A lossless resolution sidelobe suppression method

Abstract

The application provides a sidelobe suppression method without loss of resolution, which can completely remove sidelobes and does not lose signal resolution. The method is based on the characteristic that the main lobe width of IPR is twice the sidelobe width. If N sample data of IPR are set, the main lobe width is 4xpi / N, and the sidelobe width is 2xpi / N. By using the fact that the main lobe width is different from the sidelobe width, the positions of the main lobe and the sidelobe in IPR can be located. As long as the positions of the main lobe and the sidelobe are determined, the unwanted sidelobe can be eliminated. The method provided by the application does not need to limit the data sampling rate to be an integer multiple of Nyquist frequency, and is directly applied to the spectrum of a signal, and is simple to calculate.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of digital signal processing, and particularly relates to a method for suppressing sidelobes in the transform domain of a digital signal. TECHNICAL BACKGROUND

[0002] Fourier transform (FT) is the most commonly used method for transforming time domain to frequency domain, and is one of the most commonly used methods in the field of digital signal processing. The precise frequency spectrum of a signal is calculated using FT, which requires the use of an infinitely long time domain signal. However, due to practical constraints, any observable signal processed is of finite length, and therefore the frequency spectrum obtained from the actual sampled data is approximate. For example, when performing Fourier transform on a finite length sinusoidal signal, the obtained frequency spectrum is a Sinc function rather than an impulse function. The Sinc function contains a main lobe with a peak value and a set of sidelobes, and the main lobe is extended to the first zero point, and the sidelobes are composed of residual oscillation waveforms on both sides of the main lobe. The composite function composed of the main lobe and the sidelobes is called the system impulse response (IPR). In the transform domain, finite length data leads to spectral leakage and resolution degradation, which are summarized as follows:

[0003] Spectral leakage: signal energy concentrated at a single frequency is spread over the entire frequency range, which is called spectral leakage, and is described by the sidelobes in the IPR.

[0004] Spectral resolution degradation: the width of the main lobe defines the spectral resolution of the system. As the width of the main lobe expands from 0 to 4 x π / N, the spectral resolution decreases, where N is the data length.

[0005] In the IPR, the center position of the main lobe is related to the frequency of the sinusoidal function. The sidelobes of the IPR are not needed and cannot describe any information of the signal. Even, the existence of the sidelobes reduces the detectability of low amplitude frequency components, i.e. the sidelobes of strong targets affect the detection of weak targets, and in the most serious case, the sidelobes of strong targets completely overwhelm the main lobe of weak targets, causing the weak targets to be undetectable, and the sidelobes of strong targets can also be mistaken for targets. Therefore, the sidelobes in the IPR must be suppressed.

[0006] Traditionally, the sidelobes are suppressed by multiplying the data with an amplitude weighting function (window function) before FT. The window function method is simple to operate, but this method reduces the sidelobes at the expense of broadening the IPR main lobe, thus losing the spectral resolution and reducing the signal-to-noise ratio (SNR). In order to reduce the sidelobes while maintaining the resolution, a class of nonlinear sidelobe suppression techniques has been developed. This class of techniques is called nonlinear apodization (NLA) method, and the most commonly used method in engineering field is spatial apodization (SVA). SVA allows each signal sample to get a frequency aperture amplitude weighting function from a series of possible weighting functions, which can almost completely eliminate the sidelobes. But the basic SVA requires that the signal must be sampled at an integer multiple of the Nyquist frequency. Although some improved SVA algorithms do not require the limitation of the sampling rate of the signal, they will leave some sidelobes or even lose part of the main lobe energy, and the improved SVA algorithms have a large amount of calculation. SUMMARY

[0007] The present application provides a lossless resolution sidelobe suppression method, which can completely remove the sidelobes without losing the signal resolution. This method is based on the fact that the main lobe width of IPR is twice the width of the sidelobe. Assuming that the IPR has N sample data, the main lobe width is 4xpi / N, and the sidelobe width is 2xpi / N. By using the fact that the main lobe and the sidelobe have different widths, the positions of the main lobe and the sidelobe in the IPR can be located. Once the positions of the main lobe and the sidelobe are determined, the unwanted sidelobes can be eliminated. The method proposed in the present application does not require the sampling rate of the data to be an integer multiple of the Nyquist frequency, and can be directly applied to the spectrum of the signal, and the calculation is simple.

