Instantaneous signal frequency processing method for wireless acoustic sensor
By performing zero-filling and initial phase sorting splicing on the echo signal of the resonant SAW sensor, combined with FFT analysis, the problems of insufficient frequency processing accuracy and environmental influence were solved, and high-precision frequency resolution was achieved.
Patent Information
- Application Number
- CN202510965610.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-14
- Publication Date
- 2025-11-07
AI Technical Summary
Existing resonant SAW sensors lack sufficient frequency processing accuracy and are susceptible to environmental influences, making it difficult to meet the requirements of highly dynamic and complex application environments for critical equipment in nuclear facilities.
By performing zero-filling processing and initial phase sorting on the multi-segment sampled signals of the echo signal, splicing them together, and then performing FFT analysis, the instantaneous signal frequency processing result is obtained.
With the instantaneous signal lasting only 10μs, the frequency estimation error is reduced to below 1.32kHz, meeting the frequency resolution requirements of the resonant SAW sensor and reducing frequency processing errors and environmental impact.
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Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of wireless acoustic sensor, in particular to a transient signal frequency processing method for wireless acoustic sensor. BACKGROUND
[0002] Surface acoustic wave (SAW) sensor has broad prospects in the field of passive networking and real-time monitoring of nuclear facility key equipment failure and health status evaluation due to its wireless passive, multi-parameter simultaneous measurement, anti-electromagnetic interference, and stable operation in complex environment, which is of great significance and wide application to ensure the safe, long-term and effective operation of nuclear facilities. The SAW wireless sensor includes a sensor module, a wireless communication module, and a processor module. Multi-parameter decoupling and data processing are very important for high-precision measurement of the sensor.
[0003] With the development of SAW sensor technology, resonant SAW sensors have become increasingly important in nuclear facility key high-dynamic complex application environments due to their high Q value, strong anti-interference ability, and high sensitivity. However, the echo signal duration of resonant SAW sensors is usually only a few microseconds, which brings great challenges to fast frequency processing.
[0004] The commonly used frequency processing algorithms at present mainly include Rife algorithm based on FFT spectrum and signal splicing algorithm based on FFT spectrum. Rife algorithm processes frequency offset by the maximum spectral line and the adjacent second largest spectral line, and corrects the frequency processing with small calculation amount. However, when the actual frequency is near the maximum spectral line frequency, the frequency processing accuracy of this algorithm is poor and is easily affected by the environment. The signal splicing algorithm obtains multiple echo signals through multiple sampling, and then simply splices all the echo signals to increase the signal duration and improve the frequency resolution. Although this method can improve the frequency resolution to a certain extent, there is a phase discontinuity problem at the splicing place of each signal, which introduces errors for frequency processing. For example, under the condition of 32MHz sampling frequency, 256 points of each signal, and 128 signals splicing, the frequency resolution can only reach 16kHz, which cannot meet the requirements of SAW temperature sensor.
[0005] Therefore, there is an urgent need for a transient signal frequency processing method for wireless acoustic sensor to solve the problems in the prior art. SUMMARY
[0006] The present application aims to solve the problem of insufficient frequency processing accuracy and easy environmental influence in the prior art, and provides a transient signal frequency processing method for wireless acoustic sensor which can improve frequency resolution and reduce frequency processing error.
[0007] To achieve the above object, the application provides a transient signal frequency processing method for a wireless acoustic sensor, comprising the following steps:
[0008] S1, acquiring a plurality of sampled signals of an echo signal;
[0009] S2, performing zero padding processing on the plurality of sampled signals of the echo signal to acquire a spliced signal;
[0010] S3, performing FFT analysis on the spliced signal to acquire a transient signal frequency processing result.
[0011] Optionally, the plurality of sampled signals of the echo signal comprises:
[0012] performing signal processing on an initial echo signal to acquire an echo signal;
[0013] performing multiple excitations on the echo signal by using an excitation sensor based on a target sampling rate to acquire the plurality of sampled signals of the echo signal;
[0014] wherein the target sampling rate is 32 MHz, 256 points of each of the echo signals are sampled, and 128 signals are sampled.
