A short-time chirp-Fourier transform-based line spectrum enhancement method for underwater moving targets

Abstract

This invention discloses a method for enhancing the line spectrum of underwater moving targets based on short-time Chirp-Fourier transform, comprising: Step 1: enhancing the original time-domain data s ( t ) Perform windowing processing, calculate the short-time Fourier transform, and determine the number of target line spectra. N and time T Step 2: Determine the linear frequency modulation factor based on the signal duration and frequency offset range. k Search range; Step 3: For each linear frequency modulation factor k Perform a midpoint Chirp-Fourier transform and compare the signal amplitude within the target frequency band after the transform with the linear frequency modulation factor. k Step 4: Perform a short-time Chirp-Fourier transform on the original signal data to reconstruct the signal time-frequency diagram, thereby achieving target frequency offset correction. This invention utilizes the Chirp-Fourier transform to recover and enhance the frequency offset signal, and then uses the enhanced signal to reconstruct the signal time-frequency diagram, improving the signal-to-noise ratio of the target line spectrum. Sea trial results show that this method effectively enhances the target line spectrum and has good application prospects.

Description

Technical Field

[0001] This invention belongs to the field of underwater acoustic signal processing, specifically relating to underwater target line spectrum detection, and in particular to a method for enhancing the line spectrum of underwater moving targets based on short-time Chirp-Fourier transform. Background Technology

[0002] The radiated noise spectrum of a moving sound source often consists of several discrete single-frequency line spectra and a broadband continuous spectrum. The line spectra are mainly concentrated in the low frequencies and have advantages such as concentrated energy, good stability, and long propagation distance, and are often used for target detection and identification. However, when the sound source moves and the receiving point is stationary, the received signal will undergo a Doppler frequency shift, and the line spectrum signal will become a non-stationary signal whose frequency varies with time.

[0003] From a signal decomposition perspective, the Fourier transform converts a time-domain signal to the frequency domain and decomposes it into a set of line spectra in the frequency domain, with each line representing a single-frequency signal. The Chirp-Fourier transform, on the other hand, converts the time-domain signal to a two-dimensional frequency-modulation (FM) domain, decomposing the signal into multiple peak points in the two-dimensional domain. Each peak point represents an LFM signal. The frequency domain coordinates of the peak point are the midpoint frequency of its corresponding LFM signal, while the FM domain coordinates are the modulation slope of that LFM signal. Summary of the Invention

[0004] This invention addresses the problem of line spectrum detection in motion targets by proposing a method for enhancing the line spectrum of underwater moving targets based on short-time Chirp-Fourier transform. By utilizing the magnitude of the signal amplitude within the target's frequency band after Chirp-Fourier transform, the degree of frequency shift is determined, thereby restoring and enhancing the frequency-shifted signal. The enhanced signal is then used to reconstruct the time-frequency diagram of the signal, improving the signal-to-noise ratio of the target line spectrum. This method offers advantages such as good applicability, convenient processing, high efficiency, and good enhancement effect.

[0005] The technical solution of this invention is as follows:

[0006] Step 1: Window the original time-domain data s(t), then perform a short-time Fourier transform to determine the number of target line spectra and the time. Frequency offset range within;

[0007] Step 2: Determine the search range of the linear frequency modulation factor k based on the signal duration and frequency offset range;

[0008] Step 3: For each line spectrum, perform a midpoint Chirp-Fourier transform using each linear frequency modulation factor k within the search range. Search for the linear frequency modulation factor k by comparing the signal amplitude within the target frequency band after the transform. The required search result is the k value corresponding to the maximum average power spectral level within the bandwidth.

[0009] Step 4: Using the linear frequency modulation factor k obtained in Step 3, perform a short-time Chirp-Fourier transform on the original signal data and reconstruct the signal time-frequency diagram to achieve target frequency offset correction.

[0010] In step one, T represents the total signal duration, the number of target line spectra is set to N, and the center frequency of the nth line spectra is f. n The frequency offset range is [f nL f nH ], where f nL f nH These are the lower and upper limits of the frequency variation of the nth line spectrum, respectively, where n = 1, 2, ..., N.

