Spectral analysis method based on circumferential minimum sparse scale compressed sampling

Abstract

The invention discloses a spectrum analysis method based on circumferential minimum sparse scale compressed sampling, and the method comprises the steps: determining a down-sampling factor according to the frequency upper limit of a measured signal and the sampling rate of a sampling channel; determining a circumferential minimum sparse ruler mode through an optimization algorithm; performing periodic non-uniform sampling on the signal in a circumferential minimum sparse ruler mode to obtain a signal sample; estimating continuous covariance samples from the signal samples; a signal power spectrum is estimated from the consecutive covariance samples.

Description

Technical Field

[0001] The invention relates to the technical field of signal compression sampling and digital signal processing, and in particular to a spectrum analysis method based on circumferential minimum sparseness compression sampling. Background Art

[0002] With the increase of signal bandwidth and the expansion of application scenarios, the sampling rate of traditional Nyquist sampling is getting higher and higher, resulting in extremely high signal sampling, transmission and storage. Moreover, in certain scenarios, hardware devices such as analog-to-digital converters (ADCs) may not meet the Nyquist sampling requirements. Therefore, it is of great significance to develop compressed sampling that can replace Nyquist sampling. Compressed sampling, also known as sub-Nyquist sampling, samples signals at an average rate lower than the Nyquist sampling rate through a non-uniform sampling method. Compared with Nyquist sampling, compressed sampling has a lower average sampling rate and less data volume, thereby reducing the cost of signal sampling, data transmission and storage.

[0003] At present, the field of compressed sampling often samples signals based on compressed sensing theory, which has the disadvantages of high cost of hardware equipment and high pressure on data sampling, transmission and processing.

[0004] The above information disclosed in this Background section is only for enhancement of understanding of the background of the invention and therefore it may contain information that does not form the prior art that is already known to a person of ordinary skill in the art. Summary of the invention

[0005] The present invention provides a spectrum analysis method based on circumferential minimum sparseness compressed sampling, which reduces the average sampling rate to below the Nyquist rate, realizes compressed sampling of signals in a periodic non-uniform form, and realizes covariance estimation and power spectrum reconstruction, reduces the cost of hardware equipment, and alleviates the pressure of data sampling, transmission, and processing.

[0006] A spectrum analysis method based on circumferential minimum sparseness compression sampling includes:

[0007] Step 1, determining a downsampling factor according to the upper frequency limit of the measured signal and the sampling rate of the sampling channel;

[0008] Step 2, determining the circumferential minimum sparseness pattern through an optimization algorithm;

[0009] Step 3, performing periodic non-uniform sampling on the signal in a circumferential minimum sparseness mode to obtain signal samples;

[0010] Step 4, estimating continuous covariance samples from the signal samples;

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

[0012] In the spectrum analysis method based on circumferential minimum sparseness compression sampling, step 1 comprises:

[0013] make Indicates the measured signal The upper frequency limit of Represents the sampling rate of the sampling channel. The downsampling factor L that meets the conditions is determined according to the following formula

[0014] (1)

[0015] in: The round-up symbol.

[0016] In the spectrum analysis method based on circumferential minimum sparseness compression sampling, step 2 includes:

[0017] First, by solving the following optimization model, we can get the length The minimum sparseness scale of :

[0018] (2)

[0019] Where: is the minimum sparseness scale; is a set of integers; for The non-negative difference set of The absolute value of the difference between any two elements in is expressed as follows:

[0020] (3)

[0021] in and express Any two elements in , taking all cases,

[0022] Finally, according to and Determine the minimum circumferential sparseness .

[0023] In the spectrum analysis method based on circumferential minimum sparseness compression sampling, step 3 includes:

[0024] First, according to the sampling rate of the channel and the downsampling factor L determines the nominal time unit T: ,

[0025] Then the signal is periodically non-uniformly sampled according to the circumferential minimum sparseness pattern, where: and L is the minimum sparseness scale in the circumferential direction The elements in , the pth channel processes the signal for a duration of The delay is then uniformly sampled with LT as the period. , the data sequence collected by all channels is recorded as ,in

[0026] (4).

