A method for separating multi-component linear frequency modulation signals

Abstract

The application belongs to the field of radar, sonar, communication and biomedical related imaging technology, and provides a multi-component linear frequency modulation signal separation method, which mainly includes four main steps: time-frequency analysis, ridge extraction, mask construction and signal reconstruction. The application introduces dynamic programming optimization and conflict resolution mechanism, improves the accuracy and robustness of ridge extraction. At the same time, an adaptive time-frequency mask construction method is designed, and the effective separation of LFM signal is realized. The experimental results show that the method can maintain high separation performance in various complex scenes.

Description

Technical Field

[0001] This invention belongs to the field of imaging technology related to radar, sonar, communication and biomedicine, and specifically relates to a method for separating multi-component linear frequency modulated signals. Background Technology

[0002] Linear frequency modulated (LFM) signals are widely used in radar, sonar, communications, and biomedicine due to their excellent pulse compression characteristics and Doppler tolerance. In practical applications, multiple LFM signals may coexist and superimpose, forming multi-component LFM signals. For example, in radar systems, echoes from multiple moving targets may form multiple LFM signals with different modulation frequencies; in communication systems, multi-user signals may manifest as LFM signals with different parameters. Therefore, accurately separating the individual LFM components from a mixed signal has significant theoretical and practical value.

[0003] Traditional methods for separating multi-component LFM signals mainly include time-frequency filtering, fractional Fourier transform, and sparse decomposition. Time-frequency filtering is based on the separability of the signal in the time-frequency plane, but it is limited by time-frequency resolution; fractional Fourier transform can concentrate the energy of the LFM signal at a specific rotation angle, but it requires multiple searches for the optimal transformation angle for multi-component signals; sparse decomposition achieves signal separation through an overcomplete dictionary, but its computational complexity is high. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a method for separating multi-component linear frequency modulated signals, thereby resolving the issues in the prior art. The technical solution adopted by this invention is as follows: A method for separating multi-component linear frequency modulated signals includes: The first step, signal preprocessing and time-frequency transformation: first, acquire the input signal, then initialize the parameters, and finally perform time-frequency transformation; The second step is time-frequency ridge detection and extraction: set the time-frequency ridge detection parameters, then locate the time-frequency ridge of the initial frame, then track the time-frequency ridge frame by frame, and finally perform post-processing. The third step is to construct an adaptive time-frequency mask; The fourth step is signal separation and reconstruction, including time-frequency domain separation, phase consistency processing, inverse time-frequency transformation, and post-processing. Step 5: Performance evaluation and parameter optimization.

[0005] Step 6: Output the results.

[0006] Furthermore, the first step includes: Step 1.1, Obtain the input signal: Obtain the mixed time-domain signal x(t) to be processed, and determine its sampling frequency fs and the total number of sampling points N; Step 1.2, Parameter Initialization: Set the time-frequency analysis window function type; set the window function length. Determine the frame shift length H; Set the number of points for the Fast Fourier Transform. ; Step 1.3, Perform time-frequency transformation: Apply short-time Fourier transform to the input signal x(t) to obtain the time-frequency matrix S(m,k), where m is the time frame index and k is the frequency index; Calculate the time-frequency amplitude spectrum A(m,k)=|S(m,k)|; Calculate the time-frequency phase spectrum Φ(m,k)=∠S(m,k).

[0007] Furthermore, the second step includes: Step 2.1, Set time-frequency ridge detection parameters: Set the number of ridges to be extracted, K; Set the peak detection threshold. Determine the frequency search range Δf; Step 2.1, Locate the initial frame time-frequency ridge: Take the time-frequency amplitude A(1,k) of the first frame, detect all local maxima points that satisfy A(1,k)>A(1,k-1) and A(1,k)>A(1,k+1); filter those with amplitudes greater than the threshold. The peak points with the largest amplitudes are selected as the initial ridge line positions. , k=1,...,K; Step 2.3, Frame-by-frame tracing of time-frequency ridges: For the m-th frame, execute: Candidate point generation: Detect local maxima in the time-frequency amplitude A(m,k) of the m-th frame; Cost function calculation: For the k-th ridge, calculate the cost function from the position in the previous frame. The transition cost to candidate point j in the current frame: Where α, β, γ are weighting coefficients. These are predicted values ​​based on historical locations; Optimal path selection: Select the path that minimizes the cumulative cost and update the ridge position. ; Conflict detection and resolution: If the distance between two ridges is less than a threshold Reassign candidate points; Step 2.4, Ridge post-processing: For each ridge line Median filtering is performed to remove abrupt transitions; cubic spline interpolation is used to fill in missing points; and smoothing is applied. ,in This is a smoothing window function.

