Spectral analysis method based on circumferential minimum sparse size compressed sampling

Abstract

A spectrum analysis method based on a circumferential minimum sparse size compression sampling, in the method, a down-sampling factor is determined according to a frequency upper limit of a measured signal and a sampling rate of a sampling channel; a circumferential minimum sparse size mode is determined through an optimization algorithm; periodic non-uniform sampling is performed on the signal by using the circumferential minimum sparse size mode to obtain signal samples; continuous covariance samples are estimated from the signal samples; and a signal power spectrum is estimated from the continuous covariance samples.

Description

Technical Field

[0001] This invention relates to the fields of signal compression sampling and digital signal processing technology, and in particular to a spectral analysis method based on circumferential minimum sparse scale compression sampling. Background Technology

[0002] With increasing signal bandwidth and expanding application scenarios, the sampling rate of traditional Nyquist sampling is becoming increasingly higher, leading to extremely high signal sampling, transmission, and storage costs. Furthermore, in certain scenarios, hardware devices such as analog-to-digital converters (ADCs) may not be able to meet the requirements of Nyquist sampling. Therefore, developing compressed sampling as an alternative to Nyquist sampling is of great significance. Compressed sampling, also known as sub-Nyquist sampling, samples the signal at an average rate lower than the Nyquist sampling rate using a non-uniform sampling method. Compared to Nyquist sampling, compressed sampling has a lower average sampling rate and less data volume, thus reducing signal sampling, transmission, and storage costs.

[0003] Currently, the field of compressed sampling often relies on compressed sensing theory to sample signals, which has drawbacks such as high hardware costs and heavy data sampling, transmission, and processing pressures.

[0004] The information disclosed in the background section is only for enhancing the understanding of the background of this invention, and therefore may contain information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0005] This invention provides a spectral analysis method based on circumferential minimum sparse scale compression sampling, which reduces the average sampling rate to below the Nyquist rate, realizes compressed sampling of the signal in a periodic non-uniform form, and achieves covariance estimation and power spectrum reconstruction, thereby reducing the cost of hardware equipment and alleviating the pressure of data sampling, transmission and processing.

[0006] A spectral analysis method based on circumferential minimum sparse ruler compression sampling includes:

[0007] Step 1: Determine the downsampling factor based on the upper frequency limit of the measured signal and the sampling rate of the sampling channel;

[0008] Step 2: Determine the circumferential minimum sparse size pattern through an optimization algorithm;

[0009] Step 3: Perform periodic non-uniform sampling of the signal using the circumferential minimum sparse ruler pattern to obtain signal samples;

[0010] Step 4: Estimate continuous covariance samples from the signal samples;

[0011] Step 5: Estimate the signal power spectrum from continuous covariance samples.

[0012] In the aforementioned spectral analysis method based on circumferential minimum sparse ruler compression sampling, step 1 includes:

[0013] make Indicates the measured signal The upper limit of frequency; let The sampling rate of the sampling channel is represented by the following formula, and the downsampling factor L that meets the conditions is determined.

[0014] (1)

[0015] in: The rounding up symbol.

[0016] In the aforementioned spectral analysis method based on circumferential minimum sparse ruler compression sampling, step 2 includes,

[0017] First, the length is obtained by solving the following optimization model. The smallest sparse rule:

[0018] (2)

[0019] In the formula: It is the smallest sparse ruler; It is a set of integers; for The nonnegative difference set whose elements are equal to . The absolute value of the difference between any two elements in the set is expressed as follows:

[0020] (3)

[0021] in and express Take any two elements from the given set, considering all possible cases.

[0022] Finally, according to and Determine the minimum sparse size in the circumferential direction .