[0011] In step one, the calculation formula for the short-time Fourier transform is as follows:

[0012] ,

[0013] in, This represents the result matrix after the short-time Fourier transform, where s(t) is the time-domain data. Let f be a window function, and f be the frequency. This represents the segmented delay, where t represents time and j is the imaginary unit.

[0014] In step two, the search range of the linear frequency modulation factor k is [k nL k nH ],

[0015] Where, k nL k nH These are the lower and upper limits of the linear frequency modulation factor k for the nth line spectrum, respectively.

[0016] And k nL k nH It is obtained from the following formula:

[0017] , ,

[0018] Where T is the total signal duration, f nL f nH These are the lower and upper limits of the frequency variation of the nth line spectrum, respectively, where n = 1, 2, ..., N.

[0019] In step three, for each line spectrum, the search range [k] is used. nL k nH For each linear frequency modulation factor k within the range, perform a midpoint Chirp-Fourier transform, as shown in the following formula:

[0020] ,

[0021] in, This represents the result matrix after the short-time Chirp-Fourier transform, where s(t) is the time-domain data. For window functions.

[0022] In step three, the value corresponding to the maximum average power spectral level within the bandwidth is... The values ​​represent the desired search results; the obtained f and k are both expressed as... The formula for finding the maximum value of the average power spectral level within the bandwidth is as follows:

[0023] ,

[0024] In the formula, argmax is the independent variable used to find the maximum value of the function. This represents modulo operation, where s(t) is the time-domain data. For window functions.

[0025] In step four, the linear frequency modulation factor calculated in step three is... Substituting into the following calculation formula, we obtain the reconstructed time-frequency diagram of the signal:

[0026] ,

[0027] in, The reconstructed time-frequency diagram of the signal, where s(t) is the time-domain data. For window functions.

[0028] The beneficial effects of this invention are as follows: This method utilizes the Chirp-Fourier transform to recover and enhance the frequency-shifted signal, and reconstructs the time-frequency diagram of the signal using the enhanced signal, thereby improving the signal-to-noise ratio of the target line spectrum. Processing data of moving targets actually measured during sea trials shows that the proposed method effectively enhances the target line spectrum. Attached Figure Description

[0029] Figure 1 This is a flowchart illustrating the implementation of an underwater moving target line spectrum enhancement method based on short-time Chirp-Fourier transform according to the present invention.

[0030] Figure 2a The simulation results for the short-time Fourier transform are shown in the figure.

[0031] Figure 2b The figure shows the simulation results of the short-time Chirp-Fourier transform.

[0032] Figure 3 The graph shows the change of the peak value of the target line spectrum over time before and after the line spectrum transformation;

[0033] Figure 4 The signal spectrum levels are shown before and after the 90.7Hz line spectrum transformation. Detailed Implementation

[0034] The present invention will be further described below with reference to specific embodiments and accompanying drawings:

[0035] (I) Implementation process:

[0036] This invention provides a method for enhancing the line spectrum of underwater moving targets based on short-time Chirp-Fourier transform, the flowchart of which is shown below. Figure 1 As shown, the specific implementation process is as follows:

[0037] 1) Apply a window function to the original time-domain data s(t) Windowing is applied, short-time Fourier transform is calculated, and the number of target line spectra and a certain time interval are determined. The formula for calculating the frequency offset range within the range using the short-time Fourier transform is as follows:

[0038] ,

[0039] in, This represents the result matrix after the short-time Fourier transform, where s(t) is the time-domain data. Let f be a window function, and f be the frequency. This represents the segmented time delay, where t represents time and j is the imaginary unit.

[0040] Let the total signal duration be T, the number of target line spectra be N, and the center frequency of the nth line spectra be f. n The frequency offset range is [f nL f nH ], where f nL f nH These are the lower and upper limits of the frequency variation of the nth line spectrum, respectively, where n = 1, 2, ..., N.

[0041] 2) Determine the search range of the linear frequency modulation factor k based on the signal duration and frequency offset range [k]. nL k nH ], where k nL k nH Let K be the lower and upper limits of the linear frequency modulation factor k for the nth line spectrum, respectively, where n = 1, 2, ..., N.