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

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

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

[0030] In the spectrum analysis method based on circumferential minimum sparseness compression sampling, in step 4, from the signal sample Estimate the continuous covariance sample vector in include,

[0031] Enter the minimum sparseness , downsampling factor , number of channels P, signal sample vector ;

[0032] based on Estimating the covariance samples with successive lags includes,

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

[0034] n is an integer from 0 to N-1, and the length of the vector G is calculated:

[0035] ,in is the floor symbol, To obtain the maximum value operation;

[0036] Construct a vector of two congruent covariance estimates and ,

[0037] , , where m and q are two integers that satisfy and , and for The mth and qth elements in ;

[0038] The estimated delay is The covariance sample : .

[0039] In the spectrum analysis method based on circumferential minimum sparseness compression sampling, step 5 includes:

[0040] By sampling the covariance of successive Perform discrete Fourier transform to estimate signal power spectrum

[0041] (6)

[0042] in: Represents a sequence After discrete Fourier transform, the kth Fourier coefficient is obtained. express The nth element in The data length is expressed in terms of the absolute value of the Fourier coefficient vector is the vertical axis, The power spectrum of the signal is obtained as the horizontal axis.

[0043] Compared with the prior art, the present invention has the following advantages: the present invention adopts a circumferential minimum sparse ruler mode to compress sampling of wide-sense stationary signals. Compared with random sampling, the circumferential minimum sparse ruler has a deterministic periodic non-uniform sampling mode, so it has the advantage of easy hardware implementation. Compared with the minimum sparse ruler, the sample points of the circumferential minimum sparse ruler sampling are more sparse, and the compression efficiency of the circumferential minimum sparse ruler sampling is twice that of the minimum sparse ruler sampling. In terms of post-processing of sampled signals, the present invention directly estimates continuous covariance samples from the measured samples, and then performs spectral analysis based on the covariance samples, such as performing discrete Fourier transform on the covariance samples to obtain a power spectrum. Compared with the compressed sampling signal post-processing method based on compressed sensing and Lasso algorithm, it has lower computational complexity and higher robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] By reading the detailed description of the preferred specific embodiments below, various other advantages and benefits of the present invention will become clear to those of ordinary skill in the art. The drawings in the specification are only for the purpose of illustrating the preferred embodiments and are not considered to be limitations of the present invention. Obviously, the drawings described below are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can also be obtained based on these drawings without creative work. Moreover, the same reference numerals are used to represent the same components throughout the drawings.

[0045] In the attached picture:

[0046] Figure 1 A schematic diagram of the circumferential minimum sparseness rule proposed by the present invention;

[0047] Figure 2 This is a periodic non-uniform sampling structure diagram based on the circumferential minimum sparse ruler proposed by the present invention;

[0048] Figure 3 is a schematic diagram of a signal sample sequence obtained by circumferential minimum sparseness sampling in an implementation case of the present invention, Figure 3 Where (a) is the real part sequence, Figure 3 (b) is the imaginary part sequence;

[0049] Figure 4 is a schematic diagram of continuous covariance samples estimated in an implementation case of the present invention, Figure 4 Where (a) is the real part sequence, Figure 4 (b) is the imaginary part sequence;

[0050] Figure 5 is a schematic diagram of the power spectrum obtained by discrete Fourier transforming continuous covariance samples;

[0051] Figure 6 Schematic diagram of the process proposed by the present invention.

[0052] The present invention is further explained below in conjunction with the accompanying drawings and embodiments. DETAILED DESCRIPTION

[0053] The specific embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although the specific embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided in order to enable a more thorough understanding of the present invention and to fully convey the scope of the present invention to those skilled in the art.