[0008] Furthermore, the third step includes: Step 3.1, Mask bandwidth determination: Calculate the instantaneous frequency change rate of each ridge: Determine the basic bandwidth. ; Calculate adaptive bandwidth: Where η is the adjustment coefficient; Step 3.2, Mask Generation: For the k-th ridge, create a binary mask in the time-frequency plane. : Where F(n) is the actual frequency value corresponding to the nth frequency; Step 3.3, Mask Optimization: Detect mask overlap areas: ; For overlapping regions, energy is allocated proportionally: ; in This represents the estimated amplitude of the k-th ridge at (m,n).

[0009] Furthermore, the fourth step includes: Step 4.1, Time-Frequency Domain Separation: Multiply the original time-frequency matrix element-wise with each mask: , k=1,...,K We obtain K separated time-frequency matrices; Step 4.2, Phase Consistency Processing: Employ methods such as original phase or ridge line reconstruction to preserve original phase information or reconstruct a consistent phase; Step 4.3, Inverse Time-Frequency Transform: Perform inverse short-time Fourier transform on each separated time-frequency matrix using the overlapping addition method or phase reconstruction method; Step 4.4, Signal post-processing: Truncate the reconstructed signal to the original length N; apply low-pass filtering; normalize the signal amplitude to match the energy of the original mixed signal within the separated frequency band.

[0010] Furthermore, in step 4.2, the original phase is used, represented as: ; Phase reconstruction using ridges is represented as follows: .

[0011] Furthermore, in step 4.3, the overlapping addition method includes: performing an inverse FFT on the time spectrum of each frame to obtain a time-domain frame, overlapping and adding the time-domain frames by frame shift H, and normalizing using the sum of squares of the analysis window; Phase reconstruction methods include iteratively optimizing phase consistency using the Griffin-Lim algorithm.

[0012] Furthermore, the fifth step includes: Step 5.1, Calculation of quality assessment index: Calculate the correlation coefficient between the separated signal and the original signal. ; Calculate the signal-to-noise ratio improvement; Calculate the spectral similarity; Step 5.2, adaptive parameter adjustment: Adjust the window length according to the local stationarity of the signal. in The maximum frequency variation rate of all ridges in frame m; Threshold adaptation: .

[0013] The present invention has the following beneficial effects: This invention improves the accuracy and robustness of ridge extraction by introducing dynamic programming optimization and conflict resolution mechanisms. Simultaneously, an adaptive time-frequency mask construction method is designed to achieve effective separation of LFM signals. Experimental results show that this method maintains high separation performance in various complex scenarios. Attached Figure Description

[0014] Figure 1 For flowcharts; Figure 2 This is a time-frequency diagram of the original signal components and the mixed signal; Figure 3 This is a time-frequency diagram of the separated signal components. Detailed Implementation

[0015] The following will be described in conjunction with embodiments of the present invention. Figures 1-3 The technical solutions in the embodiments of the present invention will be clearly and completely described. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Unless otherwise specified, the technical means used in the embodiments are conventional means well known to those skilled in the art.

[0016] like Figure 1 Specifically, this invention proposes a method for separating multi-component linear frequency modulated signals, comprising: Step 1: Signal preprocessing and time-frequency transformation, including: Step 1.1, Obtain the input signal: Obtain the mixed time-domain signal x(t) to be processed, where t is the time variable; determine the sampling frequency fs and the total number of sampling points N. Step 1.2, parameter initialization: Set the time-frequency analysis window function type, preferably a Hamming window or a Gaussian window; set the window function length. It is recommended to set the value to a power of 2; determine the frame shift length H, setting it to 1 / 4 to 1 / 2 of the window length; set the number of points for the Fast Fourier Transform. It should not be less than the length of the window.

[0017] Step 1.3, perform time-frequency transformation: Apply a short-time Fourier transform to the input signal x(t) to obtain the time-frequency matrix S(m,k), where m is the time frame index and k is the frequency index; calculate the time-frequency amplitude spectrum A(m,k)=|S(m,k)|; calculate the time-frequency phase spectrum Φ(m,k)=∠S(m,k).