[0023] In the aforementioned spectral analysis method based on circumferential minimum sparse ruler compression sampling, step 3 includes:

[0024] First, based on the channel sampling rate The nominal time unit T is determined by the downsampling factor L: ,

[0025] Then, the signal is periodically and non-uniformly sampled according to the circumferential minimum sparse size pattern, where... And L is the minimum sparse size in the circumferential direction The elements in, i.e. The p-th channel processes the signal for a duration of... The delay is then followed by uniform sampling with a period of LT. Record the data sequences acquired from all channels as ,in

[0026] (4).

[0027] In the spectral analysis method based on circumferential minimum sparse ruler compression sampling, step 4 includes estimating the compressed covariance matrix of the signal samples. , (5),

[0028] Where: Q represents the number of snapshots;

[0029] q is the integer to be traversed, from 0 to Q-1; .

[0030] In the aforementioned spectral analysis method based on circumferential minimum sparse ruler compression sampling, in step 4, from the signal samples... Estimating continuous covariance sample vectors include,

[0031] Input minimum sparse rule downsampling factor Number of channels P, signal sample vector ;

[0032] based on Estimating covariance samples with continuous delays includes,

[0033] l is an integer ranging from 0 to L-1, and the calculation satisfies Pairs of elements with a mean difference equal to l ,Right now and ;

[0034] n is an integer ranging from 0 to N-1. Calculate the vector length G:

[0035] ,in The floor symbol is used for rounding down. This is for the operation of retrieving the maximum value;

[0036] Construct vectors for two congruent covariance estimates and ,

[0037] , where m and q are two integers that satisfy... and , and for The m-th and q-th elements in;

[0038] The estimated delay is Covariance samples : .

[0039] In the aforementioned spectral analysis method based on circumferential minimum sparse ruler compression sampling, step 5 includes:

[0040] By analyzing continuous covariance samples Perform Discrete Fourier Transform to estimate the signal power spectrum

[0041] (6)

[0042] in: Represents a sequence After performing the Discrete Fourier Transform, the k-th Fourier coefficient is obtained. express The nth element; Z is The data length is expressed in terms of the absolute value of the Fourier coefficient vector. Using the vertical axis as the ordinate, with The power spectrum of the signal is obtained by using the x-axis.

[0043] Compared with existing technologies, this invention has the following advantages: This invention employs a circumferential minimum sparse ruler mode for compressed sampling of generalized stationary signals. Compared to random sampling, the circumferential minimum sparse ruler has a deterministic periodic non-uniform sampling mode, thus offering the advantage of ease of hardware implementation. Compared to the minimum sparse ruler, the sample points sampled by the circumferential minimum sparse ruler are sparser, and the compression efficiency of circumferential minimum sparse ruler sampling is twice that of minimum sparse ruler sampling. In terms of post-processing of the sampled signal, this invention directly estimates continuous covariance samples from the measured samples, and then performs spectral analysis based on the covariance samples, such as performing a discrete Fourier transform on the covariance samples to obtain the power spectrum. Compared with post-processing methods for compressed sampled signals based on compressed sensing and the Lasso algorithm, this invention has lower computational complexity and higher robustness. Attached Figure Description

[0044] Various other advantages and benefits of the present invention will become apparent to those skilled in the art upon reading the detailed description of the preferred embodiments below. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort. Furthermore, the same reference numerals denote the same parts throughout the drawings.

[0045] In the attached diagram:

[0046] Figure 1 This is a schematic diagram of the circumferential minimum sparse ruler proposed in this invention;

[0047] Figure 2 This is a diagram of the periodic non-uniform sampling structure based on the circumferential minimum sparse ruler proposed in this invention.

[0048] Figure 3 This is a schematic diagram of the signal sample sequence obtained by circumferential minimum sparse ruler sampling in an embodiment of the present invention. Figure 3 In the sequence (a), the real part is represented. Figure 3 (b) is the imaginary part sequence;

[0049] Figure 4 This is a schematic diagram of the continuous covariance sample estimated in an embodiment of the present invention. Figure 4 In the sequence (a), the real part is represented. Figure 4 (b) is the imaginary part sequence;

[0050] Figure 5 This is a schematic diagram of the power spectrum obtained by performing a discrete Fourier transform on continuous covariance samples.

