CN107766293B

CN107766293B - Signal spectrum analysis method and system when part of sampling data is missing regularly

Info

Publication number: CN107766293B
Application number: CN201710900980.4A
Authority: CN
Inventors: 陆祖良; 杨雁; 黄璐; 王磊
Original assignee: National Institute of Metrology
Current assignee: National Institute of Metrology
Priority date: 2017-09-28
Filing date: 2017-09-28
Publication date: 2021-04-23
Anticipated expiration: 2037-09-28
Also published as: CN107766293A

Abstract

A method and system for analyzing the frequency spectrum of signal when the regularity of part of sampled data is missing are disclosed. The method can comprise the following steps: for the measurement signals with part of sampling data lacking regularity, adopting discrete Fourier transform operation in a segmented sampling mode to obtain an intermediate result of the frequency spectrum of the measurement signals; calculating a corresponding influence matrix according to a rule presented by the orthogonality of the trigonometric function under the condition of missing data, and further obtaining a plurality of reduced order matrixes; calculating an inverse matrix of the reduced order matrix; the intermediate result is converted into final spectral data based on the inverse matrix. The invention expands the signal spectrum analysis method to a new range, and has lower computation amount and higher accuracy.

Description

Signal spectrum analysis method and system when part of sampling data is missing regularly

Technical Field

The invention relates to the fields of electromagnetic measurement, electrical engineering foundation and signal processing, in particular to a signal spectrum analysis method and system when the regularity of part of sampling data is lost.

Background

The classical discrete fourier transform method (DFT) has wide application. By performing discrete fourier transform on the sampled data of the measurement signal, the frequency spectrum of the signal, i.e., the cosine coefficient and the sine coefficient of each frequency component, can be obtained. Typically the samples are equally spaced and the condition required for the discrete fourier transform is the total number of samples in a period. However, the sampled data is often missing for various reasons. One of the important ones is the lack of temporal regularity. The deletion may be derived from artificial processing, for example, some data are intentionally deleted in order to overcome the influence of a transition process in step wave measurement, the transition process exists in the data, the original signal cannot be accurately reflected, and the actual situation can be better reflected after deletion; it may also be derived from non-human processes, such as the loss of signals during transmission (or communication), which is often random, but may have a lack of regularity, or may be processed to have a lack of regularity.

Due to data loss, the method cannot meet the requirements of a common classical discrete Fourier transform method, and cosine coefficients and sine coefficients cannot be calculated. Therefore, there is a need to develop a method and system for analyzing signal spectrum when there is a regular loss of partial sampling data.

The information disclosed in this background section is only for enhancement of understanding of the general background of the invention and should not be taken as an acknowledgement or any form of suggestion that this information forms the prior art already known to a person skilled in the art.

Disclosure of Invention

The invention provides a signal spectrum analysis method and a system when part of sampling data is missing regularly, which expand the signal spectrum analysis to a new range and have lower computation amount and higher accuracy.

According to one aspect of the invention, a method for analyzing a signal spectrum when regularity of partially sampled data is missing is provided. The method may include: for the measurement signals with part of sampling data lacking regularity, adopting discrete Fourier transform operation in a segmented sampling mode to obtain an intermediate result of the frequency spectrum of the measurement signals; calculating a corresponding influence matrix according to a rule presented by the orthogonality of the trigonometric function under the condition of missing data, and further obtaining a plurality of reduced order matrixes; calculating an inverse matrix of the reduced order matrix; the intermediate result is converted into final spectral data based on the inverse matrix.

Preferably, the measurement signals with partially sampled data missing regularly are: equally spaced deletions occurred and the same number of measurement signals were missing.

Preferably, the discrete fourier transform operation of the segmented sampling mode is:

wherein the content of the first and second substances,

as an intermediate result, a_iAnd b_iCosine coefficient and sine coefficient of the ith harmonic, y_n,mSample data obtained for measuring signals, h is a sampling interval, N is the total number of uniform groups of measuring signals in a period, N is a group number of measuring signals, m is a sample data number of a medium interval in each group of measuring signals, [0, s-1]]And [ t +1, M-1]]For missing data label ranges, [ s, t ]]To preserve the data index range, M is the total number of equally spaced sampled data in each set of measurement signals.

