result as . , where ∆t is S w (n, k) time resolution specifically includes the following steps: (4-1) Initialize the parameters for extracting the instantaneous frequency of the single-frequency signal, specifically including the initialization of the following parameters: (1) The time-frequency distribution frequency resolution ∆f is initialized as follows: , where f s N is the signal sampling frequency defined in step 1. f This is the number of sampling points for the time-frequency distribution frequency axis initialized in step (2-1); (2) The time-frequency distribution narrowband bandwidth δf is initialized as: Positive integers; (3) Threshold th, a function for evaluating the peak characteristics of a single-frequency signal ω_cw Initialize to: Positive real numbers; (4) The time-frequency distribution time resolution ∆t is initialized as follows: Where N is the number of sampling points defined in step 1, N t This is the number of time axis sampling points for the time-frequency distribution initialized in step (2-1); (4-2) Update the single-frequency signal number p: ; (4-3) Using the estimated frequency parameter f of the p-th single-frequency signal cw (p) Setting the time-frequency narrowband Ω cw : ； Where n and k are S in step (2-3) respectively. w (n, k) Discrete index of time and frequency quantities; (4-4) Finding the time-frequency narrowband Ω cw The peak points of the time-frequency distribution that satisfy the peak point characteristics of a single-frequency signal are found within the range of the single-frequency signal, i.e., the existence function κ of the single-frequency signal is calculated. cw (n): ； Among them B char_cw (n, k) is the peak point characteristic image of the single-frequency signal generated in step (3-5); (4-5) Index the number of the ridge segment of the single-frequency signal within the time-frequency narrowband. Discrete-time index ; (4-6) Determine whether a certain moment is the start time of a ridge segment, that is, determine whether the following conditions are met: ； If true, then let the p-th... R The start time of the ridge line segment Update p R The value of is p R +1, then proceed to step (4-7); otherwise proceed directly to step (4-7). (4-7) Judgment Check if the condition is met. If it is met, proceed to step (4-8); otherwise, update the value of n1 to n1+1 and return to step (4-6). (4-8) Calculate the number of ridge segments of the p-th single-frequency signal. ; (4-9) Update the index of ridge segment numbers for single-frequency signals within the time-frequency narrowband. ; (4-10) Update the discrete-time index ; (4-11) Calculate the p-th... R The termination time of a ridge segment is determined by checking whether the following conditions are met: ； If not, proceed to step (4-12); otherwise, let the p-th... R Termination time of the ridge line segment Determine p R Is it not less than If true, proceed to step (4-13); otherwise, update p. R The value is p R +1, return to step (4-10); (4-12) Update the value of n1 to n1+1 and return to step (4-11). (4-13) Extract the instantaneous frequency of the p-th single-frequency signal : ； Where D cw (p) represents the time range of the p-th single-frequency signal, satisfying: ； in For set The union of sets, where I is the number of sets; (4-14) Determine whether the following conditions are true: ； Where P is the number of single-frequency signals detected in step (3-13). If it is true, it is considered that the instantaneous frequency of all single-frequency signals has been extracted and the possible time range of the frequency modulation signal is estimated. Otherwise, the single-frequency signal number p is updated and the value is p+1, and the process returns to step (4-3).

6. The method for extracting the instantaneous frequency of a combined pulse signal based on time-frequency distribution-improved Hough transform according to claim 1, characterized in that, Estimate the possible time range D of the FM signal. fm_p Specifically, it includes the following steps: Calculate the possible time range D of the frequency modulation signal. fm_p If the number of detected single-frequency signals P=0, then D fm_p The calculation is as follows: ， Otherwise D fm_p The calculation is as follows: ； Where n is the value of S in step (2-3) w (n, k) time-scale discrete index, D cw (p) represents the time range of the p-th single-frequency signal given in step (4-13). The number of detected frequency modulation signals Q is calculated. If the value is 0, the instantaneous frequency extraction result is directly output. Otherwise, frequency modulation signal detection is performed within the time range in which the frequency modulation signal may exist, the type of the detected signal is determined, and its frequency parameters are estimated.

7. The method for extracting the instantaneous frequency of a combined pulse signal based on time-frequency distribution-improved Hough transform according to claim 1, characterized in that, Output the instantaneous frequency extraction results of single-frequency and frequency-modulated signals, specifically including: like and The output will then show "No signal detected". like and Then the instantaneous frequency of the output single-frequency signal ; like and Then the instantaneous frequency of the output frequency modulation signal ; like and The instantaneous frequencies of the output single-frequency signal and frequency-modulated signal are then... and ; Where ∆t is the time resolution of the time-frequency distribution initialized in step (4-1), and p is the single-frequency signal number. P is the number of single-frequency signals detected given in step (3-13), and q is the frequency modulation signal number. Q is the number of frequency modulation signals detected in step (6-6).

8. A system for extracting the instantaneous frequency of a combined pulse signal based on time-frequency distribution and improved Hough transform, characterized in that, The method for extracting the instantaneous frequency of a combined pulse signal based on time-frequency distribution-improved Hough transform according to any one of claims 1-7, comprising: Module 1. Acquire the sampled data sequence of the signal to be processed and calculate the time-frequency distribution of the sampled data sequence of the signal to be processed; Module 2. Detect single-frequency signals based on time-frequency distribution. If a single-frequency signal is detected, estimate its frequency parameters and extract the instantaneous frequency of the single-frequency signal based on the frequency parameters, thereby estimating the possible time range of the frequency-modulated signal. Otherwise, directly estimate the possible time range of the frequency-modulated signal. Module 3. If the possible time range of the FM signal is an empty set, directly output the instantaneous frequency extraction result of the single-frequency signal. Otherwise, perform FM signal detection within the possible time range of the FM signal. If no FM signal is detected, directly output the instantaneous frequency extraction result of the single-frequency signal or no signal is detected. Otherwise, determine the type of the detected signal and estimate its frequency parameters. Extract the instantaneous frequency of the FM signal based on the frequency parameters, remove the detected FM signal, and continue to perform FM signal detection until all FM signals are detected. Finally, output the instantaneous frequency extraction results of the single-frequency and FM signals or the instantaneous frequency extraction result of the FM signal.

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