Underwater moving target line spectrum enhancement method based on short-time Chirp-Fourier transformation

Abstract

The invention discloses an underwater moving target line spectrum enhancement method based on short-time Chirp-Fourier transform, and the method comprises the steps: 1, carrying out the windowing processing of original time domain data s (t), calculating the short-time Fourier transform, and determining the number N of target line spectrums and the frequency deviation range within the time T; 2, determining a search range of a linear frequency modulation factor k according to a signal time length and a frequency deviation range; 3, performing midpoint Chirp-Fourier transformation on each linear frequency modulation factor k, and searching the maximum value of the linear frequency modulation factor k by comparing the signal amplitude in the transformed target frequency band; and 4, carrying out short-time Chirp-Fourier transformation on the original signal data, reconstructing a signal time-frequency diagram, and realizing target frequency offset correction. According to the method, the Chirp-Fourier transformation is utilized to recover and enhance the frequency offset signal, and the enhanced signal is utilized to reconstruct the signal time-frequency graph, so that the signal-to-noise ratio of the target line spectrum is improved. A sea trial processing result shows that the method effectively realizes enhancement of the target line spectrum and has a good application prospect.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of underwater acoustic signal processing, and particularly relates to the detection of line spectrum of underwater moving target, and especially to a line spectrum enhancement method for underwater moving target based on short-time Chirp-Fourier transform. BACKGROUND

[0002] The radiation noise spectrum of moving sound source is often composed of several discrete single-frequency line spectrum and wideband continuous spectrum, wherein the line spectrum is mainly concentrated in low frequency, and has the advantages of energy concentration, good stability, long propagation distance, etc., and is often used for target detection and identification. However, when the sound source moves and the receiving point is stationary, the received signal will produce Doppler shift, and the line spectrum signal will become a non-stationary signal with time-varying frequency.

[0003] From the perspective of signal decomposition, Fourier transform is to convert time-domain signal to frequency domain, and decompose the signal into a set of line spectrum in frequency domain, each line spectrum representing a single-frequency signal. Chirp-Fourier transform is to convert time-domain signal to two-dimensional frequency-chirp domain, and the signal is decomposed into multiple peak points in the two-dimensional domain, each peak point representing an LFM signal. The frequency domain coordinate of the peak point is the frequency of the midpoint of the corresponding LFM signal, and the chirp domain coordinate is the chirp slope of the LFM signal. SUMMARY

[0004] The present application proposes a line spectrum enhancement method for underwater moving target based on short-time Chirp-Fourier transform, aiming at the problem of line spectrum detection under target motion. The frequency shift degree of the signal in the target frequency band after Chirp-Fourier transform is determined to restore and enhance the frequency shift signal, and the signal time-frequency diagram is reconstructed using the enhanced signal to improve the signal-to-noise ratio of the target line spectrum, achieving the advantages of good applicability, convenient processing, high efficiency and good enhancement effect.

[0005] The technical scheme of the present application is as follows:

[0006] Step one: window processing is performed on the original time-domain data s(t), and then short-time Fourier transform is performed to determine the number of target line spectrum and the frequency shift range in time ;

[0007] Step two: the search range of linear frequency modulation factor k is determined according to the signal time length and the frequency shift range;

[0008] Step three: for each line spectrum, midpoint Chirp-Fourier transform is performed using each linear frequency modulation factor k in the search range, and the linear frequency modulation factor k is searched by comparing the signal amplitude in the target frequency band after transform, and the required search result is the k value corresponding to the maximum average power spectrum level in the bandwidth;

[0009] Step four: using the linear frequency modulation factor k obtained in step three, performing short-time Chirp-Fourier transform on the original signal data and reconstructing the signal time-frequency graph to realize target frequency offset correction.

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

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

[0012] ,

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

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

[0015] wherein k nL , k nH are the lower limit and upper limit of the linear frequency modulation factor k of the nth line spectrum respectively,

[0016] and k nL , k nH are obtained according to the following formula:

[0017] , ,

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

[0019] In step three, for each line spectrum, midpoint Chirp-Fourier transform is performed using each linear frequency modulation factor k in the search range [k nL , k nH ], and the formula is as follows:

[0020] ,

[0021] wherein, represents the result matrix after short-time Chirp-Fourier transformation, s(t) is time domain data, is a window function.

