Acoustic tomography flow measurement system and acoustic signal positive and negative code coding method applied by acoustic tomography flow measurement system

By using the sound wave signal positive and negative code encoding method in the soundtrack system, the actual receiving sound wave signal is used to perform signal matching calculation filtering, solving the problem of decreased signal recognition accuracy, significantly improved the accuracy of the calculation time of sound wave transmission time Essence

CN119357696AActive Publication Date: 2025-01-24广州远动信息技术有限公司
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Patent Information

Application Number
CN202411451437.7
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-10-17
Publication Date
2025-01-24
Estimated Expiration
2044-10-17

AI Technical Summary

Technical Problem

In the existing acoustic tomography flow measurement system, the signal recognition accuracy decreases, which affects the accuracy of the sound wave propagation time and flow rate calculation.

Method used

The forward and reverse code encoding method of the acoustic signal is used to splice the actual received acoustic signal and its reversed signal to form a forward and reverse code signal, and the signal matching and recognition accuracy are improved through signal forward and reverse code conversion.

Benefits of technology

Effectively improve the accuracy and recognition accuracy of the signal matching, reduce the possibility of signal recognition errors, improve the calculation accuracy of the sound wave reaching time, and increase the accuracy by 9-11%.

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Abstract

The invention discloses an acoustic tomography flow measurement system and an acoustic signal positive and negative code coding method applied by the acoustic tomography flow measurement system, which are characterized in that actually received signal data are used for matching, and through signal positive and negative code conversion, the matching degree of signals can be effectively improved, and the accuracy of calculating the arrival time of acoustic waves is greatly improved. The method comprises the following steps: (1) in a river acoustic tomography flow measurement system, splicing a sound wave signal S and a signal S'which is overturned in an inverted sequence to form a positive and negative code signal SS, and transmitting the positive and negative code signal SS at a probe transmitting end; (2) performing matched filtering calculation on the received sound wave signal R by using a conventional sound wave signal S at a receiving end to obtain a filtering result C, and obtaining the time ts of the maximum value point of the C; and (3) intercepting a matching fragment P from the received sound wave signal R, carrying out reverse-order overturning to obtain P ', and calculating to obtain a new matching filtering result and the arrival time of the sound wave signal R.
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Description

Technical Field

[0001] The invention belongs to the field of intelligent processing of river flow monitoring data, and in particular relates to an acoustic tomography flow measurement system and a positive and negative code encoding method of an acoustic wave signal used in the system. Background Art

[0002] The river acoustic tomography flow measurement technology has the advantages of easy installation, little influence by river surface conditions, and high accuracy. Acoustic tomography technology calculates the river flow rate based on the characteristic that the propagation speed of sound waves in the downstream is faster than that in the upstream. Therefore, accurately calculating the propagation speed and propagation time of sound waves in water is the key to acoustic tomography flow measurement. The acoustic tomography flow measurement system sends a coded sound wave signal from the hydroacoustic probe on one side of the river to the other side. The hydroacoustic probe on the other side receives the sound wave signal and identifies the arrival time of the sound wave, thereby knowing the propagation speed of the sound wave in the water and further calculating the river flow rate.

[0003] At present, due to some physical limitations of underwater acoustic probes, the conventional sound wave signals emitted will be somewhat distorted compared to the ideal sound wave signals. When the existing technology often uses the ideal signal to perform template matching filter calculations on the received signal data, the matching degree will decrease and the signal recognition will be biased. This will have a great impact on the propagation time of the sound wave and the subsequent calculation of the flow velocity.

[0004] The closest existing technology is a coastal acoustic tomography flow measurement method, application number: CN202310314955.3, which includes the following steps: n data collection points are set up in sequence along the coastal area; the n data collection points receive and transmit sound signals to each other to collect cross-correlation data; a two-dimensional flow field between the two points is established through the collected basin data and the reciprocal transmission of sound waves and the acoustic Doppler effect, and a temperature field between the two points is established through the collected cross-correlation data and the NRLⅡ sound speed empirical formula. The maximum cross-correlation peak position is obtained through the cross-correlation algorithm. According to the properties of the cross-correlation function, its ratio to the sampling rate is the propagation time of the sound signal in the direction from the transmitting data collection point to the receiving data collection point. This method is to set equidistant data collection points in advance, and it is impossible to find the collection point with the strongest signal. The measurement interference is large, and it is necessary to build a two-dimensional flow field and temperature field, resulting in poor signal recognition accuracy. Summary of the invention