[0051] Figure 6 This is a schematic diagram of the process proposed in this invention.

[0052] The present invention will be further explained below with reference to the accompanying drawings and embodiments. Detailed Implementation

[0053] Specific embodiments of the invention will now be described in more detail with reference to the accompanying drawings. While specific embodiments of the invention are shown in the drawings, it should be understood that the invention may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this invention will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.

[0054] It should be noted that certain terms are used in the specification and claims to refer to specific components. Those skilled in the art will understand that different terms may be used to refer to the same component. This specification and claims do not distinguish components based on differences in terminology, but rather on differences in function. The terms "comprising" or "including" used throughout the specification and claims are open-ended and should be interpreted as "comprising but not limited to." The following descriptions are preferred embodiments for carrying out the invention; however, these descriptions are for the purpose of understanding the general principles of the specification and are not intended to limit the scope of the invention. The scope of protection of this invention is determined by the appended claims.

[0055] To facilitate understanding of the embodiments of the present invention, further explanations and descriptions will be provided below with reference to the accompanying drawings and specific embodiments. The accompanying drawings do not constitute a limitation on the embodiments of the present invention.

[0056] like Figures 1 to 6 As shown, the spectral analysis method based on circumferential minimum sparse scale compression sampling includes the following steps:

[0057] Step 1: Determine the downsampling factor based on the upper frequency limit of the measured signal and the sampling rate of the sampling channel;

[0058] Step 2: Determine the circumferential minimum sparse size pattern through an optimization algorithm;

[0059] Step 3: Perform periodic non-uniform sampling of the signal using the circumferential minimum sparse ruler pattern to obtain signal samples;

[0060] Step 4: Estimate continuous covariance samples from the signal samples;

[0061] Step 5: Estimate the signal power spectrum from continuous covariance samples.

[0062] In a preferred embodiment of the spectral analysis method based on circumferential minimum sparse ruler compression sampling, step 1 includes:

[0063] make Indicates the measured signal The upper limit of frequency; let The sampling rate of the sampling channel is represented by the following formula, and the downsampling factor L that meets the conditions is determined.

[0064] (1)

[0065] in: The rounding up symbol.

[0066] In a preferred embodiment of the spectral analysis method based on circumferential minimum sparse ruler compression sampling, step 2 includes:

[0067] First, the length is obtained by solving the following optimization model. The smallest sparse rule:

[0068] (2)

[0069] In the formula: It is the smallest sparse ruler; It is a set of integers; for The nonnegative difference set whose elements are equal to . The absolute value of the difference between any two elements in the set is expressed as follows:

[0070] (3)

[0071] in and express Take any two elements from the given set, considering all possible cases.

[0072] Finally, according to and Determine the minimum sparse size in the circumferential direction .

[0073] In a preferred embodiment of the spectral analysis method based on circumferential minimum sparse ruler compression sampling, step 3 includes:

[0074] First, based on the channel sampling rate The nominal time unit T is determined by the downsampling factor L: ,

[0075] Then, the signal is periodically and non-uniformly sampled according to the circumferential minimum sparse size pattern, where... And L is the minimum sparse size in the circumferential direction The elements in, i.e. The p-th channel processes the signal for a duration of... The delay is then followed by uniform sampling with a period of LT. Record the data sequences acquired from all channels as ,in

[0076] (4).

[0077] In a preferred embodiment of the spectral analysis method based on circumferential minimum sparse ruler compression sampling, step 4 includes estimating the compressed covariance matrix of the signal samples. , (5),

[0078] Where: Q represents the number of snapshots;

[0079] q is the integer to be traversed, from 0 to Q-1; .