[0018] Step 2: Time-frequency ridge detection and extraction, including: Step 2.1, set the time-frequency ridge detection parameters: Set the number of ridges to be extracted, K, corresponding to the number of signal components; set the peak detection threshold. The value is 20%-40% of the maximum time-frequency amplitude; the frequency search range Δf is determined based on the maximum frequency change rate of the signal. Step 2.2, Locate the time-frequency ridge line of the initial frame: Take the time-frequency amplitude A(1,k) of the first frame; detect all local maxima that satisfy A(1,k)>A(1,k-1) and A(1,k)>A(1,k+1), and filter out amplitudes greater than the threshold. The peak points with the largest amplitudes are selected as the initial ridge line positions. , k=1,...,K; Step 2.3, trace the time-frequency ridge line frame by frame: For the m-th frame (m=2,...,M), perform the following sub-steps: (1) Candidate point generation: Detect local maxima in the time-frequency amplitude A(m,k) of the m-th frame; (2) Cost function calculation: For the k-th ridge, calculate the cost function from the position in the previous frame. The transition cost to candidate point j in the current frame: Where α, β, γ are weighting coefficients. These are predicted values ​​based on historical locations; (3) Optimal path selection: Select the path that minimizes the cumulative cost and update the ridge position. ; (4) Conflict detection and resolution: If the distance between two ridges is less than the threshold Candidate points are then reassigned.

[0019] Step 2.4, Post-processing of the ridge line: For each ridge line Median filtering was applied to remove anomalous transition points; cubic spline interpolation was used to fill in missing points. Smoothing: ,in For smoothing window functions; Step 3: Adaptive time-frequency mask construction, including: Step 3.1, Mask bandwidth determination: Calculate the instantaneous frequency change rate for each ridge: ; Determine the base bandwidth It is typically set to 1.5 times the inherent bandwidth of the signal; calculate the adaptive bandwidth: η is the adjustment coefficient, which is usually taken as 0.1-0.5.

[0020] Step 3.2, Mask Generation: For the k-th ridge, create a binary mask in the time-frequency plane. : Where F(n) is the actual frequency value corresponding to the nth frequency; Step 3.3, Mask Optimization: Detect mask overlap areas: ; For overlapping regions, energy is allocated proportionally: ,in This represents the estimated amplitude of the k-th ridge at (m,n).

[0021] Step 4: Signal separation and reconstruction, including: Step 4.1, Time-Frequency Domain Separation: Multiply the original time-frequency matrix element-wise with each mask: , k=1,...,K; We obtain K separated time-frequency matrices; Step 4.2, Phase Consistency Processing: Preserving the original phase information or reconstructing a consistent phase includes two methods: Method A: Directly use the original phase. ; Method B: Reconstruct phase from ridges. ; Step 4.3, Inverse Time-Frequency Transform: Perform the inverse short-time Fourier transform on each separated time-frequency matrix, including the following methods: Overlapping and Addition Method: Perform inverse FFT on the time spectrum of each frame to obtain the time-domain frame; overlap and add the time-domain frames by frame shift H; normalize using the sum of squares of the analysis window. Phase reconstruction method: The phase consistency is iteratively optimized using the Griffin-Lim algorithm, usually 10-20 iterations.

[0022] Step 4.4, Signal post-processing: The reconstructed signal is truncated to its original length N and a slight low-pass filter is applied (the cutoff frequency is 1.2 times the highest ridge frequency); the signal amplitude is normalized to match the energy of the original mixed signal within the separated frequency band.

[0023] Step 5: Performance evaluation and parameter optimization, including: Step 5.1, Calculation of quality assessment indicators, including: Calculate the correlation coefficient between the separated signal and the original signal (if known). ; Calculate the improvement in signal-to-noise ratio: ; Calculate spectral similarity: ; Step 5.2, adaptive parameter adjustment: Adaptive window length: Adjusts the window length based on the local stationarity of the signal. in The maximum frequency variation rate of all ridges in frame m; Threshold adaptation: ; Bandwidth adaptation: Adjust the value of η according to the local signal-to-noise ratio.

[0024] Step 6: Output Results: Output K separated time-domain signals. Output the ridge trajectory of each component. .

[0025] The experiment was conducted using the MATLAB R2021b platform, and the signal parameters are shown in Table 1. Figure 2 This is the time-frequency diagram of the original signal components and the mixed signal. Figure 3 The time-frequency diagram of the signal components separated by the method of the present invention shows that the present invention can effectively separate the mixed linear frequency modulated signal.