[0005] In order to solve the problem of reduced signal recognition accuracy in existing systems and river acoustic tomography flow measurement methods, the present invention provides an acoustic tomography flow measurement system and an acoustic wave signal positive and negative code encoding method used therein, which uses the actual received signal data for matching. By converting the signal positive and negative codes, the signal matching degree and recognition accuracy can be effectively improved, and the accuracy of calculating the arrival time of the sound wave can be greatly improved.

[0006] First, the present invention provides a method for encoding positive and negative codes of acoustic wave signals applied to an acoustic tomography flow measurement system, including the steps:

[0007] (1) In a river acoustic tomography flow measurement system, an acoustic wave signal S is spliced together with a reverse-order flipped signal S' to form a positive and negative code signal SS, and the positive and negative code signal SS is transmitted at the probe transmitting end;

[0008] (2) At the receiving end, the received acoustic wave signal R is subjected to matched filtering calculation using a conventional acoustic wave signal S to obtain a filtering result C, and the time of the maximum point of C is obtained as ts;

[0009] (3) A matching segment P is intercepted from the received acoustic wave signal R, and is reverse-order flipped to obtain P', a new matched filtering result is calculated, and the arrival time of the acoustic wave signal R is obtained.

[0010] Further, step (3) specifically includes:

[0011] A matching segment P is intercepted from the received acoustic wave signal R, the interception starting point is t0 = ts - dt, if ts < dt, then t0 = 0, and the interception duration is nS; where nS is the length of the positive and negative code signal SS, and dt is a preset time advance;

[0012] The segment P is reverse-order flipped to P', and template matching filtering calculation is performed on the acoustic wave signal R with P' as the template to obtain a new matched filtering result C', and the time of the peak point of C' is obtained as ts';

[0013] Calculated by the formula Then t is the arrival time of the acoustic wave signal R, and the obtained arrival time t is used for subsequent flow velocity calculation.

[0014] Further, in step (3): the reverse-order flipping of the segment P is to reverse the encoding order of a segment of acoustic wave signal to obtain the corresponding reverse-order flipped segment P'.

[0015] The positive and negative code encoding method uses the actually received acoustic wave signal R for matching calculation and filtering, utilizes the construction of positive and negative codes and the operation of reverse-order flipping the acoustic wave signal, and performs matching on the premise of retaining the characteristics of the actually received acoustic wave signal, improving the signal matching accuracy.

[0016] The acoustic wave signal S is an M-code acoustic wave signal S, and the M-code acoustic wave signal S is spliced together with a reverse-order flipped M-code acoustic wave signal S' to form an M-code positive and negative code signal SS; or the acoustic wave signal S is an acoustic wave signal encoded by other codes, including an acoustic wave signal encoded by a Gold sequence or an acoustic wave signal encoded by a quadratic residue sequence.

[0017] Secondly, the present invention also provides an acoustic tomography flow measurement system with positive and negative code encoding of acoustic signals, including: a signal conversion module for splicing an acoustic signal S and a reverse-flipped signal S' together to form a positive and negative code signal SS; a positive and negative code encoding and processing module for performing matched filtering calculation on the received acoustic signal R using a conventional acoustic signal S to obtain a filtering result C, and obtaining the time of the maximum point of C as ts; a signal filtering and processing module for intercepting a matching segment P from the received acoustic signal R, performing reverse flipping to obtain P', calculating a new matched filtering result, and the arrival time of the acoustic signal R.

[0018] Further, the signal filtering and processing module further includes:

[0019] A signal segment intercepting module for intercepting a matching segment P from the received acoustic signal R, with the intercepting starting point being t0 = ts - dt. If ts < dt, then t0 = 0, and the intercepting duration is nS; where nS is the length of the positive and negative code signal SS, and dt is a preset time advance amount;

[0020] A signal segment processing module for reverse flipping the segment P to P', and performing template matching filtering calculation on the acoustic signal R using P' as a template to obtain a new matched filtering result C', and obtaining the time of the peak point of C' as ts';

[0021] A signal arrival time calculation module for calculating through the formula where t is the arrival time of the acoustic signal R, and the obtained arrival time t is used for subsequent flow velocity calculation.