[0042] The search range for k here does not need to be a precise value; it can be obtained from the following formula:

[0043] , ,

[0044] Where T is the total signal duration, f nL f nH These are the lower and upper limits of the frequency variation of the nth line spectrum, respectively, where n = 1, 2, ..., N.

[0045] 3) For each line spectrum within each time window, perform a midpoint Chirp-Fourier transform using each linear frequency modulation factor k within the search range, as shown in the following formula:

[0046] ,

[0047] in, This represents the result matrix after the short-time Chirp-Fourier transform, where s(t) is the time-domain data. Let f be a window function, and f be the frequency. The segmented delay is represented by t, where t represents time, k represents the linear frequency modulation factor, and j is the imaginary unit.

[0048] Assuming the Doppler signal within each time window approximates a linearly modulated (LFM) signal, the LFM factor k can be searched by comparing the amplitude of the transformed signal within the target frequency band according to the above formula. The instantaneous frequency of the signal corresponding to the maximum average power spectral level within the bandwidth is f0, and the modulation slope is k0. Since f0 and k0 of the LFM signal approximated by the Doppler signal are different in different time periods, the obtained f and k can both be expressed as... The formula for finding the maximum value of the average power spectral level within the bandwidth of the function can be expressed as:

[0049] ,

[0050] In the formula, argmax is the independent variable used to find the maximum value of the function. This represents the modulus, where f is the frequency and k is the linear frequency modulation factor. This represents the segmented time delay, where s(t) is the time-domain data. Let t be a window function, where t represents time and j is the imaginary unit.

[0051] 4) Using the linear frequency modulation factor k obtained in step three, perform a short-time Chirp-Fourier transform on the original signal data to reconstruct the signal time-frequency diagram, thereby achieving target frequency offset correction. Specifically:

[0052] Linear frequency modulation factor under different window functions (i.e., different) Frequency modulation factor corresponding to the value Substituting these values ​​into the following short-time Chirp-Fourier transform formula, the original signal data is transformed to obtain the reconstructed time-frequency diagram of the signal. The calculation formula is as follows:

[0053] ,

[0054] in, The reconstructed time-frequency diagram of the signal, where s(t) is the time-domain data. Let f be a window function, and f be the frequency. This represents the segmented delay, where t represents time and j is the imaginary unit.

[0055] In this invention, the main parameters are set as follows:

[0056] 1) Frequency offset range: In data post-processing, the frequency offset range can generally be determined based on the STFT results of the signal. Since the frequency offset comes from the Doppler effect, it is related to the frequency, the target's speed, and the target's distance, and there are many influencing factors. Therefore, it should be determined according to the actual situation in real-time processing, such as setting it to [f0-0.005f0, f0+0.005f0], where f0 is the target line spectrum frequency.

[0057] 2) Search range of linear frequency modulation factor k: In data post-processing, as shown in the implementation process, The search range is determined by the signal duration and frequency offset range. In real-time processing, a relatively wide search range can be assigned to k, such as [-0.005Hz / s, 0.005Hz / s].

[0058] 3) Range of other parameters: such as window function The length of the window should ensure that the target frequency changes approximately linearly within the set time range; the window length is generally set to 10-30 seconds.

[0059] (II) Simulation and Sea Trial Data Test Results:

[0060] Based on "(I) Implementation Process", the processing results of this invention are presented through simulation. The simulation processing is as follows: Figures 2a to 4 As shown.

[0061] Computer Simulation 1: Assuming a signal sampling rate of 5000Hz, a target radiated noise frequency of 150Hz, a signal length of 1000s, a closest distance between the target and the receiving hydrophone of 2000m, a closest arrival time of the sound source of 500s, a received signal time range of 0-1000s, a sound speed in water of 1500m / s, and a target velocity of 10m / s, a time-domain signal exhibiting the Doppler effect is constructed based on these parameters. Short-time Fourier transform and short-time Chirp-Fourier transform are then applied to this signal, and the processing results are as follows: Figure 2a , Figure 2bAs shown, it can be seen that in areas of drastic frequency change, the line spectrum obtained by the short-time Fourier transform exhibits a broadening of the line spectrum bandwidth. This means that the line spectrum energy is dispersed within that time period. In contrast, the short-time Chirp-Fourier transform results show that the energy is effectively concentrated on the real-time line spectrum in all time periods. Compared to the short-time Fourier transform results, the line spectrum signal-to-noise ratio is higher, and the Doppler frequency change effect is more pronounced.