[0080] In a preferred embodiment of the spectral analysis method based on circumferential minimum sparse ruler compression sampling, in step 4, from the signal samples... Estimating continuous covariance sample vectors include,

[0081] Input minimum sparse rule downsampling factor Number of channels P, signal sample vector ;

[0082] based on The specific process for estimating covariance samples with continuous delays is as follows:

[0083] For (l is an integer ranging from 0 to L-1)

[0084] Calculation satisfies Pairs of elements with a mean difference equal to l ,Right now and ;

[0085] For (n is an integer ranging from 0 to N-1)

[0086] Calculate the vector length G:

[0087] ,in The floor symbol is used for rounding down. This is for the operation of retrieving the maximum value;

[0088] Construct vectors for two congruent covariance estimates and ,

[0089] , where m and q are two integers that satisfy... and , and for The m-th and q-th elements in;

[0090] The estimated delay is Covariance samples : .

[0091] In a preferred embodiment of the spectral analysis method based on circumferential minimum sparse ruler compression sampling, step 5 includes:

[0092] By analyzing continuous covariance samples Perform Discrete Fourier Transform to estimate the signal power spectrum

[0093] (6)

[0094] in: Represents a sequence After performing the Discrete Fourier Transform, the k-th Fourier coefficient is obtained. express The nth element; Z is The data length is expressed in terms of the absolute value of the Fourier coefficient vector. Using the vertical axis as the ordinate, with The power spectrum of the signal is obtained by using the x-axis.

[0095] A vibration system operating modal parameter estimation system, characterized in that it comprises,

[0096] The determining unit determines the downsampling factor based on the upper frequency limit of the measured signal and the sampling rate of the sampling channel;

[0097] The optimization unit determines the circumferential minimum sparse size pattern through an optimization algorithm.

[0098] The sampling unit periodically and non-uniformly samples the signal in a circumferential minimum sparse ruler pattern to obtain signal samples.

[0099] An estimation unit that estimates continuous covariance samples from signal samples;

[0100] The signal power spectrum unit estimates the signal power spectrum from continuous covariance samples.

[0101] A computer storage medium including computer instructions that, when run on a computer, cause the computer to perform the method.

[0102] An electronic device, the electronic device comprising:

[0103] Memory, processor, and computer programs stored in memory and executable on the processor, wherein,

[0104] The processor implements the method when executing the program.

[0105] In one embodiment, the compressed sampling and spectral analysis method based on the circumferential minimum sparse scale includes the following steps:

[0106] (1) Determine the downsampling factor based on the upper frequency limit of the measured signal and the sampling rate of the sampling channel;

[0107] make Indicates the measured signal The upper limit of frequency; let This represents the sampling rate of the sampling channel. The downsampling factor L that satisfies the following condition is determined according to the following formula.

[0108] (1)

[0109] in: The symbol is for rounding up; note that L is an integer that satisfies the above equation. The larger L is, the lower the signal compression ratio, but the higher the timing accuracy requirement and the more sensitive it is to sampling jitter. In actual engineering, L needs to be selected as needed based on the compression ratio and hardware conditions, provided that equation (1) is satisfied.

[0110] In this exemplary instance The simulation generated a superposition of sinusoidal signals containing Gaussian white noise. Its first and second moments do not change with time, therefore it is a generalized stationary signal. The simulated signal contains four sinusoidal components, expressed as follows:

[0111] (2)

[0112] in Indicates the noise term. , and Let i represent the frequency, amplitude, and phase of the i-th signal component, respectively, where i = 1, 2, 3, 4. This represents the simulated signal.

[0113] The specific parameters of the simulation are shown in Table 1:

[0114] Table 1 Simulation Parameters

[0115]

[0116] Signal For complex signals, the highest frequency is... Hz. Therefore, the downsampling factor L is an integer and must satisfy... In this exemplary example, L = 27.