[0008] The technical solutions of the present application will be described in detail as follows:

[0009] The lossless resolution sidelobe suppression method of the present application, as shown in Figure 1 , comprises the following steps:

[0010] Step 1: obtaining the N-point spectrum function y[n] of the sampled signal by FT, y[n] is a real function, and N is the number of points of FT calculation.

[0011] Step 2: searching for all zero-crossing points i of the spectrum function y[n], the zero-crossing point i satisfies the condition y[i]≤y[i-1] and y[i]≤y[i+1], and the position value i of the zero-crossing point is stored in the vector array1, and the length of array1 is L.

[0012] Step 3: obtaining the difference sequence D(j) between the continuous zero-crossing points by D(j)=array1(j+1)-array1(j). Wherein array1(j) and array1(j+1) store the position values of two adjacent zero-crossing points in the spectrum y[n], and the vector D(j) stores the position difference values of the corresponding two zero-crossing points. j=1, 2, …, L-1.

[0013] Step 4, search the maximum value Dmax and the minimum value Dmin in the difference value D(j), Dmax represents the main lobe width in the spectrum y[n], and Dmin represents the side lobe width in the spectrum y[n].

[0014] Step 5, compare Dmax and Dmin, if Dmax≥2×Dmin, then proceed to Step 6, otherwise, it is proved that there is no target in the signal, and the calculation is terminated.

[0015] Step 6, calculate the average value M of Dmax and Dmin, Symbol represents rounding up. M is taken as a threshold value for distinguishing the main lobe and the side lobe, so that the judgment process can be simplified.

[0016] Step 7, compare the zero-crossing point difference value in D(j) with the threshold value M, if D(j)≥M, then mark it as the main lobe, represented by a logic value 1, otherwise, mark it as the side lobe, represented by a logic value 0.

[0017] Step 8, according to the main lobe and side lobe marks in the difference value vector D(j), determine the positions of the main lobe zero-crossing points and the side lobe zero-crossing points in array1 respectively. For the position index j marked as the main lobe in D(j), find the zero-crossing point position values stored in the position indexes j and j+1 in the vector array1, that is, obtain the left and right first zero-crossing point position values of a main lobe, find all the main lobe zero-crossing point position values and mark them as logic value 1 in the corresponding positions in array1. Similarly, find all the side lobe zero-crossing point position values and mark them as logic value 0 in the corresponding positions in array1.

[0018] Step 9, according to the positions marked as the side lobe zero-crossing points in array1, set the amplitude values between the adjacent two side lobe zero-crossing points (including the zero-crossing points) in y[n] to zero, eliminate the side lobes, and retain the amplitude values between the main lobe zero-crossing points marked in array1, that is, retain the main lobes. At this time, only the widened main lobes are left in y[n].

[0019] Step 10, retain the amplitude values at the centers of the two zero-crossing points of the main lobe in y[n] to represent the main lobe, and set the other spectrum values in the main lobe due to the widening of the main lobe to zero. In this way, not only the information of the signal is retained, but also the redundant spectrum lines caused by energy leakage are further removed, and the data amount for subsequent processing is reduced.

[0020] The application has the advantages and beneficial effects that the sidelobe suppression method with lossless resolution is proposed by using the property that the main lobe width is twice the sidelobe width, which can completely remove the sidelobe of the non-integer multiple Nyquist frequency sampling signal while maintaining the resolution. Unlike the SVA method, the application can process absolute value sequences or images, the calculation process is simpler, there is no limitation on the signal sampling rate, and is suitable for but not limited to spectrum estimation, multi-target detection, imaging and other processing in engineering applications. BRIEF DESCRIPTION OF DRAWINGS

[0021] Figure 1 is a flowchart of the application.

[0022] Figure 2 is a noise-free signal spectrum diagram.

[0023] Figure 3 is a noise-free signal spectrum diagram after sidelobe suppression by the proposed method.

[0024] Figure 4 is a spectrum diagram of a signal with a signal-to-noise ratio of 15 dB.