[0054] It should be noted that certain words are used in the specification and claims to refer to specific components. Those skilled in the art should understand that technicians may use different nouns to refer to the same component. This specification and claims do not use the difference in nouns as a way to distinguish components, but use the difference in the functions of the components as the criterion for distinction. As mentioned throughout the specification and claims, "including" or "comprising" is an open term, so it should be interpreted as "including but not limited to". The subsequent description of the specification is a preferred embodiment of the present invention, but the description is based on the general principles of the specification and is not intended to limit the scope of the present invention. The scope of protection of the present invention shall be determined by the attached claims.

[0055] To facilitate understanding of the embodiments of the present invention, further explanation will be given below by taking specific embodiments as examples in conjunction with the accompanying drawings, and each of the accompanying drawings does not constitute a limitation on the embodiments of the present invention.

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

[0057] Step 1, determining a downsampling factor according to the upper frequency limit of the measured signal and the sampling rate of the sampling channel;

[0058] Step 2, determining the circumferential minimum sparseness pattern through an optimization algorithm;

[0059] Step 3, performing periodic non-uniform sampling on the signal in a circumferential minimum sparseness mode to obtain signal samples;

[0060] Step 4, estimating continuous covariance samples from the signal samples;

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

[0062] In a preferred implementation of the spectrum analysis method based on circumferential minimum sparseness compression sampling, step 1 comprises:

[0063] make Indicates the measured signal The upper frequency limit of Represents the sampling rate of the sampling channel. The downsampling factor L that meets the conditions is determined according to the following formula

[0064] (1)

[0065] in: The round-up symbol.

[0066] In a preferred implementation of the spectrum analysis method based on circumferential minimum sparseness compression sampling, step 2 includes:

[0067] First, by solving the following optimization model, we can get the length The minimum sparseness scale of :

[0068] (2)

[0069] Where: is the minimum sparseness scale; is a set of integers; for The non-negative difference set of The absolute value of the difference between any two elements in is expressed as follows:

[0070] (3)

[0071] in and express Any two elements in , taking all cases,

[0072] Finally, according to and Determine the minimum circumferential sparseness .

[0073] In a preferred implementation of the spectrum analysis method based on circumferential minimum sparseness compression sampling, step 3 includes:

[0074] First, according to the sampling rate of the channel and the downsampling factor L determines the nominal time unit T: ,

[0075] Then the signal is periodically non-uniformly sampled according to the circumferential minimum sparseness pattern, where: and L is the minimum sparseness scale in the circumferential direction The elements in , the pth channel processes the signal for a duration of The delay is then uniformly sampled with LT as the period. , the data sequence collected by all channels is recorded as ,in

[0076] (4).

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

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

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

[0080] In a preferred embodiment of the spectrum analysis method based on circumferential minimum sparseness compression sampling, in step 4, the signal samples are Estimate the continuous covariance sample vector in include,

[0081] Enter the minimum sparseness , downsampling factor , number of channels P, signal sample vector ;

[0082] based on Estimate the covariance samples with continuous delays as follows

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

[0084] Calculation Satisfaction Pairs of elements whose median difference is equal to l ,Right now and ;

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

[0086] Calculate the vector length G:

[0087] ,in is the floor symbol, To obtain the maximum value operation;

[0088] Construct a vector of two congruent covariance estimates and ,

[0089] , , where m and q are two integers that satisfy and , and for The mth and qth elements in ;

[0090] The estimated delay is The covariance sample : .

[0091] In a preferred implementation of the spectrum analysis method based on circumferential minimum sparseness compression sampling, step 5 includes:

[0092] By sampling the covariance of successive Perform discrete Fourier transform to estimate signal power spectrum

[0093] (6)

[0094] in: Represents a sequence After discrete Fourier transform, the kth Fourier coefficient is obtained. express The nth element in The data length is expressed in terms of the absolute value of the Fourier coefficient vector is the vertical axis, The power spectrum of the signal is obtained as the horizontal axis.