[0015] Optionally, the zero padding processing on the plurality of sampled signals of the echo signal to acquire the spliced signal comprises:
[0016] performing zero padding processing on the plurality of sampled signals of the echo signal at non-sampling points to acquire a zero padding signal;
[0017] performing splicing processing on the zero padding signal to acquire the spliced signal.
[0018] Optionally, a calculation formula of the zero padding signal is as follows:
[0019]
[0020] wherein y i [n] is the zero padding signal, f0 is an echo signal frequency, n is a sampling point index, T s is a sampling period, φ i is an initial phase of the i-th signal, and N is a sampling point number of each signal.
[0021] Optionally, the splicing processing on the zero padding signal to acquire the spliced signal comprises:
[0022] acquiring an initial phase of the zero padding signal according to the zero padding signal;
[0023] sorting the zero padding signal according to the initial phase of the zero padding signal to acquire a sorting result of the zero padding signal;
[0024] The sorting result of the zero-padding signal is spliced to obtain a spliced signal.
[0025] Optionally, the sorting of the zero-padding signal according to the initial phase of the zero-padding signal comprises:
[0026] The initial phase continuity zero-padding signal is obtained by sorting the zero-padding signal according to the initial phase of the zero-padding signal.
[0027] The last initial phase of the first segment signal and the first initial phase of the second segment signal are obtained according to the initial phase continuity zero-padding signal.
[0028] It is judged whether the last initial phase of the first segment signal is less than or equal to the first initial phase of the second segment signal, if yes, the initial phase continuity zero-padding signal is obtained as the sorting result of the zero-padding signal, otherwise, the initial phase continuity zero-padding signal is obtained by sorting the zero-padding signal according to the initial phase of the zero-padding signal.
[0029] Optionally, the FFT analysis of the spliced signal comprises:
[0030] The frequency spectrum distribution of the spliced signal is obtained by performing fast Fourier transform on the spliced signal.
[0031] The spliced signal frequency is obtained by performing spectrum analysis based on the frequency spectrum distribution of the spliced signal as the processing result of the instantaneous signal frequency.
[0032] Optionally, the calculation formula of the spliced signal frequency based on the frequency spectrum distribution of the spliced signal is as follows:
[0033]
[0034] Y[k] = Y0[k] + Y1[k] + Y2[k] + … + Y c [k]
[0035] Y i [k] is the Fourier transform of the i-th segment zero-padding signal, i = 0, 1, 2, 3, …, c, Y[k] is the Fourier transform of the spliced signal, Y0[k], Y1[k], Y2[k], …, Y c [k] are the Fourier transforms of the 0th, 1st, 2nd, …, cth segment zero-padding signals, k is the frequency point index of the frequency domain, i and j are the segment indexes of the multiple segment signals, N is the sampling point number of each segment signal, L is the total point number after signal splicing, x i [n] is the echo signal, and n is the sampling point index.
[0036] Compared with the closest prior art, the present application has the beneficial effects:
[0037] The FFT frequency estimation processing method for phase splicing of instantaneous signals provided by the present application reduces the frequency estimation error of the signal to below 1.32 kHz in the case that the instantaneous signal can only last for 10 μs, and can meet the frequency resolution requirement of the resonant SAW sensor. Compared with the prior art, the present application effectively reduces the phase discontinuity at the splicing position by sorting the initial phase of the signal before splicing, reduces the frequency processing error, improves the frequency resolution, and is less affected by the environment. BRIEF DESCRIPTION OF DRAWINGS
[0038] In order to more clearly illustrate the specific embodiments of the present application or the technical solutions in the prior art, the drawings needed to be used in the specific embodiments or the prior art description will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor on the basis of these drawings.
[0039] Figure 1 A flow chart of a frequency processing method for instantaneous signals of a wireless acoustic sensor according to an embodiment of the present application;
[0040] Figure 2 A spliced cosine signal diagram according to an embodiment of the present application;
[0041] Figure 3 An FFT spectrum diagram according to an embodiment of the present application. DETAILED DESCRIPTION
[0042] In order to make the purpose, technical solutions and advantages of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below in combination with the specific embodiments of the present application and the corresponding drawings. Obviously, the described embodiments are only some of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.