[0025] Figure 5 is a spectrum diagram of a signal with a signal-to-noise ratio of 15 dB after sidelobe suppression by the proposed method. DETAILED DESCRIPTION

[0026] In order to more clearly illustrate the technical solutions in the embodiments of the application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiment or prior art description. Obviously, the drawings in the following description are only some embodiments of the application, and other drawings can also be obtained by those skilled in the art without any novelty labor.

[0027] In order to prove the advantages of the method proposed in the application, a multi-frequency sinusoidal signal commonly used in practice is used for verification. Three frequency components are set as 250 kHz (frequency one), 370 kHz (frequency two) and 382 kHz (frequency three), the signal sampling rate is 1 MHz, and 128 points of data are sampled. For frequency one, it is an integer multiple Nyquist frequency sampling, for frequency two and frequency three, it is a non-integer multiple Nyquist frequency sampling, and the interval between frequency two and frequency three is relatively close, about 1.5 resolution units. Verification is carried out in two cases of noise-free signal and noisy signal.

[0028] First, the noise-free signal is verified:

[0029] 1. Get the N-point spectrum function y[n] of the signal by FT, and in order to improve the calculation accuracy, N is 256 here. The spectrum of the signal is as follows: Figure 2The spectrum is centrosymmetric because the signal is a real signal, and there are 6 main lobe peaks.

[0030] 2. Search all zero-crossing points i of the spectrum y[n] that satisfy the condition y[i]≤y[i-1] and y[i]≤y[i+1], and store the zero-crossing point position values i in the vector arrayl. The length of arrayl is L=120.

[0031] 3. Obtain the difference sequence D(j) between consecutive zero-crossing points using D(j)=arrayl(j+1)-arrayl(j). The values stored in arrayl(j) and arrayl(j+1) are the position values of two adjacent zero-crossing points in the spectrum y[n], and the values stored in the vector D(j) are the position differences of the corresponding two zero-crossing points. The length of D(j) is L-1=119.

[0032] 4. Search for the maximum value Dmax=4 and the minimum value Dmin=2 in the difference values D(j). The value Dmax=4 indicates that the main lobe of the spectrum y[n] occupies 5 frequency points, and the value Dmin=2 indicates that the side lobe of the spectrum y[n] occupies 3 frequency points.

[0033] 5. Compare Dmax and Dmin. If Dmax≥2xDmin, it is proved that there is a target frequency, and step 6 is performed.

[0034] 6. Calculate the mean value M of Dmax and Dmin. Symbol represents the upward rounding. Take M as the threshold value for distinguishing the main lobe and the side lobe, so as to simplify the judgment process. After calculation, M=3.

[0035] 7. Compare the zero-crossing point difference values in D(j) with M. If D(j)≥M, mark it as a main lobe, and represent it by the logic value 1; otherwise, mark it as a side lobe, and represent it by the logic value 0. After comparison, 6 main lobes are obtained, and the remaining 113 are side lobes.

[0036] 8. According to the main lobe and side lobe marks in the difference value vector D(j), determine the positions of the main lobe zero-crossing points and the side lobe zero-crossing points in arrayl. For the position index j marked as a main lobe in D(j), find the zero-crossing point position values stored in the position indexes j and j+1 in the vector arrayl, that is, obtain the left and right first zero-crossing point position values of a main lobe. For example, in this embodiment, the first main lobe mark of D(j) corresponds to j=31, and the zero-crossing point position values stored in the indexes 31 and 32 in arrayl are 63 and 67, respectively. Find all main lobe zero-crossing point position values and mark the corresponding positions in arrayl as the logic value 1. Similarly, find all side lobe zero-crossing point position values and mark the corresponding positions in arrayl as the logic value 0.

[0037] 9. Based on the positions marked as zero-crossing points of the side lobes in array1, set the amplitude values ​​between (including) the zero-crossing points of adjacent side lobes in y[n] to zero, thus eliminating the side lobes. Retain the amplitude values ​​marked as between the zero-crossing points of the main lobe in array1, i.e., retain the main lobe. At this point, only the broadened main lobe remains in y[n].