[0022] The system uses the actually received acoustic signal R for matching calculation and filtering, utilizes the construction of positive and negative codes and the operation of reverse flipping the acoustic signal, and performs matching on the premise of retaining the characteristics of the actually received acoustic signal, improving the signal matching accuracy.

[0023] The acoustic signal S is an M-code acoustic signal S. The M-code acoustic signal S and a reverse-flipped M-code acoustic signal S' are spliced together to form an M-code positive and negative code signal SS; or the acoustic signal S is an acoustic signal with other encodings, including an acoustic signal encoded with a Gold sequence, or an acoustic signal encoded with a quadratic residue sequence.

[0024] Next, by comparing with the prior art, the technical advantages brought by the system and method of the present invention are introduced:

[0025] 1) Underwater acoustic signal detection has its own particularity. It is not as easy as detecting acoustic signals in the atmosphere. The underwater acoustic probe of the acoustic tomography flow measurement system has some physical hardware conditions. The emitted acoustic signals will have a certain degree of distortion compared to the ideal acoustic signals, such as attenuation, deformation, superposition and other interference. The existing measurement technology uses conventional acoustic signal encoding. When the template matching filter calculation is performed on the received signal data with the ideal waveform signal, the matching degree will decrease and the signal recognition will be biased, resulting in a decrease in the accuracy of calculating the arrival time of the sound wave.

[0026] Due to the differences in hardware and water environment, the shapes of sound wave signals emitted by different probes are different. If the ideal waveform signal is used to match the actual signal with differences, it may be difficult to match and the accuracy may decrease. Compared with the prior art, the method and system of the present invention adopts a newly constructed positive and negative code signal, uses the actual received signal to perform matching calculation filtering, utilizes the construction of the positive and negative code and the operation of reverse flipping the signal, and performs accurate matching while retaining the actual signal characteristics. It can avoid the influence of the error between the ideal waveform signal and the actual signal on the matching result, and can effectively improve the signal matching accuracy, so that the propagation time of the sound wave can be accurately calculated, greatly reducing the error. Through experiments, it is found that the accuracy is improved by 9-11% compared with the prior art.

[0027] 2) The method and system of the present invention splices a positive sequence signal and a reverse sequence signal together to form a positive and negative code signal transmission, then intercepts the matching segment P from the received sound wave signal R, and reverses it to obtain P', and calculates a new matched filtering result, which can improve the signal matching degree and resolution. Experiments have shown that the use of positive and negative code signals in acoustic tomography flow measurement is helpful for signal recognition, is not easily affected by noise, and effective peak signals are easy to identify, and the accuracy and stability of sound wave arrival time estimation are significantly improved.

[0028] 3) The system of the present invention comprehensively considers the actual situation that the shapes of the sound wave signals emitted by multiple different probes are different. By encoding the signals with positive and negative codes, the hardware differences of different probes can be well balanced. Finally, the arrival time of the sound wave signal calculated by the special encoding signal filtering formula is more accurate and in line with the actual hydrological situation. The system has a simple architecture, reduces a large amount of data sample training, reduces the amount of calculation by about 15% compared with the existing technology, has a short measurement time and high stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 The figure is a flow chart of the method for encoding the positive and negative codes of acoustic wave signals of the present invention.

[0030] Figure 2 Schematic diagram of ideal received signal and actual received signal.

[0031] Figure 3 Schematic diagram of the matching results using an ideal signal and the matching results using an actual received signal.

[0032] Figure 4 Schematic diagram of the waveform of the received signal of the present invention.

[0033] Figure 5 It is a schematic diagram of the results of matched filtering processing using a normal coded signal and the results of matched filtering processing using the positive and negative code signals of the present invention. DETAILED DESCRIPTION

[0034] The technical solution in the embodiment of the invention will be clearly and completely described below in conjunction with the drawings in this embodiment.

[0035] The present invention provides a method for encoding positive and negative codes of acoustic wave signals applied to an acoustic layer tomography flow measurement system, which splices a positive sequence signal and a reverse sequence signal together to form a positive and negative code signal. The river acoustic layer tomography flow measurement system uses the positive and negative code signal and performs signal analysis processing according to a specific signal processing flow, which can improve signal matching and resolution, reduce the possibility of signal recognition errors, and improve the calculation accuracy of the sound wave arrival time.