[0026] Table 1: Experimental signal parameters

[0027] The above embodiments are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Any modifications, alterations, alterations, or substitutions made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for separating multi-component linear frequency modulated signals, characterized in that, include: The first step, signal preprocessing and time-frequency transformation: first, acquire the input signal, then initialize the parameters, and finally perform time-frequency transformation; The second step is time-frequency ridge detection and extraction: set the time-frequency ridge detection parameters, then locate the time-frequency ridge of the initial frame, then track the time-frequency ridge frame by frame, and finally perform post-processing. The third step is to construct an adaptive time-frequency mask; The fourth step is signal separation and reconstruction, including time-frequency domain separation, phase consistency processing, inverse time-frequency transformation, and post-processing. Step 5: Performance evaluation and parameter optimization; Step 6: Output the results; The second step includes: Step 2.1, Set time-frequency ridge detection parameters: Set the number of ridges to be extracted, K; Set the peak detection threshold. Determine the frequency search range Δf; Step 2.1, Locate the initial frame time-frequency ridge: Take the time-frequency amplitude A(1,k) of the first frame, detect all local maxima points that satisfy A(1,k)>A(1,k-1) and A(1,k)>A(1,k+1); filter those with amplitudes greater than the threshold. The peak points with the largest amplitudes are selected as the initial ridge line positions. , k=1,...,K; Step 2.3, Frame-by-frame tracing of time-frequency ridges: For the m-th frame, execute: Candidate point generation: Detect local maxima in the time-frequency amplitude A(m,k) of the m-th frame; Cost function calculation: For the k-th ridge, calculate the cost function from the position in the previous frame. The transition cost to candidate point j in the current frame: Where α, β, γ are weighting coefficients. These are predicted values ​​based on historical locations; Optimal path selection: Select the path that minimizes the cumulative cost and update the ridge position. ; Conflict detection and resolution: If the distance between two ridges is less than a threshold Reassign candidate points; Step 2.4, Ridge post-processing: For each ridge line Median filtering is performed to remove abrupt transitions; cubic spline interpolation is used to fill in missing points; and smoothing is applied. ,in For smoothing window functions; Step 3.1, Mask bandwidth determination: Calculate the instantaneous frequency change rate of each ridge: Determine the basic bandwidth. H is the frame shift length. The sampling frequency; Calculate adaptive bandwidth: Where η is the adjustment coefficient; Step 3.2, Mask Generation: For the k-th ridge, create a binary mask in the time-frequency plane. : Where F(n) is the actual frequency value corresponding to the nth frequency; Step 3.3, Mask Optimization: Detect mask overlap areas: ; For overlapping regions, energy is allocated proportionally: ; in Let be the estimated amplitude of the k-th ridge at (m,n).

2. The method for separating multi-component linear frequency modulated signals according to claim 1, characterized in that, The first step includes: Step 1.1, Obtain the input signal: Obtain the mixed time-domain signal x(t) to be processed, and determine its sampling frequency fs and the total number of sampling points N; Step 1.2, Parameter Initialization: Set the time-frequency analysis window function type; set the window function length. Determine the frame shift length H; Set the number of points for the Fast Fourier Transform. ; Step 1.3, Perform time-frequency transformation: Apply short-time Fourier transform to the input signal x(t) to obtain the time-frequency matrix S(m,k), where m is the time frame index and k is the frequency index; Calculate the time-frequency amplitude spectrum A(m,k)=|S(m,k)|; Calculate the time-frequency phase spectrum Φ(m,k)=∠S(m,k).

3. The method for separating multi-component linear frequency modulated signals according to claim 1, characterized in that, The fourth step includes: Step 4.1, Time-Frequency Domain Separation: Multiply the original time-frequency matrix element-wise with each mask: , k=1,...,K We obtain K separated time-frequency matrices; Step 4.2, Phase Consistency Processing: Employ methods such as original phase or ridge line reconstruction to preserve original phase information or reconstruct a consistent phase; Step 4.3, Inverse Time-Frequency Transform: Perform inverse short-time Fourier transform on each separated time-frequency matrix using the overlapping addition method or phase reconstruction method; Step 4.4, Signal post-processing: Truncate the reconstructed signal to the original length N; apply low-pass filtering; normalize the signal amplitude to match the energy of the original mixed signal within the separated frequency band.

4. The method for separating multi-component linear frequency modulated signals according to claim 3, characterized in that, In step 4.2, the original phase is used, represented as: ; Phase reconstruction using ridges is represented as follows: .

5. The method for separating multi-component linear frequency modulated signals according to claim 3, characterized in that, In step 4.3, the overlapping addition method includes: performing an inverse FFT on the time spectrum of each frame to obtain a time-domain frame, overlapping and adding the time-domain frames according to frame shift H, and normalizing using the sum of squares of the analysis window; Phase reconstruction methods include iteratively optimizing phase consistency using the Griffin-Lim algorithm.

6. The method for separating multi-component linear frequency modulated signals according to claim 3, characterized in that, The fifth step includes: Step 5.1, Calculation of quality assessment index: Calculate the correlation coefficient between the separated signal and the original signal. ; Calculate the signal-to-noise ratio improvement; Calculate the spectral similarity; Step 5.2, adaptive parameter adjustment: Adjust the window length according to the local stationarity of the signal. in The maximum frequency variation rate of all ridges in frame m; Threshold adaptation: .

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