Preferably, the influence matrix is:

where AA (i, j) is an element of the cosine and cosine interaction matrix AA, BB (i, j) is an element of the sine and sine interaction matrix BB, and AB (i, j) is an element of the cosine and sine interaction matrix AB.

Preferably, when t + s ═ M, all elements of the impact matrix AB are zero, and the matrix AA is decomposed into three classes of reduced order matrices: a. the^k，A^0.5NAnd A and^Nthe impact matrix BB is decomposed into three classes of reduced order matrices: b is^k，B^0.5NAnd B^N。

Preferably, the cosine result of the final spectrum data is:

wherein, a_kIs a frequency of kf₁Cosine coefficient of the spectral end result of (A)^k)^-1,(A^0.5N)^-1，(A^N)^-1Is the inverse of the three reduced value matrices of the matrix AA.

Preferably, the sinusoidal result of the final spectrum data is:

wherein, b_kIs a frequency of kf₁(ii) the sine coefficient of the spectral end result of (B)^k)^-1,(B^0.5N)^-1，(B^N)^-1Is the inverse of the three reduced-value matrices of the matrix BB.

Preferably, the signal spectrum analysis method when the regularity of the part of the sampling data is missing is applied to the quantum measurement of the spectrum analysis.

According to another aspect of the present invention, a system for analyzing a signal spectrum when regularity of partially sampled data is missing is provided, which may include: a memory storing computer executable instructions and partially missing signal sample data; a processor executing computer executable instructions in the memory to perform the steps of: for the measurement signal with part of sampling data lacking regularity, performing classical discrete Fourier transform operation in a segmented sampling mode to obtain an intermediate result of a measurement signal frequency spectrum; calculating a corresponding influence matrix according to a rule presented by the orthogonality of the trigonometric function under the condition of missing data, and further obtaining a plurality of reduced order matrixes; calculating an inverse matrix of the reduced order matrix; the intermediate result is converted into final spectral data based on the inverse matrix.

The method and apparatus of the present invention have other features and advantages which will be apparent from or are set forth in detail in the accompanying drawings and the following detailed description, which are incorporated herein, and which together serve to explain certain principles of the invention.

Drawings

The above and other objects, features and advantages of the present invention will become more apparent by describing in more detail exemplary embodiments thereof with reference to the attached drawings, in which like reference numerals generally represent like parts.

Fig. 1 shows a flow chart of the steps of a method of signal spectrum analysis in the absence of regularity in part of the sampled data according to the invention.

Fig. 2 shows an explanatory diagram of the steps of the signal spectrum analysis method according to the invention in the absence of regularity of the partially sampled data.

Fig. 3a, 3b and 3c show schematic diagrams of a measured signal curve, full sample data, and sample data after loss, respectively, according to an embodiment of the invention.

Fig. 4 shows a schematic diagram of the step-wave aliasing effect according to an embodiment of the invention.

Fig. 5 is a schematic diagram illustrating the alignment relationship between two signals in the differential measurement of the non-sinusoidal periodic signal based on the step wave according to an embodiment of the present invention.

Detailed Description

The invention will be described in more detail below with reference to the accompanying drawings. While the preferred embodiments of the present invention are shown in the drawings, it should be understood that the present invention may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.

In this embodiment, the method for analyzing a signal spectrum when the regularity of the partially sampled data is missing according to the present invention may include:

step 101, for a measurement signal with part of sampling data lacking regularity, adopting discrete Fourier transform operation in a segmented sampling mode to obtain an intermediate result of a measurement signal frequency spectrum;

102, calculating a corresponding influence matrix according to a rule of orthogonality of the trigonometric function under the condition of missing data, and further obtaining a plurality of reduced order matrixes;

step 103, calculating an inverse matrix of the reduced-order matrix;

and 104, converting the intermediate result into final spectrum data based on the inverse matrix.

In one example, the measurement signals for which the partially sampled data is regularly missing are: equally spaced deletions occurred and the same number of measurement signals were missing.