[0043] The terms used in the embodiment part of the present application are only used to explain the specific embodiments of the present application, and are not intended to limit the present application.
[0044] For the SAW temperature sensor, the sampling frequency is high, the frequency processing progress is not affected by the environment, the existing Rife algorithm based on the fast Fourier transform (FFT) spectrum has poor frequency processing accuracy near the maximum value of the spectrum line and is easily affected by the environment; and the signal splicing algorithm based on the FFT spectrum improves the frequency resolution, but since the phase of each signal is discontinuous at the splicing position, it also introduces error for frequency processing, and therefore cannot meet the requirements of the SAW temperature sensor.
[0045] It is known that Δf = 1 / T, where Δf is the frequency resolution and T is the echo signal duration. When T = 10us, Δf = 100kHz, the conventional FFT transform cannot meet the temperature resolution requirement of the SAW sensor. The signal splicing algorithm based on the FFT spectrum can increase the signal duration to improve the frequency resolution, but the phase discontinuity of the spliced signal is another reason for the frequency processing error. If the initial phase of each sampled signal is sorted from large to small based on the signal splicing algorithm, and then the signal splicing is performed in this order, the phase discontinuity can be reduced, and the frequency processing error can be further reduced. Based on this, the present application provides a kind of instantaneous signal frequency processing method for wireless acoustic sensor.
[0046] As shown in Figure 1 The embodiment of the present application provides a kind of instantaneous signal frequency processing method for wireless acoustic sensor, comprising:
[0047] S1, the multiple sampled signals of echo signal are acquired;
[0048] S2, the multiple sampled signals of echo signal are used for zero padding processing to obtain spliced signal;
[0049] S3, the FFT analysis is carried out according to the spliced signal to obtain instantaneous signal frequency processing result.
[0050] In summary, step S1 to step S3 first acquires the multiple sampled signals of echo signal, then carries out zero padding processing to each sampled signal, then splices the zero padding signals according to initial phase, and finally carries out FFT analysis to the spliced signal to obtain frequency information. The present application effectively reduces the phase discontinuity at the splicing place by splicing after sorting the initial phase of signal, reduces the frequency processing error, and can reduce the frequency estimation error of signal to below 1.32kHz under the condition that instantaneous signal can only last 10us, can meet the frequency resolution requirement of resonant SAW sensor, and solves the problems of insufficient frequency processing precision and being easily affected by environment in the prior art.
[0051] As a possible implementation manner, in the above embodiment, step S1 can specifically include the following steps:
[0052] Based on the initial echo signal, signal processing is carried out to obtain echo signal;
[0053] Based on the target sampling rate, the echo signal is excited by excitation sensor multiple times to obtain multiple sampled signals of echo signal;
[0054] Wherein, the target sampling rate is 32MHz, 256 points are sampled for each echo signal, and 128 signals are sampled.
[0055] The echo signal is an exponentially decaying sinusoidal signal. In signal processing, an exponential growth factor can be multiplied to the signal to offset the effect of the exponential decay factor. Therefore, the derivation process treats the echo signal as a sinusoidal signal.
[0056] Let the echo signal x i [n] be:
[0057] x i [n]=cos(2πf0t+φ i ) (1)
[0058] where f0is the frequency of the echo signal, t is the time, φ i is the initial phase of the i-th segment of the signal, φ j is the initial phase of the j-th segment of the signal, i and j are the segment indexes of the multi-segment signal, and φ i < φ j (i < j).
[0059] Each time the sensor is excited, a segment of the echo signal is obtained. Multiple excitations obtain multiple segments of the echo signal. At a sampling rate f s = 32 MHz, 256 points are sampled for each segment, and a total of 128 segments are sampled, then
[0060] x i [n]=cos(2πf0nT s +φ i ) (2)
[0061] where n is the sampling point index, T s = 1 / 32 MHz is the sampling period. The number of sampling points is generally 2 N’ , N' is the number of FFT points, and 2 N’ = 256 is the setting of the present embodiment. Changing the number of points will affect the experimental error.