[0036] See attached Figure 1 , Embodiment 1, the method of the present invention comprises:

[0037] Step (1) In a river acoustic tomography flow measurement system, a sound wave signal S is spliced ​​with a reversed signal S' to form a positive and negative code signal SS, and the positive and negative code signal SS is sent at the probe transmitting end.

[0038] The frequency of the positive and negative code signal SS remains unchanged, and the waveform is the same as the original sound wave signal S. In actual operation, the sound wave signal S is an M-code sound wave signal S, and the M-code sound wave signal S is spliced ​​with an M-code sound wave signal S' that is reversed in reverse order to form an M-code positive and negative code signal SS; or the sound wave signal S is a sound wave signal of other encodings, such as a sound wave signal encoded by a Gold sequence, or a sound wave signal encoded by a secondary residue sequence, which can be converted into a positive and negative code signal using the method of the present invention.

[0039] Step (2) At the receiving end, the received sound wave signal R is subjected to matched filtering calculation using a conventional sound wave signal S to obtain a filtering result C, and the time of the maximum value of C is obtained as ts.

[0040] The sound wave signal R received by the receiving end is the original positive and negative code signal SS in an ideal state without considering interference. However, in reality, the complex river conditions will cause interference such as weakening, deformation, and superposition of the waveform signal. Therefore, the sound wave signal R received by the receiving end is different from the positive and negative code signal SS sent by the transmitting end.

[0041] Step (3) intercepts the matching segment P from the received acoustic wave signal R, reverses it in order to obtain P', calculates the new matched filtering result, and the arrival time of the acoustic wave signal R.

[0042] The specific process is as follows. Intercept the matching segment P from the received acoustic wave signal R. The starting point of interception is t0 = ts - dt. If ts < dt, then t0 = 0. The interception duration is nS; where nS is the length of the positive and negative code signal SS, and dt is a preset time advance, generally set to one-tenth of nS.

[0043] Reverse the segment P to P'. Use P' as a template to perform template matching filtering calculation on the acoustic wave signal R to obtain the new matched filtering result C'. The time of the peak point of C' is obtained as ts'; reversing the segment P means reversing the encoding order of a segment of the acoustic wave signal to obtain the corresponding reversed segment P'. For example, if the original signal encoding is 12345, the reversed signal encoding is 54321.

[0044] Calculate through the formula Then t is the arrival time of the acoustic wave signal R, and the obtained arrival time t is used for subsequent flow velocity calculation.

[0045] The derivation process of the above formula assumes that the acoustic wave signal actually arrives at t, the signal length is nS, and the starting point of interception is t0. Then the actually intercepted first t - t0 sampling points are noise points, and the ending point of interception is located at the last t - t0 points of the actual signal; reverse the intercepted segment P and perform the matched filtering process again. The maximum point ts' of the matched filtering result is located at the t - t0th point after the starting point t of the actual signal, ts' = t + t - t0. Therefore

[0046] The positive and negative code encoding method of the present invention uses the actually received acoustic wave signal R to perform matching calculation and filtering. By utilizing the structure of the positive and negative codes and the operation of reversing the acoustic wave signal in order, matching is performed on the premise of retaining the characteristics of the actually received acoustic wave signal, which can avoid the influence of the error between the ideal signal and the actual signal on the matching result, effectively improve the signal matching accuracy, and thus accurately calculate the propagation time of the acoustic wave.

[0047] See the appendix Figure 2-5 , and through simulation and comparison of experimental data, the excellent effect of the method of the present invention is proved.

[0048] I. The ideal acoustic wave signal and the actually received acoustic wave signal are as Figure 2 , and it can be seen that the difference in the signal waveforms is relatively obvious.

[0049] Compare the matching result of the ideal signal with the ideal received signal with the matching result of the actual received signal as follows Figure 3 , it can be seen that the matching degree of the actual matching result is slightly lower than the ideal situation, Figure 3 The right waveform diagram in shows that there is a secondary peak after the highest peak of the actual matching waveform, which will affect the subsequent identification of the arrival time of the sound wave.