[0022] In the step three, the value corresponding to the maximum average power spectrum level in the bandwidth is the required search result, the obtained f and k are expressed as functions of , and the formula for finding the maximum value of the average power spectrum level in the bandwidth is as follows:

[0023] ,

[0024] In the formula, argmax is the independent variable for finding the maximum value of the function, s(t) is time domain data, is a window function.

[0025] In the step four, the linear frequency modulation factor calculated in the step three is substituted into the following calculation formula to obtain the reconstructed signal time-frequency graph:

[0026] ,

[0027] wherein, s(t) is time domain data, is a window function.

[0028] The method has the beneficial effects that: the method utilizes Chirp-Fourier transformation to recover and enhance the frequency offset signal, and reconstructs the signal time-frequency graph by using the enhanced signal, thereby improving the signal-to-noise ratio of the target line spectrum. The data of the moving target actually measured in the sea trial are processed, and the results show that the proposed method effectively realizes the enhancement of the target line spectrum. BRIEF DESCRIPTION OF DRAWINGS

[0029] Figure 1 is a flow chart of the implementation process of the underwater moving target line spectrum enhancement method based on short-time Chirp-Fourier transformation;

[0030] Figure 2a is a simulation data result graph of short-time Fourier transformation;

[0031] Figure 2b is a simulation data result graph of short-time Chirp-Fourier transformation;

[0032] Figure 3 is a graph of the target line spectrum peak value change with time before and after line spectrum transformation;​​

[0033] Figure 4 The signal spectrum level diagram before and after the transformation of the 90.7Hz line spectrum. DETAILED DESCRIPTION

[0034] The application will be further described below in conjunction with specific embodiments and the accompanying drawings:

[0035] (I) Implementation process:

[0036] The underwater moving target line spectrum enhancement method based on short-time Chirp-Fourier transform provided by the application has the implementation flow block diagram as shown in the figure, and the specific implementation process is as follows: Figure 1

[0037] 1) The original time domain data s(t) is windowed using a window function to calculate the short-time Fourier transform, determine the target line spectrum number and the frequency offset range within a certain time The calculation formula of the short-time Fourier transform is as follows:

[0038] ,

[0039] Wherein, represents the result matrix after the short-time Fourier transform, s(t) is the time domain data, is the window function, f is the frequency, represents the segmented time delay, t represents the time, and j is the imaginary unit;

[0040] Let the total signal duration be T, the target line spectrum number be N, the center frequency of the nth line spectrum be f n , the frequency offset range be [f nL , f nH ], wherein f nL , f nH are the lower limit and the upper limit of the frequency change of the nth line spectrum respectively, n=1, 2, …, N.

[0041] 2) According to the signal time length and the frequency offset range, the linear frequency modulation factor k search range [k nL , k nH ] is determined, wherein k nL , k nH are the lower limit and the upper limit of the linear frequency modulation factor k of the nth line spectrum respectively, n=1, 2, …, N,

[0042] The k search range here does not need to be an accurate value, which can be obtained according to the following formula:

[0043] , ,

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

[0045] 3) For each line spectrum in each time window, the midpoint Chirp-Fourier transform is performed using each linear frequency modulation factor k in the search range, and the formula is as follows:

[0046] ,

[0047] Where, represents the result matrix after short-time Chirp-Fourier transform, s(t) is the time domain data, is the window function, and f is the frequency. represents the segment delay, t represents the time, k represents the linear frequency modulation factor, and j is the imaginary unit.

[0048] Assuming that the Doppler signal in each time window is approximately a linear frequency modulation signal, the linear frequency modulation factor k can be searched according to the above formula by comparing the signal amplitude in the target frequency band after transformation, and the signal instantaneous frequency corresponding to the maximum average power spectrum level in the bandwidth is f0, and the frequency modulation slope is k0. Since the f0 and k0 of the approximate linear frequency modulation signal of the Doppler signal in different time periods are different, the obtained f and k can be expressed as functions of , and the formula for finding the maximum value of the average power spectrum level in the bandwidth can be expressed as:

[0049] ,

[0050] In the formula, argmax is the independent variable that makes the function take the maximum value, represents the modulus, f is the frequency, and k represents the linear frequency modulation factor. represents the segment delay, s(t) is the time domain data, is the window function, t represents the time, and j is the imaginary unit.