In one example, the discrete fourier transform operation of the segmented sampling approach is:

wherein the content of the first and second substances,

as preliminary result of the signal spectrum, a_iAnd b_iCosine coefficient and sine coefficient of the ith harmonic, y_n,mSample data obtained for measuring signals, h is a sampling interval, N is the total number of uniform groups of measuring signals in a period, N is a group number of measuring signals, m is a sample data number of a medium interval in each group of measuring signals, [0, s-1]]And [ t +1, M-1]]For missing data label ranges, [ s, t ]]To preserve the data index range, M is the total number of equally spaced sampled data in each set of measurement signals.

In one example, the impact matrix is:

In one example, when t + s ═ M, all elements of the impact matrix AB are zero, the matrix AA is decomposed into three classes of reduced order matrices: a. the^k，A^0.5NAnd A and^Nthe impact matrix BB is decomposed into three classes of reduced order matrices: b is^k，B^0.5NAnd B^N。

In one example, the cosine result of the final spectral data is:

In one example, the sinusoidal result of the final spectral data is:

Specifically, based on a measurement signal with partly sampling data lacking regularity, adopting discrete Fourier transform operation in a segmented sampling mode to obtain an intermediate result of a frequency spectrum of the measurement signal; the regularity missing of the data can be derived from artificial processing, for example, some data are intentionally deleted for overcoming the influence of a transition process in step wave measurement, the transition process exists in the data, the original signal cannot be accurately reflected, and the actual situation can be better reflected after the deletion; it may also originate from non-human processes, such as the loss of a signal during transmission (or communication), which, although often random, may be the case where the described regularity is missing or, by transformation, regular. The partial sampling data regularity missing can be further described as that sampling data of one period is divided into N groups, and the group index N is 0,1,2, …, N-1; each group has M sampling data with equal intervals, and each group has the data label M which is 0,1,2, … and M-1; the same deletion occurs in each set of data, with the data labeled M0, 1,2, …, s-1 and M t +1, t +2, …, M-1, and the remaining data labeled from s to t, i.e., M s, s +1, …, t, for a total of (t-s +1), typically 0 < s < 0.5M < t < M-1. For ease of description, it is referred to as segmented sampling, denoted as (s, t-s +1, M-1-t), which includes the meaning that the discrete Fourier transform is performed only on the remaining (t-s +1) samples in the middle. In the above description, the deletions are located on both sides of each set of data, and in the case where the deletions are not located on both sides, it is not difficult to arrange the deletions on both sides of a set of data by reselecting the start points of the periods, and therefore, the measurement signals in which the partially sampled data are regularly missing have wide applicability.

The measurement signals are:

wherein y is the measurement signal, a_iAnd b_iCosine coefficient and sine coefficient of the ith harmonic, f₁Is the fundamental frequency, omega is the circular frequency, the classic discrete Fourier transform operation is carried out by adopting the segmented sampling mode to be formula (2), wherein, the sampling interval is formula (6), and then the intermediate result is obtained,

h＝2π/(NM) (6)。

from the rule that the orthogonality of the trigonometric functions appears in the absence of data, the corresponding influence matrix is calculated as equation (3). When t + s ═ M, all elements of the impact matrix AB are zero; when t + s ═ M, the matrix AA is affectedThe decomposition is into three classes of reduced order matrices: a. the^k，A^0.5NAnd A and^N(ii) a When t + s is equal to M, the impact matrix BB is decomposed into three classes of reduced order matrices: b is^k，B^0.5NAnd B^N。

Wherein, the order-reduced matrix A^k(B^kLikewise) is part of the original matrix aa (bb) and is composed of elements of the original matrix with the row designations k, N-k, N + k, 2N-k, 2N + k, … and the column designations k, N-k, N + k, 2N-k, 2N + k, …, wherein the final row designation (column designation) is determined by the highest order of the required analysis. If the last row index (column index) is denoted as wN-k (or wN + k), it should generally satisfy 2 ω ≦ (t-s +1) < M. Reduced order matrix A^k(B^k) The diagonal element of (a) is 1. When k is 1,2, …,0_.5N-1, all A^k(B^kLikewise) have the same form, and in fig. 4 these matrices correspond to the dashed lines starting from point k-1, 2, …, 0.5N-1.

