Sidelobe suppression method of lossless resolution

Abstract

According to the side lobe suppression method without losing the resolution, the side lobe can be completely removed, and the signal resolution is not lost. The method is based on the characteristic that the IPR main lobe width is twice of the side lobe width. The IPR is set to have N sample data, the width of a main lobe is 4 * pi / N, and the width of a side lobe is 2 * pi / N; by utilizing the fact that the widths of the main lobe and the side lobe are different, the positions of the main lobe and the side lobe in the IPR can be positioned. As long as the positions of the main lobe and the side lobe are determined, the unwanted side lobe can be eliminated. The method provided by the invention does not need to limit the data sampling rate to be an integral multiple of Nyquist frequency, is directly applied to the frequency spectrum of the signal, and is simple in calculation.

Description

Technical Field

[0001] The invention belongs to the field of digital signal processing applications, and in particular relates to a digital signal transform domain sidelobe suppression method. Technical Background

[0002] Fourier transform (FT) is the most commonly used method for transforming from time domain to frequency domain, and it is also one of the most commonly used methods in the field of digital signal processing. Using FT to calculate the precise spectrum of a signal requires the use of a time domain signal of infinite length. However, due to practical limitations, any observable signal processed is of finite length, so the spectrum calculated from the actual sampled data is approximate. For example, when a finite-length sinusoidal signal is subjected to Fourier transform, the spectrum obtained is a Sinc function rather than an impulse function. The Sinc function contains a main lobe and a set of side lobes. The main lobe has a peak value, and its width extends to the first zero crossing point. The side lobes are composed of residual oscillation waveforms on both sides of the main lobe. The composite function composed of the main lobe and the side lobes is called the system impulse response (IPR). In the transform domain, finite-length data leads to spectrum leakage and resolution deterioration. These two problems are summarized as follows:

[0003] Spectrum leakage: The signal energy concentrated on a single frequency spreads to the entire frequency range. This phenomenon is called spectrum leakage and is described by side lobes in IPR.

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

[0005] In IPR, the center position of the main lobe is related to the frequency of the sine function. The side lobes of IPR are unnecessary and cannot describe any information of the signal. In fact, the existence of side lobes reduces the detectability of low-amplitude frequency components, that is, the side lobes of strong targets affect the detection of weak targets. In the worst case, the side lobes of strong targets completely submerge the main lobes of weak targets, making it impossible to detect weak targets, and the side lobes of strong targets may also be regarded as targets. Therefore, the side lobes in IPR must be suppressed.

[0006] Traditionally, side lobes are suppressed by multiplying the data by an amplitude weighting function (window function) before FT. The window function method is simple to operate, but this method reduces the side lobes while broadening the IPR main lobe, thus losing spectral resolution and reducing the signal-to-noise ratio (SNR). In order to maintain resolution while reducing the side lobes, a class of nonlinear side lobe suppression techniques has been developed. This type of technology is called the nonlinear apodization (NLA) method, and the spatial apodization method (SVA) is widely used in the engineering field. SVA allows each signal sample to obtain a self-frequency aperture amplitude weight function from a series of possible weight functions, which can almost completely eliminate side lobes. However, the basic SVA requires that the signal must be sampled at integer multiples of the Nyquist frequency. Although some improved SVA algorithms do not need to limit the sampling rate of the signal, some side lobes will remain, or even some main lobe energy will be lost, and the improved SVA algorithm has a large amount of calculation. Summary of the invention

[0007] The present invention proposes a sidelobe suppression method with lossless resolution, which can completely remove sidelobes without losing signal resolution. This method is based on the characteristic that the main lobe width of the IPR is twice the sidelobe width. Assuming that the IPR has N sample data, the main lobe width is 4×π / N, and the sidelobe width is 2×π / N. Utilizing the fact that the main lobe and sidelobe widths are different, the positions of the main lobe and sidelobe in the IPR can be located. As long as the positions of the main lobe and sidelobe are determined, the unnecessary sidelobes can be eliminated. The method proposed by the present invention does not need to limit the data sampling rate to an integer multiple of the Nyquist frequency, and is directly applied to the spectrum of the signal, and the calculation is simple.