[0050] II. In the method of the present invention, the sound wave signal R received by the system receiving end is as follows Figure 4 . For Figure 4 The signal is subjected to matching filtering processing using the existing technology normal coding signal, and the result is shown in Figure 5 The left small diagram in, compared with the matching filtering processing using the positive and negative code signals of the present invention, is shown in Figure 5 The right small diagram in.

[0051] It can be seen that at the same sampling point position, the matching degree of the sampling point matching result (the first peak) of the positive and negative code signal is higher than that of the normal coding signal, which is the highest value of the whole result. There are no other secondary peaks near the matching result, that is, the interference clutter is excluded, which is easy to distinguish and filter out, indicating that the result is better, proving that the signal encoded by the positive and negative codes of the present invention helps to effectively measure signal recognition, is not easily affected by noise, and greatly improves the accuracy and stability of the sound wave arrival time estimation. Since theoretically the first peak of the sampling point waveform diagram is the sound wave reaching through the shortest distance, it is least affected by the river bottom reflection and has the highest intensity. The subsequent secondary peaks are signals that have undergone more reflections or other noises. Therefore, the highest first peak proves the best signal recognition.

[0052] The present invention also provides an acoustic tomography flow measurement system with positive and negative code encoding of sound wave signals. Using the method of the above embodiment, it includes: a signal conversion module for splicing an acoustic wave signal S and a reverse-order flipped signal S' together to form a positive and negative code signal SS; a positive and negative code encoding processing module for performing matching filtering calculation on the received acoustic wave signal R using a conventional acoustic wave signal S to obtain a filtering result C, and obtaining the time of the maximum value point of C as ts; a signal filtering processing module for intercepting a matching segment P from the received acoustic wave signal R, performing reverse-order flipping to obtain P', calculating a new matching filtering result, and the arrival time of the acoustic wave signal R.

[0053] The signal filtering processing module further includes:

[0054] A signal segment intercepting module for intercepting a matching segment P from the received acoustic wave signal R, the intercepting starting point being t0 = ts - dt. If ts < dt, then t0 = 0, and the intercepting duration is nS; where nS is the length of the positive and negative code signal SS, and dt is a preset time advance amount;

[0055] A signal segment processing module is used to reverse the segment P to P', use P' as a template to perform template matching filter calculation on the sound wave signal R, obtain a new matching filter result C', and obtain the time of the peak point of C' as ts';

[0056] Signal arrival time calculation module, used to calculate by formula Then t is the arrival time of the sound wave signal R, and the arrival time t is used for subsequent flow velocity calculation.

[0057] The system uses the actual received sound wave signal R to perform matching calculation filtering, utilizes the construction of positive and negative codes and the operation of reverse flipping the sound wave signal, performs matching while retaining the characteristics of the actual received sound wave signal, and improves the signal matching accuracy.

[0058] The sound wave signal S is an M-code sound wave signal S, which is spliced ​​together with an M-code sound wave signal S' that is reversed in reverse order to form an M-code positive and negative code signal SS; or the sound wave signal S is a sound wave signal encoded by other codes, including a sound wave signal encoded by a Gold sequence, or a sound wave signal encoded by a quadratic residue sequence.

[0059] The system of the present invention comprehensively considers the actual situation that the shapes of the sound wave signals emitted by multiple different probes are different. By encoding the signals with positive and negative codes, the hardware differences of different probes can be well balanced. Finally, the arrival time of the sound wave signal calculated by the special encoding signal filtering formula on the host is more accurate and in line with the actual hydrological situation. The system has a simple architecture, reduces a large amount of data sample training, and has a high degree of intelligent operation.

Claims

1. A method for encoding the positive and negative codes of acoustic wave signals in an acoustic tomography flow measurement system, characterized in that: Including the steps: (1) In the river acoustic tomography flow measurement system, splice an acoustic wave signal S with a reverse-order flipped signal S' together to form a positive and negative code signal SS, and transmit the positive and negative code signal SS at the transmitter end of the probe; (2) At the receiving end, perform matched filtering calculation on the received acoustic wave signal R using the conventional acoustic wave signal S to obtain a filtering result C, and obtain the time of the maximum point of C as ts; (3) Intercept a matching segment P from the received acoustic wave signal R, reverse its order to obtain P', calculate a new matched filtering result, and the arrival time of the acoustic wave signal R.