[0117] (2) Determine the circumferential minimum sparse size pattern by optimizing the algorithm or by directly looking up a table;

[0118] First, the length is obtained by solving the following optimization model. The smallest sparse rule:

[0119] (3)

[0120] If we do not use the optimization model (3) to obtain The length can then be determined directly by looking up a table. Minimum sparse size mode

[0121] Finally, according to and Determine the minimum sparse size in the circumferential direction .

[0122] In this exemplary instance Given L = 27, the following optimization model exists.

[0123] (4)

[0124] There are 3 optimal solutions: or or Choose one of them as In this exemplary example, take .

[0125] If the minimum sparse scale contains lengths of... For sparse rulers, the value can be directly determined by looking up a table. By directly looking up the table, we can see that the length is... The sparse scale is .therefore .

[0126] Minimum Sparse Table

[0127]

[0128] Finally, according to and The minimum circumferential sparseness measure in this example is determined as follows: .

[0129] (3) Periodically non-uniformly sample the signal using the circumferential minimum sparse scale pattern;

[0130] First, based on the channel sampling rate The nominal time unit T is determined by the downsampling factor L: .

[0131] Then, the signal is periodically and non-uniformly sampled according to the circumferential minimum sparse size pattern, specifically in the form of... Figure 2 As stated above.

[0132] in, And L is the minimum sparse size in the circumferential direction The elements in, i.e. In the picture, This is a delay module. The p-th channel processes the signal for a duration of... The delay is then followed by uniform sampling with a period of LT. Without loss of generality, let the delay time of the first channel be 0 as a reference, that is... Assume the sampling time duration is... Then the sampled from the p-th channel is

[0133] (5)

[0134] The data sequences acquired from all channels are denoted as ,in

[0135] (6)

[0136] In this exemplary instance , Hz and Therefore, the nominal unit of time Second

[0137] Then, the signal is periodically and non-uniformly sampled according to the circumferential minimum sparse size pattern, specifically in the form of... Figure 2 As shown.

[0138] In exemplary cases The samples sampled from channels 1 to 6 are respectively

[0139] (7)

[0140] The data sequence obtained from sampling channels 1 through 6 is as follows:

[0141] (8)

[0142] (4) Estimate continuous covariance samples from signal samples; see the table below.

[0143]

[0144] In this exemplary instance , , ,

[0145] Iterate through l from 0 to 26. When l = 0, Pairs of elements that satisfy the condition that the difference is 0 have ,Right now .

[0146] Then iterate through n from 0 to 99. When n = 0, Construct two vectors for covariance estimation of congruence. and ,

[0147] , Estimate the covariance of samples with a delay of 0: When n = 1, Construct two vectors for covariance estimation of congruence. and , , Estimate the covariance of the sample with a lag of 27: .

[0148] And so on, until n = 99.

[0149] When l = 1, Pairs of elements that satisfy the condition that the difference is 1 have ,Right now .

[0150] Then iterate through n from 0 to 99. When n = 0, Construct two vectors for covariance estimation of congruence. and , , Estimate the covariance of a sample with a delay of 1: .

[0151] And so on, until l = 26.

[0152] (5) Estimate the signal power spectrum from continuous covariance samples.

[0153] By analyzing continuous covariance samples Perform Discrete Fourier Transform to estimate the signal power spectrum

[0154] (9)

[0155] in: Represents a sequence The k-th Fourier coefficient obtained after performing a discrete Fourier transform. express The nth element; Z is The data length. The absolute value of the Fourier coefficient vector. Using the vertical axis as the ordinate, with Using the x-axis as the horizontal axis, the power spectrum of the signal can be obtained.

[0156] In this exemplary instance The continuous signal samples obtained by the equation Length Z = 2687.

[0157] Obtained by Discrete Fourier Transform Using the vertical axis as the ordinate, with Using the x-axis as the horizontal axis, the power spectrum can be obtained.