[0038] 10. Retain the amplitude values ​​at the two zero-crossing points of the main lobe in y[n] to represent the main lobe, and set other spectral values ​​in the main lobe that are caused by the broadening of the main lobe to zero. For example, if the positions of the two first zero-crossing points of the main lobe at frequency one are 63 and 67, then take the amplitude value at position 65 in y[n] to represent the main lobe, and set the amplitude values ​​at positions 63, 64, 66, and 67 to zero. This not only preserves the signal information but also further removes energy leakage and reduces the amount of data in subsequent processing.

[0039] The spectrum after sidelobe suppression is as follows: Figure 3 As shown. Figure 2 and Figure 3 The comparison shows that the side lobes in the signal spectrum have been completely suppressed, the main lobe has been preserved, and the resolution has not been reduced. This demonstrates that the method is effective.

[0040] The following verification is performed on a noisy signal, with the signal-to-noise ratio (SNR) set to SNR = 15 dB.

[0041] 1. Obtain the N-point spectrum function y[n] of the signal through Fourier Transform (FT). To improve calculation accuracy, N is set to 256 here. The signal spectrum is as follows: Figure 4 As shown. Since the signal is a real signal, its spectrum is centrally symmetrical, with a total of 6 main lobe peaks. Under the influence of noise, the waveform of the spectrum changes.

[0042] 2. Search for all zero-crossing points i in the spectrum y[n]. The zero-crossing points i satisfy the conditions y[i]≤y[i-1] and y[i]≤y[i+1]. Store the zero-crossing point position values ​​i in the vector array1, and the length of array1 is L=116.

[0043] 3. Use D(j) = array1(j+1) - array1(j) to obtain the difference sequence D(j) between consecutive zero-crossing points. Here, array1(j) and array1(j+1) store the position values ​​of two adjacent zero-crossing points in the spectrum y[n], and the vector D(j) stores the position difference between the corresponding two zero-crossing points. The length of D(j) is L-1 = 115.

[0044] 4、Search the maximum value Dmax=4 and the minimum value Dmin=2 in the difference value D(j). Dmax=4 means that the main lobe of the spectrum y[n] occupies 5 frequency points, and Dmin=2 means that the side lobe of the spectrum y[n] occupies 3 frequency points.

[0045] 5、Compare Dmax and Dmin. If Dmax≥2xDmin, it proves that there is a target frequency, and step 6 is performed.

[0046] 6、Calculate the mean value M of Dmax and Dmin. Symbol represents rounding up. M is used as a threshold value for distinguishing the main lobe and the side lobe, which can simplify the judgment process. After calculation, M=3.

[0047] 7、Compare the zero-crossing point difference value in D(j) with M. If D(j)≥M, it is marked as the main lobe, and represented by a logic value 1; otherwise, it is marked as the side lobe, and represented by a logic value 0. After comparison, 6 main lobes are obtained, and the remaining 109 are side lobes.

[0048] 8、According to the main lobe and side lobe marks in the difference value vector D(j), the positions of the main lobe zero-crossing points and the side lobe zero-crossing points are determined in arrayl. For the position index j marked as the main lobe in D(j), the zero-crossing point position values stored in the position indexes j and j+1 in the vector arrayl are found, that is, the left and right first zero-crossing point position values of a main lobe are obtained. For example, in this embodiment, the first main lobe mark of D(j) corresponds to j=31, and the zero-crossing point position values stored in the position indexes 31 and 32 in arrayl are 63 and 67, respectively. All the main lobe zero-crossing point position values are found and marked as logic value 1 in the corresponding positions in arrayl. Similarly, all the side lobe zero-crossing point position values are found and marked as logic value 0 in the corresponding positions in arrayl.

[0049] 9、According to the positions of the side lobe zero-crossing points marked in arrayl, the amplitude values between the adjacent two side lobe zero-crossing points (including the zero-crossing points) in y[n] are set to zero, the side lobes are eliminated, and the amplitude values between the main lobe zero-crossing points marked in arrayl are retained, that is, the main lobes are retained. At this time, only the widened main lobes are left in y[n].

[0050] 10、The amplitude value at the center of the two zero-crossing points of the main lobe in y[n] is retained to represent the main lobe, and the other spectrum values in the main lobe due to the widening of the main lobe are set to zero. For example, the first two zero-crossing point positions of the main lobe are 63 and 67, respectively, the amplitude value at the position 65 in y[n] is taken to represent the main lobe, and the amplitude values at the positions 63, 64, 66 and 67 are all set to zero. In this way, not only the information of the signal is retained, but also the energy leakage is further removed, and the data amount for subsequent processing is reduced.