[0062] As a possible implementation, in the above embodiment, step S2 can specifically include the following steps:
[0063] S2-1, zero-padding processing is performed on the multiple segments of the echo signal at non-sampling points to obtain a zero-padded signal;
[0064] S2-2, splicing processing is performed on the zero-padded signal to obtain a spliced signal.
[0065] Each segment of the sampling signal is expanded in the time axis, and is filled with zero at the non-sampling points to form a zero-padded signal y i [n] with a length of c*N. The calculation formula of the zero-padded signal y i [n] is as follows:
[0066] (3)
[0067] Wherein, c=128 is the number of sampling segments, N=256 is the number of sampling points of each segment signal.
[0068] As a possible implementation, in the above embodiment, step S2-2 can specifically include the following steps:
[0069] S2-2-1, obtaining the initial phase of the zero-padded signal according to the zero-padded signal;
[0070] S2-2-2, sorting the zero-padded signal to obtain the sorting result of the zero-padded signal by using the initial phase of the zero-padded signal;
[0071] S2-2-3, performing splicing processing on the sorting result of the zero-padded signal to obtain a spliced signal.
[0072] On the basis of the signal splicing method, by sorting the initial phase of the signal from small to large and then splicing, the frequency processing error is reduced, wherein the sorting method of the signal can be sorted according to other rules. After splicing the signal, it is equivalent to zero-padded and then added to obtain the spliced signal, for example, each segment signal has 10 numbers, a total of 10 segment signals, a total of 100 numbers, which is equivalent to a 10*100 matrix, the i-th row of the matrix represents the i-th segment data, and the i-th column to i+10 column in the i-th row is the sampled 10 numbers, and the rest is 0; Then, the data is added by column to obtain a 1*100 array, which is the final signal. Each row can be Fourier transformed, and the Fourier transform results of 10 rows are added to be the Fourier transform of the final signal. Wherein, the calculation formula of the spliced signal y[n] is as follows:
[0073] y[n]=y1[n]+y2[n]+…+y c [n] (4)
[0074] Wherein, y1[n], y2[n], …, y c [n] is the zero-padded signal of the first, second, …, c-th segment of the initial phase sorted signal.
[0075] In summary, steps S2-2-1 to S2-2-3 first obtain the initial phase of the zero-padded signal when constructing the spliced signal, then sort the zero-padded signal using the initial phase to obtain a sorting result, and finally splice the sorting result to obtain the spliced signal. This operation significantly reduces the phase discontinuity at the splicing position of the signal by sorting the initial phase, avoids introducing additional frequency errors due to phase jumps, makes the spliced signal more continuous in the time domain, and significantly improves the frequency estimation accuracy when performing Fourier transform analysis, making the final obtained instantaneous signal frequency more reliable, suitable for harsh application scenarios such as resonant SAW sensors that require high frequency resolution, and effectively enhancing the accuracy and stability of wireless acoustic sensor signal processing.
[0076] As a possible implementation, in the above embodiment, step S2-2-2 can specifically include the following steps:
[0077] S2-2-2-1, sort the zero-padded signal using the initial phase of the zero-padded signal to obtain an initial phase continuity zero-padded signal;
[0078] S2-2-2-2, obtain the last initial phase of the first signal and the first initial phase of the second signal according to the initial phase continuity zero-padded signal;
[0079] S2-2-2-3, determine whether the last initial phase of the first signal is less than or equal to the first initial phase of the second signal, if yes, obtain the initial phase continuity zero-padded signal as the sorting result of the zero-padded signal, otherwise, return to S2-2-2-1.
[0080] In summary, steps S2-2-2-1 to S2-2-2-3 verify the effectiveness of the sorting by judging the size relationship of the two adjacent initial phases, significantly reducing the frequency spectrum leakage problem caused by phase jumps in the traditional splicing method, reducing the frequency estimation error, and effectively improving the frequency resolution.
[0081] As a possible implementation, in the above embodiment, step S3 can specifically include the following steps:
[0082] S3-1, performing fast Fourier transform on the spliced signal to obtain the frequency spectrum distribution of the spliced signal;
[0083] S3-2, performing frequency spectrum analysis based on the frequency spectrum distribution of the spliced signal to obtain the spliced signal frequency as the instantaneous signal frequency processing result.