[0095] A vibration system operation modal parameter estimation system, characterized in that it includes:

[0096] a determination unit, which determines a downsampling factor according to an upper frequency limit of a measured signal and a sampling rate of a sampling channel;

[0097] An optimization unit, which determines the circumferential minimum sparseness pattern through an optimization algorithm;

[0098] A sampling unit, which performs periodic non-uniform sampling on the signal in a circumferential minimum sparseness mode to obtain signal samples;

[0099] an estimation unit that estimates successive covariance samples from the signal samples;

[0100] Signal power spectrum unit estimates the signal power spectrum from consecutive covariance samples.

[0101] A computer storage medium includes computer instructions, which, when executed on a computer, cause the computer to execute the method described.

[0102] An electronic device, comprising:

[0103] A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein:

[0104] When the processor executes the program, the method described is implemented.

[0105] In one embodiment, the compressed sampling and spectrum analysis method based on the circumferential minimum sparseness rule 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 frequency limit of Represents the sampling rate of the sampling channel. Determine the downsampling factor L that meets the conditions according to the following formula

[0108] (1)

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

[0110] In this illustrative example , the simulation generates a sine superposition signal containing Gaussian white noise, whose first-order and second-order moments do not change with time, so it is a wide-sense stationary signal. The simulation signal contains 4 sinusoidal components, and the expression is shown in the following formula:

[0111] (2)

[0112] in represents the noise term, , and Respectively represent the frequency, amplitude, and phase of the i-th signal component, i = 1, 2, 3, 4, Represents a simulated analog signal.

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

[0114] Table 1 Simulation parameters

[0115]

[0116] Signal is a complex-valued signal with the highest frequency Hz. Therefore, the downsampling factor L is an integer and must satisfy . In this exemplary example, L = 27.

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

[0118] First, by solving the following optimization model, we can get the length The minimum sparseness scale of :

[0119] (3)

[0120] If we do not use the optimization model (3) to obtain , the length can be directly determined by looking up the table. The minimum sparseness scale mode

[0121] Finally, according to and Determine the minimum circumferential sparseness .

[0122] In this illustrative example , L = 27, the following optimization model is obtained

[0123] (4)

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

[0125] If the minimum sparse size table contains a length of The sparseness scale can be directly determined by looking up the table . Directly looking up the table shows that the length is The sparseness scale is .therefore .

[0126] Minimum sparseness table

[0127]

[0128] Finally, according to and Determine the minimum circumferential sparseness in this example as .

[0129] (3) Perform periodic non-uniform sampling of the signal using a circumferential minimum sparseness pattern;

[0130] First, according to the sampling rate of the channel and the downsampling factor L determines the nominal time unit T: .

[0131] Then the signal is periodically non-uniformly sampled according to the circumferential minimum sparseness pattern, the specific form is as follows Figure 2 described.

[0132] in, and L is the minimum sparseness scale in the circumferential direction The elements in In the figure, is the delay module. The pth channel processes the signal for a time period of The delay is then uniformly sampled with LT as the period. Without loss of generality, let the delay time of the first channel be 0 as a reference, that is, Assume that the sampling time duration is , then the sample sampled by the pth channel is

[0133] (5)

[0134] The data sequence collected by all channels is recorded as ,in

[0135] (6)

[0136] In this illustrative example , Hz and , so the nominal time unit Second

[0137] Then the signal is periodically non-uniformly sampled according to the circumferential minimum sparseness pattern, the specific form is as follows Figure 2 shown.

[0138] In the exemplary example , then the samples sampled by the 1st to 6th channels are

[0139] (7)

[0140] The data sequence obtained by sampling the 1st to 6th channels is

[0141] (8)

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

[0143]

[0144] In this illustrative example , , ,

[0145] Traverse l from 0 to 26. When l = 0, The pairs of elements whose difference is equal to 0 have ,Right now .

[0146] Then traverse n from 0 to 99, when n = 0, . Construct a vector of two congruent covariance estimates and ,

[0147] , . Estimate the covariance sample for lag 0: When n = 1, . Construct a vector of two congruent covariance estimates and , , . Estimate the covariance sample for a lag of 27: .

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

[0149] When l = 1, The pairs of elements whose difference is equal to 1 have ,Right now .