Wherein, the order-reduced matrix A^0.5N(B^0.5NLikewise) is part of the original matrix AA (BB) and is composed of elements with row labels of 0.5N,1.5N, … and column labels of 0.5N,1.5N, …, and the final row label (column label) is required to be identical to the reduced order matrix A^kIn fig. 4, this matrix corresponds to the line starting from point 0.5N, which is located at the rightmost side (not shown).

Wherein, the order-reduced matrix A^N(B^NSimilarly) is part of the original matrix aa (bb) and is composed of elements with row labels N,2N, … and column labels N,2N, … in the original matrix, and the final row label (column label) is required to be identical to the reduced order matrix a^kIn fig. 4, this matrix corresponds to the leftmost line (not shown) starting from point 0 (N).

Calculating respective inverse matrices from the reduced order matrices: (A)^k)^-1，(A^0.5N)^-1And (A)^N)^-1；(B^k)^-1，(B^0.5N)^-1And (B)^N)^-1The inverse matrix can be calculated by those skilled in the art as the case may be.

The intermediate result is converted into final spectral data based on the inverse matrix. Taking cosine coefficients as an example, the intermediate results are first divided into three types of column vectors according to the following relationship:

further, the cosine result of the final spectrum data is obtained as formula (4), and the sine result is obtained as formula (5).

The method expands the signal spectrum analysis method to a new range, and has lower operation amount and higher accuracy.

To facilitate understanding of the aspects of the embodiments of the present invention and their effects, two specific application examples are given below. It will be understood by those skilled in the art that this example is merely for the purpose of facilitating an understanding of the present invention and that any specific details thereof are not intended to limit the invention in any way.

Application example 1

Table 1 gives the settings for an original signal, including the magnitude and phase angle of each frequency component. The shape of the curve is shown in fig. 3 a. As can be seen from fig. 3a, the curves are within ± 1V, which facilitates the later calculation of the error, the resulting absolute errors are all for 1V and can therefore also be considered as relative errors.

TABLE 1

Original signal setting	1	3	4	15	24
						Amplitude value	0.800	-0.320	0.200	-0.045	0.023
Phase angle	-π/5	π/3	0	-π/2.3	π/10

Uniformly sampling the signal, wherein 960 points are divided into 20 groups in one period, and each group comprises 48 samples; the first 12 and the last 11 data in each group are deleted, and the middle 25 data are reserved for subsequent operations. There are 500 samples to participate in the operation per cycle. Therefore, the harmonic can be analyzed to 250 orders at most, and the highest harmonic is 60 orders.

N is 20, M is 48, the segmented samples are (12,25,11), s is 12, t is 36, and the conditions of s + t is M are met. And (4) carrying out segmented DFT operation on the samples according to the formula (2). Intermediate results of the signal spectrum were obtained as shown in table 2.

Fig. 4 shows a schematic diagram of the step-wave aliasing effect according to an embodiment of the invention. The classical fourier transform can obtain accurate results without difficulty when the frequency of analysis is less than 0.5N, and the present invention should be employed to obtain accurate results when the frequency of analysis is 0.5N or more and less than 0.5N (t-s + 1).

The influence matrix is then calculated according to equation (3), which is:

A^kis a 6 x 6 matrix with row (column) indices of (k, 20-k, 20+ k, 40-k, 40+ k, 60-k) and the matrix is

A¹⁰Is a 3 x 3 matrix with row (column) indices of (10,30,50) and the matrix is

A²⁰Is a 3 x 3 matrix with row (column) indices (20,40,60) and the matrix is

B^kIs composed of

B¹⁰Is composed of

B²⁰Is composed of

Their inverse matrices are respectively:

(A^k)^-1is composed of

(A¹⁰)^-1Is composed of

(A²⁰)^-1Is composed of

(B^k)^-1Is composed of

(B¹⁰)^-1Is composed of

(B²⁰)^-1Is composed of

Finally, the intermediate results obtained in the first step are restored by using the inverse matrices, and the final spectrum data is obtained, as shown in table 2. The two rightmost columns of errors in the table are the differences of the final spectral data and the original settings. As before, since the maximum amplitude of the measurement signal is close to 1V, the result can be regarded as a relative value.