[0084] In summary, steps S3-1 to S3-2 obtain the frequency spectrum distribution of the spliced signal by performing FFT on the spliced signal, and obtain the spliced signal frequency as the processing result of the instantaneous signal frequency by performing spectrum analysis. This process effectively improves the frequency resolution of the FFT spectrum analysis, reduces the spectrum leakage, and significantly improves the accuracy and stability of the instantaneous signal frequency estimation. When processing microsecond-level short duration echo signals such as resonant SAW sensors, this method can reduce the frequency estimation error to less than 1.32 kHz, meeting the high-precision measurement requirements, while reducing the dependence on the hardware sampling rate and reducing the system cost.
[0085] Further, the spliced signal frequency calculation formula based on the frequency spectrum distribution of the spliced signal is as follows:
[0086] (5)
[0087] Y[k] = Y0[k] + Y1[k] + Y2[k] +... + Y c [k] (6)
[0088] where L is the total number of points after signal splicing, k is the frequency point index of the frequency domain, i and j are the segment indexes of the multiple signal segments, Y i [k] is the Fourier transform of the i-th zero-padded signal, i = 0, 1, 2, 3,..., c, Y[k] is the Fourier transform of the spliced signal, Y0[k], Y1[k], Y2[k],..., Y c [k] is the Fourier transform of the i-th zero-padded signal. Since the resonant signal length generated by the surface acoustic wave sensor under a single excitation is short, the number of sampling points is small, so multiple excitations and multiple samplings are required. Here, one segment of resonant signal is sampled for each excitation, with N = 256 points, c = 128 excitations, 128 segments of signal are sampled, and the total number of points L after signal splicing is c*N.
[0089] According to the above analysis, data simulation analysis is performed using Matlab. 128 segments of cosine signals with 256 points each and random initial phase are generated, the sampling frequency is 32 MHz, and the signal frequency is 1 MHz. After sorting the initial phase from small to large, the signal is spliced, Figure 2 is a schematic diagram of part of the spliced signal. The FFT analysis of the spliced signal is performed, Figure 3 is its frequency spectrum, and the error is about 488 Hz. Randomly generate a cosine signal in the range of 1 MHz to 2 MHz, and perform the same processing, calculate the frequency average of 100 times, and perform 1000 experiments, calculate the root mean square error, which is 1.32 kHz.
[0090] Those skilled in the art will appreciate that embodiments of the application can be devised for a method, a system, or a computer program product. Accordingly, the present application can be embodied in the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application can take the form of a computer program product on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROMs, optical storage devices, etc.) embodying computer readable program code.
[0091] The present application is described in reference to the flowchart and / or block diagrams of the method, apparatus (system) and computer program product according to embodiments of the present application. It should be understood that each flow and / or block in the flowchart and / or block diagrams, and a combination of flows and / or blocks in the flowchart and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general purpose computer, a special purpose computer, an embedded processor or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart and / or block diagrams block or blocks. Figure 1 one or more flows and / or blocks Figure 1 means for carrying out the function specified in the flowchart and / or block diagram block or blocks.
[0092] These computer program instructions can also be stored in a computer readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer readable memory produce an article of manufacture including instructions means which implement the function specified in the flowchart and / or block diagrams block or blocks. Figure 1 one or more flows and / or blocks Figure 1 means for carrying out the function specified in the flowchart and / or block diagram block or blocks.
[0093] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart and / or block diagrams block or blocks. Figure 1 one or more flows and / or blocks Figure 1 means for carrying out the function specified in the flowchart and / or block diagram block or blocks.
[0094] Finally, it should be noted that the above-mentioned embodiments are merely intended for describing the technical solutions of the present application, but not for limiting the present application. Although the present application is described in detail with reference to the above embodiments, those skilled in the art should understand that the specific embodiments of the present application can be modified or replaced equivalently without departing from the spirit and scope of the present application, and any modification or equivalent replacement without departing from the spirit and scope of the present application should be covered in the protection scope of the claims of the present application.