[0158]

Application Examples

[0159] (1) In this exemplary instance The simulation generated a superposition of sinusoidal signals containing Gaussian white noise. Its first and second moments do not change with time, therefore it is a generalized stationary signal. The simulated signal contains four sinusoidal components, expressed as follows:

[0160]

[0161] in Indicates the noise term. , and Let i represent the frequency, amplitude, and phase of the i-th signal component, respectively, where i = 1, 2, 3, 4. This represents the simulated signal.

[0162] The specific parameters of the simulation are shown in Table 1:

[0163] Table 1 Simulation Parameters

[0164]

[0165] Signal For complex signals, the highest frequency is... Hz. Therefore, the downsampling factor L is an integer and must satisfy... In this exemplary example, L = 27.

[0166] (2) Determine the circumferential minimum sparse size pattern by optimizing the algorithm or by directly looking up a table;

[0167] In this exemplary instance Given L = 27, the following optimization model exists.

[0168]

[0169] There are 3 optimal solutions: or or Choose one of them as In this exemplary example, take .

[0170] If the minimum sparse scale contains lengths of... For sparse rulers, you can refer to the smallest sparse ruler table.

[0171] Directly determine By directly looking up the table, we can see that the length is... The sparse scale is .therefore Finally, according to and The minimum circumferential sparseness measure in this example is determined as follows: The smallest sparse ruler in the circumference is 27, with graduations only at 0, 1, 2, 6, 10, and 13, yet it can measure all integer distances from 0 to 27. Figure 1 As shown in the figure. Note that only the measurement method for integer distances from 0 to 13 is shown in the figure. Integer distances from 14 to 27 can be obtained by taking the corresponding major arc of the minor arc with a distance of 0 to 13. This circumferential sparse ruler is the sparse ruler with the fewest graduations among all circumferential sparse rulers that can measure distances from 0 to 27, and is therefore called the smallest circumferential sparse ruler.

[0172] (3) Periodically non-uniformly sample the signal using the circumferential minimum sparse scale pattern;

[0173] In this exemplary instance , Hz and Therefore, the nominal unit of time Second

[0174] Then, the signal is periodically and non-uniformly sampled according to the circumferential minimum sparse size pattern, specifically in the form of... Figure 2 As shown.

[0175] In the exemplary example, let The samples sampled from channels 1 to 6 are respectively

[0176]

[0177] The data sequence obtained from sampling channels 1 through 6 is as follows:

[0178]

[0179] The signal sample sequence obtained from the above circumferential minimum sparse scale sampling is as follows: Figure 3 As shown.

[0180] (4) Estimate continuous covariance samples from signal samples; see the table below.

[0181]

[0182] In this exemplary instance , , ,

[0183] Iterate through l from 0 to 26. When l = 0, Pairs of elements that satisfy the condition that the difference is 0 have ,Right now .

[0184] Then iterate through n from 0 to 99. When n = 0, Construct two vectors for covariance estimation of congruence. and ,

[0185] , Estimate the covariance of samples with a delay of 0: When n = 1, Construct two vectors for covariance estimation of congruence. and , , Estimate the covariance of the sample with a lag of 27: .

[0186] And so on, until n = 99.

[0187] When l = 1, Pairs of elements that satisfy the condition that the difference is 1 have ,Right now .

[0188] Then iterate through n from 0 to 99. When n = 0, Construct two vectors for covariance estimation of congruence. and , , Estimate the covariance of a sample with a delay of 1: .

[0189] And so on, until l = 26.

[0190] The recovered continuous covariance waveform is as follows Figure 4 As shown.

[0191] (5) Estimate the signal power spectrum from continuous covariance samples.

[0192] By analyzing continuous covariance samples Perform Discrete Fourier Transform to estimate the signal power spectrum

[0193]

[0194] in: Represents a sequence The k-th Fourier coefficient obtained after performing a discrete Fourier transform. express The nth element; Z is The data length. The absolute value of the Fourier coefficient vector. Using the vertical axis as the ordinate, with Using the x-axis as the horizontal axis, the power spectrum of the signal can be obtained.