TABLE 2

As can be seen from table 2, the deviation of the intermediate result from the original setting value is large, which is the result of performing classical discrete fourier transform on the segmented samples; but after the inverse matrix recovery, the difference between the final result and the set value is 10^-9Magnitude, is basically a computational error caused by the bit-limited setting of the computer itself. (the data in the table are given to 7 bits after decimal point, but the actual calculation has no limitation on the number of bits, so 10 can be obtained^-9Error of magnitude).

In principle, the influence matrix of the present invention is actually related to the orthogonality of the trigonometric functions, and the deviations caused by the classical discrete fourier transform of the segmented samples are caused by these influence matrices. The inverse matrix recovers the original result. Due to the regularity of data loss in time, the basis function, namely the trigonometric function, involved in the classical discrete fourier transform can be directly written out, or the measurement mode can be designed in advance or determined afterwards, so that the method has wide application.

Compared with the general classical discrete fourier transform method, in the case of the loss of the sampling data due to the time regularity and the general requirement that the highest harmonic wave is 60 times, the 120 × 120 influence matrix and the inverse matrix thereof need to be solved, which is very heavy in workload. But with the invention, only 2 6 × 6 matrixes and 4 3 × 3 matrixes are needed for calculation and inversion, compared with the method, the calculation amount is not complicated, but the obtained accuracy is very high.

Application example 2

In one example, the signal spectrum analysis method when the regularity of the partially sampled data is missing is applied to quantum measurement of spectrum analysis.

The quantum measurement method of harmonic analysis is actually demonstrated based on the demonstration experiment of differential measurement of non-sinusoidal periodic signals of step waves.

The measured non-sinusoidal periodic signal is provided by a signal source, the signal and a quantum step wave signal (a general step signal is output by a DAC in a demonstration experiment) enter an analog-to-digital converter (ADC) for differential sampling, a sampling value is added with known step values of the quantum step wave signal (the step values are obtained by ADC measurement in the demonstration experiment), then classic discrete Fourier transform of sectional sampling is carried out, and the result is restored through a related inverse matrix to obtain the Fourier coefficient of each subharmonic of the measured signal.

Here, it is to be solved first from which the step data of the step wave comes, which involves the problem of alignment of the two waveforms. In principle, the step data of the step wave should follow the sampling data of the measurement signal. Specifically, the method comprises the following steps.

The measurement signal is sampled by the ADC. If N groups of samples are sampled in one period according to the description of the loss due to the time regularity of the present invention, each group of M sample data has a sampling interval represented by formula (6), the step value of the nth step should be taken as the sample data in the middle of the nth group of measurement signal samples, that is:

z_n＝y(nMh+Mh/2) (7)

The alignment of the two signal waveforms is shown in fig. 5. This places the intersection of the two waveforms in the middle of each group, and when data on both sides of each group is discarded, the smaller differential value is in the middle, which is required for differential measurements.

The parameters of the demonstration experiment are as follows, the step wave frequency is 1.0416kHz, 20 steps are adopted, and the width of each step is 48 mus; the frequency component setting of the non-sinusoidal periodic signal is the same as that of table 1, and the fundamental frequency is also 1.0416 kHz; the sampling frequency is 1MHz, so there are 48 samples M per step (or no group), 960 samples per cycle; segmented sampling selection (12,25, 11); the synchronous signal is taken from a non-sinusoidal periodic signal source, and the DAC and the ADC are controlled to synchronously operate.

The ADC has two input ports A and B, and step waves and non-sinusoidal periodic signals are respectively connected to the input ports A and B.

The measurements are first made in modes a & B, i.e. two waveforms are measured separately. The step value is obtained from the sampling data of the step wave, the frequency spectrum of the measuring signal is obtained from the sampling data of the non-sinusoidal periodic signal through the common classical discrete Fourier transform, namely, the data in one period are all involved in calculation without discarding the data and without the help of an inverse matrix, the result is used as the calculation reference of the following error, and the obtained error is the comparison between the invention and the common classical discrete Fourier transform.