[0008] The technical solution of the present invention is described in detail below:

[0009] The present invention provides a method for sidelobe suppression without loss of resolution, such as Figure 1 As shown, the following steps are included:

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

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

[0012] Step 3, use D(j) = array1(j+1)-array1(j) to obtain the difference sequence D(j) between consecutive zero-crossing points. 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. j = 1, 2, ..., L-1.

[0013] Step 4: Search and obtain the maximum value Dmax and the minimum value Dmin in the difference D(j), where 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, 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 mean M of Dmax and Dmin. symbol Indicates rounding up. Using M as the threshold for distinguishing the main lobe from the side lobe can simplify the judgment process.

[0016] Step 7: Compare the zero-crossing point difference in D(j) with the threshold M. If D(j)≥M, it is marked as the main lobe, represented by a logical value of 1; otherwise, it is marked as the side lobe, represented by a logical value of 0.

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

[0018] Step 9: According to the position of the side lobe zero crossing point marked in array1, the amplitude values ​​between the two adjacent side lobe zero crossing points (including the zero crossing point) in y[n] are set to zero to eliminate the side lobe, and the amplitude values ​​between the main lobe zero crossing points marked in array1 are retained, that is, the main lobe is retained. At this point, only the widened main lobe remains in y[n].

[0019] Step 10: retain the amplitude value of the center of the two zero-crossing points of the main lobe in y[n] to represent the main lobe, and set other spectrum values ​​in the main lobe due to the broadening of the main lobe to zero. This not only retains the signal information, but also further removes the redundant spectrum lines generated by energy leakage, reducing the amount of data for subsequent processing.

[0020] The advantages and beneficial effects of the present invention are as follows: the present invention utilizes the property that the main lobe width is twice the side lobe width, and proposes a lossless resolution side lobe suppression method, which can completely remove the side lobes of the non-integer multiple Nyquist frequency sampling signal while maintaining the resolution. Unlike the SVA method, the present invention can process absolute value sequences or images, the calculation process is simpler, there is no limit on the signal sampling rate, and it is applicable to, but not limited to, spectrum estimation, multi-target detection, imaging and other processing in engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 It is a flow chart of the present invention.

[0022] Figure 2 It is the spectrum of the noise-free signal.

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

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

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

[0026] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without expending any novel work.

[0027] In order to prove the advantages of the method proposed in the present invention, a multi-frequency sinusoidal signal commonly used in practice is used for verification. The three frequency components are set to 250kHz (frequency one), 370kHz (frequency two) and 382kHz (frequency three), the signal sampling rate is 1MHz, and 128 points of data are sampled. For frequency one, it is an integer multiple of the Nyquist frequency sampling, and for frequency two and frequency three, it is a non-integer multiple of the 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: noise-free signal and noisy signal.

[0028] First, verify the noise-free signal:

[0029] 1. Obtain the N-point spectrum function y[n] of the signal through FT. In order to improve the calculation accuracy, N is 256 here. The spectrum of the signal is as follows Figure 2As shown in Figure 2, since the signal is a real signal, the spectrum is centrally symmetrical and has 6 main lobe peaks.

[0030] 2. Search for all zero-crossing points i of the spectrum y[n], where the zero-crossing point i satisfies the conditions y[i]≤y[i-1] and y[i]≤y[i+1], and store the zero-crossing point position value i in vector array1, where the length of array1 is L=120.

[0031] 3. Use D(j)=array1(j+1)-array1(j) to obtain the difference sequence D(j) between consecutive zero-crossing points. 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 two corresponding zero-crossing points. The length of D(j) is L-1=119.

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

[0033] 5. Compare Dmax and Dmin. If Dmax ≥ 2 × Dmin, it proves that the target frequency exists and proceed to step 6.

[0034] 6. Calculate the mean M of Dmax and Dmin, symbol Indicates rounding up. M is used as the threshold for distinguishing the main lobe from the side lobe, which can simplify the judgment process. After calculation, M = 3.