[0051] The spectrum diagram after the sidelobe suppression is shown in Figure 5 As shown in Figure 4 and Figure 5 It can be seen that the sidelobes are completely removed, only the main lobe is left, and the resolution is not reduced. Under the influence of noise, the shape and number of sidelobes change, but it does not affect the suppression effect of sidelobes, which shows that even if there is a certain influence of noise, the present application is still effective.

[0052] In practical engineering applications, the method proposed by the present application can be applied to sidelobe suppression for any dimensional signal processing. For signals with poor signal-to-noise ratio, noise filtering, pre-detection and other methods can be used to filter part of the noise before applying the present method for sidelobe suppression. In addition, the present method can also be applied to 2-D signal processing such as imaging, that is, the present method is applied to each row of the 2-D signal, and then the present method is applied to each column of the signal, and after two times of sidelobe suppression, the influence of sidelobes can be removed.

Claims

1. A method of lossless resolution sidelobe suppression, characterized by, The method comprises the following steps: Step 1, obtaining an N-point spectrum function y[n] of a sampling signal by FT, y[n] is a real function, and N is a point number of FT calculation; Step 2, searching all zero-crossing points i of the spectrum function y[n], and storing the zero-crossing point position values i in a vector array1, the length of array1 is L; Step 3, obtaining a difference value sequence D(j) between continuous zero-crossing points by D(j) = array1(j+1)-array1(j); Step 4, searching to obtain a maximum value Dmax and a minimum value Dmin in the difference value D(j), Dmax represents a main lobe width in the spectrum y[n], and Dmin represents a side lobe width in the spectrum y[n]; Step 5, comparing Dmax and Dmin, if Dmax≥2×Dmin, then step 6 is performed, otherwise, it is proved that the target does not exist in the signal, and the calculation is terminated; Step 6, calculating a mean value M of Dmax and Dmin; Step 7, comparing the zero-crossing point difference value in D(j) with a threshold value M, if D(j)≥M, then the main lobe is marked, and a logic value 1 is represented, otherwise, the side lobe is marked, and a logic value 0 is represented; Step 8, according to the main lobe and side lobe marks in the difference value vector D(j), the positions of the main lobe zero-crossing points and the side lobe zero-crossing points in array1 are determined respectively; Step 9, according to the positions of the side lobe zero-crossing points marked in array1, the amplitude values of the zero-crossing points contained between the adjacent two side lobe zero-crossing points in y[n] are set to zero, the side lobes are eliminated, and the amplitude values between the main lobe zero-crossing points marked in array1 are retained, that is, the main lobes are retained; at this time, only the widened main lobes are left in y[n]; Step 10, retaining the amplitude values of the centers of the two zero-crossing points in the main lobes in y[n] to represent the main lobes, and setting other spectrum values in the main lobes to zero due to the widening of the main lobes.

2. The method of lossless resolution sidelobe suppression of claim 1, wherein: In step 2, the zero-crossing point i satisfies the condition y[i]≤y[i-1] and y[i]≤y[i+1].

3. The method of lossless resolution sidelobe suppression of claim 1, wherein: In step 3, array1(j) and array1(j+1) store the position values of two adjacent zero-crossing points in the spectrum y[n], and the vector D(j) stores the position difference values of the corresponding two zero-crossing points; j = 1, 2, …, L-1.

4. The method of lossless resolution sidelobe suppression of claim 1, wherein: In step 6, symbols denotes rounding up; taking M as a threshold value for distinguishing the main lobe and the side lobe, the judgment process is simplified.

5. The method of claim 1 or 3, wherein: In step 8, for the position index j marked as the main lobe in D(j), the zero-crossing point position values stored in the position index j and j+1 in the vector array1 are found, that is, the left and right first zero-crossing point position values of a main lobe are obtained, all the main lobe zero-crossing point position values are found and marked as logic values 1 in the corresponding positions in array1; similarly, all the side lobe zero-crossing point position values are found and marked as logic values 0 in the corresponding positions in array1.

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