And then, measuring in a mode A-B to obtain a differential sampling value, calculating according to the classical discrete Fourier transform of segmented sampling to obtain an intermediate result of a signal frequency spectrum, and then, recovering through an inverse matrix to obtain a final result of the frequency spectrum.

To overcome the Common Mode Rejection Ratio (CMRR) present in differential measurements, and the difference between the two channels, two handshakes were connected to input ports a and B in the experiment and multiple measurements were made.

Table 3 shows the experimental results, where the error is the difference between the final result of the present invention and the typical result of the classical discrete fourier transform, and the result can be regarded as the relative value of the error since the maximum amplitude of the measurement signal is close to 1V.

TABLE 3

When the frequency f_i/f₁At 20,40,60, large errors often occur, at f_i/f₁When the error is 10,30, or 50, a large error may occur. These errors are not included in the table. Preliminary experiments show that the error is within +/-40 muV/V under the two segmented sampling modes in the table.

The demonstration experiment shows that the error reaches 10^-6Order of magnitude, much larger than simulation result 10 of application example 1^-9Magnitude. This is in the experimentIs caused by noise, typically at 10^-5Magnitude, average effect of classical discrete Fourier transform makes the result in table 10^-6The magnitude is reasonable. It is also observed that in the case of N-20M-48, (12,25,11), the error is up to ± 40.0 μ V/V, since the classical discrete fourier transform of segmented sampling can be roughly understood as the process of knowing the whole from the part, and similar to extrapolation, the presented calculation coefficients are often larger than 1, which is shown in the above-mentioned inverse matrix. From such knowledge, we can increase the sampling utilization, i.e. the ratio of part to whole, with the goal of reducing such errors.

For this purpose, a further segmented sample is selected, whose pattern N is 20M 100, (15,71,14), where s is 15, t is 85, and s + t is 100M, where the sample utilization is (71/100) and is greater than (25/48) of the previous pattern. The experimental results show that the error of most frequency points in the mode is within +/-4.0 muV/V and is obviously smaller than that in the former mode.

It was also observed in the demonstration experiments that the frequency f_i/f₁When the frequency f is 20,40 or 60, a large error often occurs, and the frequency f is_i/f₁In the case of 10,30 and 50, large errors sometimes occur, and preliminary experiments show that the errors are up to ± 40 μ V/V in the two piecewise sampling modes. The reason for this error is due to the frequency f_i/f₁20,40,60 relates to the number of steps (or groups) N-20. If similar noise exists on each step, errors will occur at these frequency points; as to f_i/f₁The situation is generally similar when the speed is 10,30 and 50. However, the contribution of these noise distributions to other frequency points will reduce the error due to the cancellation effect.

In practical measurements, such errors can be overcome by changing the number of segments N.

In the quantum measurement of harmonic analysis, the step wave generated by the DAC in the demonstration experiment is changed into direct input of programmable quantum voltage, the ADC does not need to perform sampling measurement of modes A and B, and the final result is uncertainty instead of error, wherein the uncertainty data and the level of the quantum voltage, the level of the ADC, the measurement method and the measurement method are related and need to be obtained through specific analysis and evaluation.

In summary, the invention expands the signal spectrum analysis method to a new range, and has lower computation amount and higher accuracy.

It will be appreciated by persons skilled in the art that the above description of embodiments of the invention is intended only to illustrate the benefits of embodiments of the invention and is not intended to limit embodiments of the invention to any examples given.

According to an embodiment of the present invention, there is provided a system for analyzing a signal spectrum when regularity of partially sampled data is missing, including: a memory storing computer executable instructions and partially missing signal sample data; a processor executing computer executable instructions in the memory to perform the steps of: for the measurement signals with part of sampling data lacking regularity, adopting discrete Fourier transform operation in a segmented sampling mode to obtain an intermediate result of the frequency spectrum of the measurement signals; calculating a corresponding influence matrix according to a rule presented by the orthogonality of the trigonometric function under the condition of missing data, and further obtaining a plurality of reduced order matrixes; calculating an inverse matrix of the reduced order matrix; the intermediate result is converted into final spectral data based on the inverse matrix.

The invention expands the signal spectrum analysis method to a new range, and has lower computation amount and higher accuracy.

Having described embodiments of the present invention, the foregoing description is intended to be exemplary, not exhaustive, and not limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments.