[0035] 7. Compare the zero-crossing point difference in D(j) with M. If D(j) ≥ M, it is marked as the main lobe, represented by a logical value of 1. Otherwise, it is marked as a side lobe, represented by a logical value of 0. After comparison, a total of 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 vector D(j), the positions of the main lobe zero-crossing point and the side lobe zero-crossing point are determined in array1 respectively. For the position index j marked as the main lobe in D(j), find the zero-crossing position values ​​stored in the position indexes j and j+1 respectively in the vector array1, that is, obtain the left and right first zero-crossing 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 position values ​​stored in the corresponding indexes 31 and 32 in array1 are 63 and 67 respectively. Find all the main lobe zero-crossing position values ​​and mark the corresponding positions in array1 as logical value 1. Similarly, find all the side lobe zero-crossing position values ​​and mark the corresponding positions in array1 as logical value 0.

[0037] 9. According to the position of the side lobe zero crossing point marked in array1, set the amplitude value between the two adjacent side lobe zero crossing points (including the zero crossing point) in y[n] to zero, eliminate the side lobe, and keep the amplitude value between the main lobe zero crossing points marked in array1, that is, keep the main lobe. At this point, only the widened main lobe remains in y[n].

[0038] 10. The amplitude values ​​at the centers of the two zero crossing points of the main lobe in y[n] are retained to represent the main lobe, and other spectrum values ​​in the main lobe due to the broadening of the main lobe are set to zero. For example, if the two first zero crossing points of the main lobe of frequency 1 are 63 and 67, the amplitude value at position 65 in y[n] is taken to represent the main lobe, and the amplitude values ​​at positions 63, 64, 66, and 67 are all set to zero. This not only retains the information of the signal, but also further removes energy leakage, reducing the amount of data for subsequent processing.

[0039] The spectrum after sidelobe suppression is as follows Figure 3 shown. Figure 2 and Figure 3 By comparison, we can see that the side lobes in the signal spectrum have been completely suppressed, the main lobe has been retained, and the resolution has not been reduced, which shows that this method is effective.

[0040] The following is a verification of a noisy signal, where the signal-to-noise ratio is set to SNR=15dB.

[0041] 1. Obtain the N-point spectrum function y[n] of the signal through FT. In order to improve the calculation accuracy, N is 256 here. The spectrum of the signal is as follows Figure 4 As shown in the figure. Since the signal is a real signal, the spectrum is centrally symmetrical and has 6 main lobe peaks. Under the influence of noise, the waveform of the spectrum changes.

[0042] 2. Search for all zero-crossing points i of the spectrum y[n], where the zero-crossing point i satisfies the conditions y[i]≤y[i-1] and y[i]≤y[i+1], and store the zero-crossing point position value i in vector array1, where 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. 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 two corresponding zero-crossing points. The length of D(j) is L-1=115.

[0044] 4. The maximum value Dmax=4 and the minimum value Dmin=2 in the difference D(j) are searched. Dmax=4 indicates that the main lobe of the spectrum y[n] occupies a width of 5 frequency points, and Dmin=2 indicates that the side lobe of the spectrum y[n] occupies a width of 3 frequency points.

[0045] 5. Compare Dmax and Dmin. If Dmax ≥ 2 × Dmin, it proves that the target frequency exists and proceed to step 6.

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

[0047] 7. Compare the zero-crossing point difference in D(j) with M. If D(j) ≥ M, it is marked as the main lobe, represented by a logical value of 1. Otherwise, it is marked as a side lobe, represented by a logical value of 0. After comparison, a total of 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 vector D(j), the positions of the main lobe zero-crossing point and the side lobe zero-crossing point are determined in array1 respectively. For the position index j marked as the main lobe in D(j), find the zero-crossing position values ​​stored in the position indexes j and j+1 respectively in the vector array1, that is, obtain the left and right first zero-crossing 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 position values ​​stored in the corresponding indexes 31 and 32 in array1 are 63 and 67 respectively. Find all the main lobe zero-crossing position values ​​and mark the corresponding positions in array1 as logical value 1. Similarly, find all the side lobe zero-crossing position values ​​and mark the corresponding positions in array1 as logical value 0.

[0049] 9. According to the position of the side lobe zero crossing point marked in array1, set the amplitude value between the two adjacent side lobe zero crossing points (including the zero crossing point) in y[n] to zero, eliminate the side lobe, and keep the amplitude value between the main lobe zero crossing points marked in array1, that is, keep the main lobe. At this point, only the widened main lobe remains in y[n].