Claims
1. A method for instantaneous signal frequency processing of a wireless acoustic sensor, characterized in that, The method comprises the following steps: S1, obtaining a plurality of sampled signals of an echo signal; S2, performing zero padding processing on the plurality of sampled signals of the echo signal to obtain a spliced signal; S3, performing FFT analysis on the spliced signal to obtain an instantaneous signal frequency processing result.
2. A method for processing the instantaneous signal frequency of a wireless acoustic sensor according to claim 1, characterized in that, The method for obtaining a plurality of sampled signals of an echo signal comprises: performing signal processing on an initial echo signal to obtain an echo signal; performing excitation on the echo signal multiple times by using an excitation sensor to obtain a plurality of sampled signals of the echo signal based on a target sampling rate; wherein the target sampling rate is 32 MHz, 256 points are sampled for each segment of the echo signal, and 128 segments of signals are sampled.
3. A method for processing the instantaneous signal frequency of a wireless acoustic sensor according to claim 1, characterized in that, The method for performing zero padding processing on the plurality of sampled signals of the echo signal to obtain a spliced signal comprises: performing zero padding processing on the plurality of sampled signals of the echo signal at non-sampling points to obtain a zero padding signal; performing splicing processing on the zero padding signal to obtain a spliced signal.
4. A method for processing the instantaneous signal frequency of a wireless acoustic sensor according to claim 3, characterized in that, The calculation formula of the zero padding signal is as follows:
5. wherein, y i [n] is a zero padding signal, f0 is the echo signal frequency, n is the sampling point index, T s is the sampling period, φ i is the initial phase of the i-th segment signal, and N is the number of sampling points of each segment signal.
6. A method for processing the instantaneous signal frequency of a wireless acoustic sensor according to claim 3, characterized in that, The method for performing splicing processing on the zero padding signal to obtain a spliced signal comprises: obtaining an initial phase of the zero padding signal based on the zero padding signal; performing sorting on the zero padding signal based on the initial phase of the zero padding signal to obtain a sorting result of the zero padding signal; performing splicing processing on the sorting result of the zero padding signal to obtain a spliced signal.
7. A method for processing the instantaneous signal frequency of a wireless acoustic sensor according to claim 5, characterized in that, The method for performing sorting on the zero padding signal based on the initial phase of the zero padding signal to obtain a sorting result of the zero padding signal comprises: performing sorting on the zero padding signal based on the initial phase of the zero padding signal to obtain an initial-phase-continuity zero padding signal; obtaining a last initial phase of a first segment of signal and a first initial phase of a second segment of signal based on the initial-phase-continuity zero padding signal; determining whether the last initial phase of the first segment of signal is less than or equal to the first initial phase of the second segment of signal, if yes, obtaining the initial-phase-continuity zero padding signal as the sorting result of the zero padding signal, otherwise, returning to perform sorting on the zero padding signal based on the initial phase of the zero padding signal to obtain an initial-phase-continuity zero padding signal.
8. A method for processing the instantaneous signal frequency of a wireless acoustic sensor according to claim 1, characterized in that, The method for performing FFT analysis on the spliced signal to obtain an instantaneous signal frequency processing result comprises: performing fast Fourier transform on the spliced signal to obtain a frequency spectrum distribution of the spliced signal; performing frequency spectrum analysis on the frequency spectrum distribution of the spliced signal to obtain a spliced signal frequency as an instantaneous signal frequency processing result.
9. A method for processing the instantaneous signal frequency of a wireless acoustic sensor according to claim 5, characterized in that, The calculation formula for performing frequency spectrum analysis on the frequency spectrum distribution of the spliced signal to obtain a spliced signal frequency is as follows:
10. Y[k] = Y0[k] + Y1[k] + Y2[k] +... + Y c [k] wherein, Y i [k] is the Fourier transform of the i-th segment zero-padded signal, i = 0, 1, 2, 3, …, c, Y[k] is the Fourier transform of the spliced signal, Y0[k], Y1[k], Y2[k], …, Y c [k] is the Fourier transform of the i-th segment zero-padded signal, i = 0, 1, 2, 3, …, c, Y[k] is the Fourier transform of the spliced signal, Y0[k], Y1[k], Y2[k], …, Y i [n] is the echo signal, n is the sampling point index.