Claims

1. A method for analyzing a signal spectrum in the absence of regularity in partially sampled data, comprising:

for the measurement signal with partial sampling data regularity missing, adopting discrete Fourier transform operation in a segmented sampling mode to obtain an intermediate result of the frequency spectrum of the measurement signal;

calculating a corresponding influence matrix according to a rule presented by the orthogonality of the trigonometric function under the condition of missing data, and further obtaining a plurality of reduced order matrixes;

calculating an inverse matrix of the reduced order matrix;

converting the intermediate result into final spectral data based on the inverse matrix;

wherein the influence matrix is:

AA (i, j) is an element of a cosine and cosine interaction matrix AA, BB (i, j) is an element of a sine and sine interaction matrix BB, AB (i, j) is an element of a cosine and sine interaction matrix AB, N is the total number of uniform grouping of measurement signals in a period, N is a group mark number of the measurement signals, M is a sampling data mark number of a middle interval in each group of the measurement signals, [0, s-1] and [ t +1, M-1] are missing data mark ranges, and [ s, t ] is a reserved data mark range.

2. The method for analyzing a signal spectrum when the regularity of the partially sampled data is missing according to claim 1, wherein the measurement signal when the regularity of the partially sampled data is missing is: equally spaced deletions occurred and the same number of measurement signals were missing.

3. The method for analyzing a signal spectrum when the regularity of the partially sampled data is missing according to claim 1, wherein the discrete fourier transform operation in the segmented sampling method is:

wherein the content of the first and second substances,

as an intermediate result, a_iAnd b_iCosine coefficient and sine coefficient of the ith harmonic, y_n,mAnd the sampling data obtained for the measurement signals, h is the sampling interval, and M is the total number of the sampling data of the equal interval in each group of the measurement signals.

4. The method for signal spectrum analysis when the regularity of the partially sampled data is missing according to claim 1, wherein when t + s is M, all elements of the impact matrix AB are zero, and the matrix AA is decomposed into three types of reduced order matrices: a. the^k，A^0.5NAnd A and^Nthe impact matrix BB is decomposed into three classes of reduced order matrices: b is^k，B^0.5NAnd B^NAnd M is the total number of equally spaced sampled data in each set of measurement signals.

5. The method for analyzing signal spectrum when the regularity of the partial sampling data is missing according to claim 1, wherein the cosine result of the final spectrum data is:

wherein, a_kIs a frequency of kf₁Cosine coefficient of the spectral end result of (A)^k)^-1,(A^0.5N)^-1，(A^N)^-1Is the inverse of the three reduced order matrices of the matrix AA, N being the total number of uniform groups of measurement signals in a period, f₁Is the frequency of the fundamental wave and is,

an intermediate result.

6. The method for signal spectrum analysis when the regularity of the partial sampling data is missing according to claim 1, wherein the sinusoidal result of the final spectrum data is:

wherein, b_kIs a frequency of kf₁(ii) the sine coefficient of the spectral end result of (B)^k)^-1,(B^0.5N)^-1，(B^N)^-1Is the inverse of the three reduced-order matrices of the matrix BB, N is the total number of uniform groups of measurement signals in one period, f₁Is the frequency of the fundamental wave and is,

an intermediate result.

7. The method for analyzing a signal spectrum when regularity of the partially sampled data is missing according to any one of claims 1 to 6, which is applied to quantum measurement of spectrum analysis.

8. A system for analyzing a spectrum of a signal in the absence of regularity in a portion of the sampled data, the system comprising:

a memory storing computer executable instructions and partially missing signal sample data;

a processor executing computer executable instructions in the memory to perform the steps of:

for a measuring signal with part of sampling data lacking regularity, performing classical discrete Fourier transform operation in a segmented sampling mode to obtain an intermediate result of a frequency spectrum of the measuring signal;

calculating an inverse matrix of the reduced order matrix;

wherein the influence matrix is:

9. The system for signal spectrum analysis when the regularity of the partially sampled data is missing according to claim 8, wherein the measurement signal when the regularity of the partially sampled data is missing is: equally spaced deletions occurred and the same number of measurement signals were missing.