[0150] Then traverse n from 0 to 99, when n = 0, . Construct a vector of two congruent covariance estimates and , , . Estimate the covariance sample with lag 1: .

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

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

[0153] By sampling the covariance of successive Perform discrete Fourier transform to estimate signal power spectrum

[0154] (9)

[0155] in: Represents a sequence After discrete Fourier transform, the kth Fourier coefficient is obtained. express The nth element in The absolute value of the Fourier coefficient vector is the vertical axis, As the horizontal axis, the power spectrum of the signal can be obtained.

[0156] In this illustrative example , the continuous signal samples estimated by the formula Length Z = 2687.

[0157] The discrete Fourier transform is the vertical axis, As the horizontal axis, the power spectrum can be obtained.

[0158]

Application examples

[0159] (1) In this exemplary embodiment , the simulation generates a sine superposition signal containing Gaussian white noise, whose first-order and second-order moments do not change with time, so it is a wide-sense stationary signal. The simulation signal contains 4 sinusoidal components, and the expression is shown in the following formula:

[0160]

[0161] in represents the noise term, , and Respectively represent the frequency, amplitude, and phase of the i-th signal component, i = 1, 2, 3, 4, Represents a simulated analog signal.

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

[0163] Table 1 Simulation parameters

[0164]

[0165] Signal is a complex-valued signal with the highest frequency Hz. Therefore, the downsampling factor L is an integer and must satisfy . In this exemplary example, L = 27.

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

[0167] In this illustrative example , L = 27, the following optimization model is obtained

[0168]

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

[0170] If the minimum sparse size table contains a length of Sparse ruler, you can check the minimum sparse ruler table,

[0171] Direct determination . Directly looking up the table shows that the length is The sparseness scale is .therefore Finally, according to and Determine the minimum circumferential sparseness in this example as The circumference of the circumferential minimum sparse ruler is 27, and there are scales only at 0, 1, 2, 6, 10, and 13, but it can measure all integer distances from 0 to 27, such as Figure 1 As shown. Note that the figure only shows the measurement method of integer distances of 0 to 13. Integer distances of 14 to 27 can be obtained by taking the corresponding major arcs of the minor arcs with distances of 0 to 13. This circumferential sparse ruler is the sparse ruler with the least scales among all circumferential sparse rulers that can measure distances of 0 to 27, so it is called the minimum circumferential sparse ruler.

[0172] (3) Perform periodic non-uniform sampling of the signal using a circumferential minimum sparseness pattern;

[0173] In this illustrative example , Hz and , so the nominal time unit Second

[0174] Then the signal is periodically non-uniformly sampled according to the circumferential minimum sparseness pattern, the specific form is as follows Figure 2 shown.

[0175] In the exemplary example, , then the samples sampled by the 1st to 6th channels are

[0176]

[0177] The data sequence obtained by sampling the 1st to 6th channels is

[0178]

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

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

[0181]

[0182] In this illustrative example , , ,

[0183] Traverse l from 0 to 26. When l = 0, The pairs of elements whose difference is equal to 0 have ,Right now .

[0184] Then traverse n from 0 to 99, when n = 0, . Construct a vector of two congruent covariance estimates and ,

[0185] , . Estimate the covariance sample for lag 0: When n = 1, . Construct a vector of two congruent covariance estimates and , , . Estimate the covariance sample for a lag of 27: .

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

[0187] When l = 1, The pairs of elements whose difference is equal to 1 have ,Right now .

[0188] Then traverse n from 0 to 99, when n = 0, . Construct a vector of two congruent covariance estimates and , , . Estimate the covariance sample with lag 1: .

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

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

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

[0192] By sampling the covariance of successive Perform discrete Fourier transform to estimate signal power spectrum

[0193]

[0194] in: Represents a sequence After discrete Fourier transform, the kth Fourier coefficient is obtained. express The nth element in The absolute value of the Fourier coefficient vector is the vertical axis, As the horizontal axis, the power spectrum of the signal can be obtained.

[0195] In this illustrative example , the continuous signal samples estimated by the formula Length Z = 2687.