[0051] 4) Using the linear frequency modulation factor k obtained in step three, the original signal data is subjected to short-time Chirp-Fourier transform, and the signal time-frequency diagram is reconstructed to realize target frequency offset correction. Specifically:

[0052] Substitute the linear frequency modulation factor (i.e., the frequency modulation factor corresponding to different values) under different window functions into the following calculation formula of short-time Chirp-Fourier transform to transform the original signal data and obtain the reconstructed signal time-frequency diagram. The calculation formula is:

[0053] ,

[0054] wherein, is the reconstructed signal time-frequency map, s(t) is the time domain data, is the window function, f is the frequency, represents the segment time delay, t represents the time, and j is the imaginary unit.

[0055] In the present application, the main parameter setting mode is as follows:

[0056] 1) Frequency offset range: in data post-processing, the frequency offset range can be determined according to the STFT result of the signal. Since the frequency offset comes from the Doppler effect, it is related to the frequency, target motion speed, target distance, and has many influencing factors, therefore, in real-time processing, it should be determined according to the actual situation, such as setting [f0-0.005f0, f0+0.005f0], f0 is the target line spectrum frequency.

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

[0058] 3) Other parameter range: such as the length of the window function should ensure that the target frequency changes approximately linearly within the set time range, and the window length is generally set to 10-30s.

[0059] (II) Simulation and sea trial data test results:

[0060] On the basis of "(I) Implementation process", the processing results of the present application are given through simulation, and the simulation processing is as shown in Figures 2a to 4 .

[0061] Computer simulation 1: assuming that the signal sampling rate is 5000Hz, the target radiation noise frequency is 150Hz, the signal length is 1000s, the closest distance between the target and the receiving hydrophone is 2000m, the arrival time of the closest point of the sound source is 500s, the receiving signal time range is 0-1000s, the underwater sound speed is 1500m / s, and the target motion speed is 10m / s, from which the time domain signal with Doppler effect is constructed, and the short-time Fourier transform and the short-time Chirp-Fourier transform are used for processing respectively, and the processing results are as shown in Figure 2a , Figure 2bIt can be seen from the figure that the line spectrum band broadening phenomenon occurs in the short-time Fourier transform processing at the place where the frequency changes sharply, which means that the line spectrum energy is dispersed in this time period, while the short-time Chirp-Fourier transform processing result shows that the energy is effectively concentrated on the real-time line spectrum at all time periods, compared with the short-time Fourier transform processing result, the line spectrum signal-to-noise ratio is higher, and the Doppler frequency change effect is more obvious.

[0062] Actual data processing: for a lake experiment, the target is a boat, the target line spectrum is 90.7 Hz, the total length of the data is 400 s, and the Chirp-Fourier transform is used to enhance the signal, so that the 90.7 Hz signal peak value before and after the transformation changes with time is obtained as shown in Figure 3 As shown in the figure, since the frequency of the signal is basically stable in 0-50 s, the nonlinear transformation of the signal is very weak, and the Chirp-Fourier transform cannot theoretically obtain benefits at this time, and the gain of the method is more obvious in 50 s-400 s, and there is a large signal-to-noise ratio gain. The CFT transform is performed on the data at a certain time, and the result is as shown in Figure 4 As shown in the figure, the line spectrum obtains a large gain, and the maximum can reach about 4 dB.

[0063] The simulation analysis results show that: through the short-time Chirp-Fourier transform based on the line spectrum enhancement method of the underwater moving target. The method uses Chirp-Fourier transform to restore and enhance the frequency offset signal, and uses the enhanced signal to reconstruct the signal time-frequency diagram, and improves the signal-to-noise ratio of the target line spectrum. The data of the moving target measured in the sea trial are processed, and the results show that the method proposed in the application effectively realizes the enhancement of the target line spectrum, and has good application prospect.

[0064] It should be noted that the above embodiments are only preferred embodiments of the present application, and are not used to limit the protection scope of the present application, and equivalent transformations made on the basis of the above embodiments all belong to the protection scope of the present application.

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.

2. The underwater moving target line spectrum enhancement method based on short-time Chirp-Fourier transform according to claim 1, characterized in that: 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 delay, where t represents time and j is the imaginary unit.

3. The underwater moving target line spectrum enhancement method based on short-time Chirp-Fourier transform according to claim 2, characterized in that: 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.

4. The underwater moving target line spectrum enhancement method based on short-time Chirp-Fourier transform according to claim 3, characterized in that: 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.

5. The underwater moving target line spectrum enhancement method based on short-time Chirp-Fourier transform according to claim 4, characterized in that: 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.

6. The underwater moving target line spectrum enhancement method based on short-time Chirp-Fourier transform according to claim 5, characterized in that: 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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