[0195] In this exemplary instance The continuous signal samples obtained by the equation Length Z = 2687.

[0196] Obtained by Discrete Fourier Transform Using the vertical axis as the ordinate, with Using the x-axis, the power spectrum can be obtained, such as... Figure 5 As shown. Observation Figure 5 It can be seen that the power spectrum recovered by the circumferential minimum sparse scale sampling is very close to the true power value. The power amplitude errors of the three characteristic frequencies are only 1.98%, 0.28%, and -1.51%, respectively, which proves the effectiveness of the method.

[0197] Although embodiments of the present invention have been described above in conjunction with the accompanying drawings, the present invention is not limited to the specific embodiments and application fields described above. The specific embodiments described above are merely illustrative and instructive, and not restrictive. Those skilled in the art can make many other forms based on the guidance of this specification and without departing from the scope of protection of the claims of the present invention, and all of these are within the scope of protection of the present invention.

Claims

1. A spectral analysis method based on circumferential minimum sparse ruler compression sampling, characterized in that, Includes the following steps: Step (1): Determine the downsampling factor based on the upper frequency limit of the measured signal and the sampling rate of the sampling channel; Step (2): Determine the circumferential minimum sparse size pattern through an optimization algorithm; Step (3): The signal is periodically and non-uniformly sampled using the circumferential minimum sparse ruler pattern to obtain signal samples; Step (4): Estimate continuous covariance samples from the signal samples; Step (5): Perform discrete Fourier transform on continuous covariance samples to estimate the signal power spectrum; Step (1) includes: make Indicates the measured signal The upper limit of frequency; let The sampling rate of the sampling channel is represented by the following formula, and the downsampling factor L that meets the conditions is determined. (1)， in: The rounding up symbol; Step (2) includes, First, the length is obtained by solving the following optimization model. The smallest sparse rule: (2)， In the formula: It is the smallest sparse ruler; It is a set of integers; for The nonnegative difference set whose elements are equal to . The absolute value of the difference between any two elements in the set is expressed as follows: (3)， in and express Take any two elements from the given set, considering all possible cases. Finally, according to and Determine the minimum sparse size in the circumferential direction ; Step (3) includes, First, based on the channel sampling rate The nominal time unit T is determined by the downsampling factor L: , Then, the signal is periodically and non-uniformly sampled according to the circumferential minimum sparse size pattern, where... And L is the minimum sparse size in the circumferential direction The elements in, i.e. The p-th channel processes the signal for a duration of... The delay is then followed by uniform sampling with a period of LT. Record the data sequences acquired from all channels as ,in (4)； Step (4) includes estimating the compressed covariance matrix of the signal samples. , (5), Where: Q represents the number of snapshots; q is the integer to be traversed, from 0 to Q-1; ; In step (4), from the signal sample Estimating continuous covariance sample vectors include, Input minimum sparse rule downsampling factor Number of channels P, signal sample vector ; based on Estimating covariance samples with continuous delays includes, l is an integer ranging from 0 to L-1, and the calculation satisfies Pairs of elements with a mean difference equal to l ,Right now and ; n is an integer ranging from 0 to N-1. Calculate the vector length G: ,in The floor symbol is used for rounding down. This is for the operation of retrieving the maximum value; Construct vectors for two congruent covariance estimates and , , where m and q are two integers that satisfy... and , and for The m-th and q-th elements in; The estimated delay is Covariance samples : .

2. The spectral analysis method based on circumferential minimum sparse ruler compression sampling according to claim 1, characterized in that, Step (5) includes, By analyzing continuous covariance samples Perform Discrete Fourier Transform to estimate the signal power spectrum (6)， in: Represents a sequence After performing the Discrete Fourier Transform, the k-th Fourier coefficient is obtained. express The nth element; Z is The data length is expressed in terms of the absolute value of the Fourier coefficient vector. Using the vertical axis as the ordinate, with The power spectrum of the signal is obtained by using the x-axis.

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