[0050] 10. The amplitude values ​​at the centers of the two zero crossing points of the main lobe in y[n] are retained to represent the main lobe, and other spectrum values ​​in the main lobe due to the broadening of the main lobe are set to zero. For example, if the two first zero crossing points of the main lobe of frequency 1 are 63 and 67, the amplitude value at position 65 in y[n] is taken to represent the main lobe, and the amplitude values ​​at positions 63, 64, 66, and 67 are all set to zero. This not only retains the information of the signal, but also further removes energy leakage, reducing the amount of data for subsequent processing.

[0051] The spectrum after sidelobe suppression is as follows Figure 5 As shown. Figure 4 and Figure 5 It can be seen that the side lobes are completely removed, leaving only the main lobe, and the resolution is not reduced. Under the influence of noise, the shape and number of the side lobes change, but the side lobe suppression effect is not affected, which shows that even if there is a certain amount of noise, the present invention is still effective.

[0052] In practical engineering applications, the method proposed in the present invention 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 out part of the noise before applying this method for sidelobe suppression. In addition, this method can also be applied to 2-D signal processing such as imaging, that is, the method is first applied to each row of the 2-D signal, and then to each column of the signal. After two sidelobe suppressions, the sidelobe effect can be removed.

Claims

1. A method for sidelobe suppression without loss of resolution, characterized in that: The steps include: Step 1: Obtain the N-point spectrum function y[n] of the sampled signal through FT, where y[n] is a real function and N is the number of points calculated by FT; Step 2, search for all zero-crossing points i of the spectrum function y[n], and store the zero-crossing point position value i in vector array1, where the length of array1 is L; Step 3, using D(j)=array1(j+1)-array1(j) to obtain the difference sequence D(j) between consecutive zero-crossing points; Step 4, search and obtain the maximum value Dmax and the minimum value Dmin in the difference D(j), where Dmax represents the main lobe width in the spectrum y[n], and Dmin represents the side lobe width in the spectrum y[n]; Step 5: Compare Dmax and Dmin. If Dmax ≥ 2 × Dmin, proceed to step 6. Otherwise, it is proved that there is no target in the signal and the calculation is terminated. Step 6, calculate the mean M of Dmax and Dmin; Step 7, compare the zero-crossing point difference in D(j) with the threshold M, if D(j) ≥ M, mark it as the main lobe, represented by a logical value of 1, otherwise, mark it as the side lobe, represented by a logical value of 0; Step 8, according to the main lobe and side lobe marks in the difference vector D(j), determine the positions of the main lobe zero crossing point and the side lobe zero crossing point in array1 respectively; Step 9: according to the position of the side lobe zero crossing point marked in array1, set the amplitude value including the zero crossing point between two adjacent side lobe zero crossing points in y[n] to zero, eliminate the side lobe, and retain the amplitude value between the main lobe zero crossing points marked in array1, that is, retain the main lobe; at this point, only the widened main lobe remains in y[n]; Step 10: retain the amplitude values ​​of the centers of the two zero-crossing points of the main lobe in y[n] to represent the main lobe, and set other spectrum values ​​in the main lobe caused by the broadening of the main lobe to zero.

2. The method for sidelobe suppression without loss of resolution according to claim 1, characterized in that: In step 2, the zero-crossing point i satisfies the conditions y[i]≤y[i-1] and y[i]≤y[i+1].

3. The method for sidelobe suppression without loss of resolution according to claim 1, characterized in that: 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 vector D(j) stores the position difference between the two corresponding zero-crossing points; j=1, 2,…, L-1.

4. The method for sidelobe suppression without loss of resolution according to claim 1, characterized in that: In step 6, symbol Indicates rounding up; M is used as the threshold for distinguishing the main lobe from the side lobe to simplify the judgment process.

5. A method for sidelobe suppression without loss of resolution according to claim 1 or 3, characterized in that: In step 8, for the position index j marked as the main lobe in D(j), find the zero-crossing position values ​​stored in the position index j and j+1 respectively in the vector array1, that is, obtain the two first zero-crossing position values ​​on the left and right of a main lobe, find all the main lobe zero-crossing position values ​​and mark the corresponding positions in array1 as logical value 1; similarly, find all the side lobe zero-crossing position values ​​and mark the corresponding positions in array1 as logical value 0.

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