[0062] Actual data processing: For a certain lake experiment, the target was a small boat with a target spectrum of 90.7 Hz and a total data length of 400 s. The Chirp-Fourier transform was used to enhance the signal, resulting in the following changes in the peak value of the 90.7 Hz signal over time before and after the transform: Figure 3 As shown, since the signal frequency is basically stable during the 0-50s time period, the nonlinear transformation of the signal is very weak. Therefore, the Chirp-Fourier transform theoretically yields no benefit during this period. However, the method shows a significant gain between 50s and 400s, exhibiting a substantial signal-to-noise ratio gain. Taking data from a specific time point and performing a CFT transform yields the following results: Figure 4 As shown, the line spectrum achieves a large gain, up to approximately 4 dB.

[0063] The simulation results above demonstrate the effectiveness of the proposed underwater moving target line spectrum enhancement method based on short-time Chirp-Fourier transform. This method utilizes Chirp-Fourier transform to recover and enhance the frequency-shifted signal, and then reconstructs the time-frequency diagram of the enhanced signal, thereby improving the signal-to-noise ratio of the target line spectrum. Processing data from actual moving targets measured during sea trials shows that the proposed method effectively enhances the target line spectrum and has promising application prospects.

[0064] It should be noted that the above embodiments are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Equivalent modifications made based on the above embodiments are all within the scope of protection of the present invention.

Claims

1. A method for enhancing the line spectrum of underwater moving targets based on short-time Chirp-Fourier transform, characterized in that, include: Step 1: Window the original time-domain data s(t) and then perform a short-time Fourier transform to determine the number of target line spectra and the frequency offset range within time T; Step 2: Determine the search range of the linear frequency modulation factor k based on the signal duration and frequency offset range; Step 3: For each line spectrum, perform midpoint Chirp-Fourier transform using the linear frequency modulation factor k. Search for the linear frequency modulation factor k by comparing the signal amplitude within the target frequency band after the transformation. The required search result is the k value corresponding to the maximum average power spectral level within the bandwidth. Step 4: Using the linear frequency modulation factor k obtained in Step 3, perform a short-time Chirp-Fourier transform on the original signal data and reconstruct the signal time-frequency diagram to achieve target frequency offset correction; In step one, the calculation formula for the short-time Fourier transform is as follows: ， in, This represents the result matrix after the short-time Fourier transform, where s(t) is the time-domain data. Let f be a window function, and f be the frequency. This represents the segmented time delay, where t represents time and j is the imaginary unit. In step two, the search range of the linear frequency modulation factor k is [k nL k nH ], Where, k nL k nH These are the lower and upper limits of the linear frequency modulation factor k for the nth line spectrum, respectively. And k nL k nH It is obtained from the following formula: ， ， Where T is the total signal duration, f nL f nH These are the lower and upper limits of the frequency variation of the nth line spectrum, respectively, where n = 1, 2, ..., N; In step three, for each line spectrum, the search range [k] is used. nL k nH For each linear frequency modulation factor k within the range, perform a midpoint Chirp-Fourier transform, as shown in the following formula: ， in, This represents the result matrix after the short-time Chirp-Fourier transform, where s(t) is the time-domain data. For window functions; In step three, the k value corresponding to the maximum average power spectral level within the bandwidth is the desired search result. The obtained f and k are both expressed as... The formula for finding the maximum value of the average power spectral level within the bandwidth is as follows: ， In the formula, argmax is the independent variable used to find the maximum value of the function. This represents modulo operation, where s(t) is the time-domain data. For window functions; In step four, the linear frequency modulation factor calculated in step three is... Substituting the values ​​into the following short-time Chirp-Fourier transform formula, the original signal data is transformed to obtain the reconstructed time-frequency diagram of the signal: ， in, The reconstructed time-frequency diagram of the signal, where s(t) is the time-domain data. For window functions.

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