[0196] The discrete Fourier transform is the vertical axis, As the horizontal axis, the power spectrum can be obtained, such as Figure 5 Observation Figure 5 It can be seen that the power spectrum restored by circumferential minimum sparse sampling is very close to the true power value, and 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 the embodiments of the present invention are described above in conjunction with the accompanying drawings, the present invention is not limited to the above specific embodiments and application fields, and the above specific embodiments are only illustrative and instructive, rather than restrictive. A person of ordinary skill in the art can also make many forms under the guidance of this specification and without departing from the scope of protection of the claims of the present invention, all of which belong to the protection of the present invention.

Claims

1. A spectrum analysis method based on circumferential minimum sparseness compression sampling, characterized in that: The steps include: Step (1), determining a downsampling factor according to the upper frequency limit of the measured signal and the sampling rate of the sampling channel; Step (2), determining the circumferential minimum sparseness pattern through an optimization algorithm; Step (3), performing periodic non-uniform sampling on the signal in a circumferential minimum sparseness mode to obtain signal samples; Step (4), estimating continuous covariance samples from signal samples; Step (5), estimate the signal power spectrum from continuous covariance samples.

2. The spectrum analysis method based on circumferential minimum sparseness compression sampling according to claim 1 is characterized in that: Preferably, the step (1) comprises: make Indicates the measured signal The upper frequency limit of Represents the sampling rate of the sampling channel. The downsampling factor L that meets the conditions is determined according to the following formula (1)， in: The symbol for rounding up.

3. The spectrum analysis method based on circumferential minimum sparseness compression sampling according to claim 2 is characterized in that: The step (2) comprises: First, by solving the following optimization model, we can get the length The minimum sparseness scale of : (2)， Where: is the minimum sparseness scale; is a set of integers; for The non-negative difference set of The absolute value of the difference between any two elements in is expressed as follows: (3)， in and express Any two elements in , taking all cases, Finally, according to and Determine the minimum circumferential sparseness .

4. The spectrum analysis method based on circumferential minimum sparseness compression sampling according to claim 2 is characterized in that: The step (3) comprises: First, according to the sampling rate of the channel and the downsampling factor L determines the nominal time unit T: , Then the signal is periodically non-uniformly sampled according to the circumferential minimum sparseness pattern, where: and L is the minimum sparseness scale in the circumferential direction The elements in , the pth channel processes the signal for a duration of The delay is then uniformly sampled with LT as the period. , the data sequence collected by all channels is recorded as ,in (4)。 5. The spectrum analysis method based on circumferential minimum sparseness compression sampling according to claim 4 is characterized in that: The step (4) includes estimating the compressed covariance matrix of the signal samples , (5) Where: Q is the number of snapshots; , q is the integer to be traversed, from 0 to Q-1; .

6. The spectrum analysis method based on circumferential minimum sparseness compression sampling according to claim 5, characterized in that: In step (4), from the signal sample Estimate the continuous covariance sample vector in include, Enter the minimum sparseness , downsampling factor , number of channels P, signal sample vector ; based on Estimating the covariance samples with successive lags includes, l is an integer from 0 to L-1, and the calculation satisfies Pairs of elements whose median difference is equal to l ,Right now and ; n is an integer from 0 to N-1, and the length of the vector G is calculated: ,in is the floor symbol, To obtain the maximum value operation; Construct a vector of two congruent covariance estimates and , , , where m and q are two integers that satisfy and , and for The mth and qth elements in ; The estimated delay is The covariance sample : .

7. The spectrum analysis method based on circumferential minimum sparseness compression sampling according to claim 5 is characterized in that: Step (5) includes, By sampling the covariance of successive Perform discrete Fourier transform to estimate signal power spectrum (6) in: Represents a sequence After discrete Fourier transform, the kth Fourier coefficient is obtained. express The nth element in The data length is the absolute value of the Fourier coefficient vector is the vertical axis, The power spectrum of the signal is obtained as the horizontal axis.

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