2. According to claim 1, a method for encoding the forward and reverse codes of acoustic wave signals in an acoustic tomography flow measurement system, characterized in that: Step (3) specifically includes: Intercept a matching segment P from the received acoustic wave signal R, the intercept starting point is t0 = ts - dt, if ts < dt, then t0 = 0, and the intercept duration is nS; where nS is the length of the positive and negative code signal SS, and dt is a preset time advance; Reverse the order of the segment P to obtain P', perform template matching filtering calculation on the acoustic wave signal R with P' as the template to obtain a new matched filtering result C', and obtain the time of the peak point of C' as ts'; Calculate by formula Then t is the arrival time of the sound wave signal R, and the arrival time t is used for subsequent flow velocity calculation.

3. According to claim 1, a method for encoding the forward and reverse codes of acoustic wave signals used in an acoustic tomography flow measurement system, characterized in that: In step (3): Reversing the order of the segment P means reversing the coding order of a segment of acoustic wave signal to obtain the corresponding reversed segment P'.

4. The method for encoding positive and negative codes of acoustic wave signals applied to an acoustic tomography flow measurement system according to claim 1, characterized in that The positive and negative code encoding method uses the actually received acoustic wave signal R for matched calculation filtering, utilizes the construction of positive and negative codes and the operation of reversing the order of the acoustic wave signal, and performs matching on the premise of retaining the characteristics of the actually received acoustic wave signal, improving the signal matching accuracy.

5. The method for encoding positive and negative codes of acoustic wave signals applied to an acoustic tomography flow measurement system according to claim 1 or 2, characterized in that The acoustic wave signal S is an M-code acoustic wave signal S, splice this M-code acoustic wave signal S with a reverse-order flipped M-code acoustic wave signal S' together to form an M-code positive and negative code signal SS; or the acoustic wave signal S is an acoustic wave signal encoded by other codes, including an acoustic wave signal encoded by a Gold sequence or an acoustic wave signal encoded by a quadratic residue sequence.

6. An acoustic chromatography flow measurement system with positive and negative coding of acoustic wave signals, characterized in that: Including a signal conversion module for splicing an acoustic wave signal S with a reverse-order flipped signal S' together to form a positive and negative code signal SS; A positive and negative code encoding and processing module for performing matched filtering calculation on the received acoustic wave signal R using the conventional acoustic wave signal S to obtain a filtering result C, and obtaining the time of the maximum point of C as ts; A signal filtering and processing module for intercepting a matching segment P from the received acoustic wave signal R, reversing its order to obtain P', calculating a new matched filtering result, and the arrival time of the acoustic wave signal R.

7. The acoustic tomography flow measurement system with acoustic wave signal positive and negative code encoding according to claim 6, characterized in that: The signal filtering and processing module further includes: A signal segment intercepting module for intercepting a matching segment P from the received acoustic wave signal R, the intercept starting point is t0 = ts - dt, if ts < dt, then t0 = 0, and the intercept duration is nS; where nS is the length of the positive and negative code signal SS, and dt is a preset time advance; A signal segment processing module is used to reverse the segment P to P', use P' as a template to perform template matching filter calculation on the sound wave signal R, obtain a new matching filter result C', and obtain the time of the peak point of C' as ts'; Signal arrival time calculation module, used to calculate by formula Then t is the arrival time of the sound wave signal R, and the arrival time t is used for subsequent flow velocity calculation.

8. The acoustic tomography flow measurement system with acoustic wave signal positive and negative code encoding according to claim 6, characterized in that: The system uses the actual received sound wave signal R to perform matching calculation filtering, utilizes the construction of positive and negative codes and the operation of reverse flipping the sound wave signal, performs matching while retaining the characteristics of the actual received sound wave signal, and improves the signal matching accuracy.

9. The acoustic tomography flow measurement system with acoustic wave signal positive and negative code encoding according to claim 6, characterized in that: The sound wave signal S is an M-code sound wave signal S, which is spliced ​​together with an M-code sound wave signal S' that is reversed in reverse order to form an M-code positive and negative code signal SS; or the sound wave signal S is a sound wave signal encoded by other codes, including a sound wave signal encoded by a Gold sequence, or a sound wave signal encoded by a quadratic residue sequence.

Citation Information

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