CN107766293A - Signal spectral analysis method and system when fractional-sample data rule lacks - Google Patents
Signal spectral analysis method and system when fractional-sample data rule lacks Download PDFInfo
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Abstract
Disclose signal spectral analysis method and system during a kind of fractional-sample data rule missing.This method can include：For the measurement signal of fractional-sample data rule missing, using the Discrete Fourier transform operation of block sampling mode, the intermediate result of acquisition measurement signal frequency spectrum；The rule presented from orthogonality of trigonometric function in the case of missing data, influence matrix corresponding to calculating, and then obtain multiple degree reduction matrixes；Calculate the inverse matrix of degree reduction matrix；Based on inverse matrix, intermediate result is converted into final frequency spectrum data.Signal spectral analysis method is expanded to new scope by the present invention, has relatively low operand and the higher degree of accuracy.
Description
Technical field
The present invention relates to electromagnetic measurement, Fundamental Theory of Electrical Engineering, field of signal processing, more particularly, to a kind of fractional-sample number
Signal spectral analysis method and system when being lacked according to systematicness.
Background technology
Classical discrete fourier transform method (DFT) has a wide range of applications.The sampled data of measurement signal is carried out from
Fourier transform is dissipated, then can obtain the frequency spectrum of signal, i.e., the cosine coefficient and sinusoidal coefficients of each frequency component.Generally sampling is
Interval, the condition required for DFT is whole samplings in a cycle.But for various reasons, sampling
Data often produce missing.Wherein important one kind, belong to the missing of time rule.This missing is probably derived from artificial
Processing, such as delete some data intentionally to overcome the influence of transient process in ladder wave measurement, deposited in these data
In transient process, it is impossible to accurately reflect original signal, actual conditions can be preferably reflected after deletion；It may also derive from non-
Artificial process, such as loss of the signal during (or communication) is transmitted, this lose is often random, it is likely that depositing
In the situation of systematicness missing, or by processing, turn into the situation that systematicness lacks.
Due to shortage of data, it is impossible to meet the requirement of common classical discrete fourier transform method, tend not to carry out
The calculating of cosine coefficient and sinusoidal coefficients.A kind of therefore, it is necessary to signal frequency when developing fractional-sample data rule missing
Spectral analysis method and system.
The information for being disclosed in background of invention part is merely intended to deepen the reason of the general background technology to the present invention
Solution, and be not construed as recognizing or imply known to those skilled in the art existing of the information structure in any form
Technology.
The content of the invention
The present invention proposes signal spectral analysis method and system during a kind of fractional-sample data rule missing, will believe
Number spectrum analysis is expanded to new scope, has relatively low operand and the higher degree of accuracy.
A kind of according to an aspect of the invention, it is proposed that signal spectral analysis side during fractional-sample data rule missing
Method.Methods described can include：For fractional-sample data rule missing measurement signal, using block sampling mode from
Fourier transformation computation is dissipated, obtains the intermediate result of measurement signal frequency spectrum；From orthogonality of trigonometric function in missing data situation
The rule of lower presentation, influence matrix corresponding to calculating, and then obtain multiple degree reduction matrixes；Calculate the inverse matrix of degree reduction matrix；Base
In inverse matrix, intermediate result is converted into final frequency spectrum data.
Preferably, the measurement signal of fractional-sample data rule missing is：Appearance lacks and lacks quantity phase at equal intervals
Same measurement signal.
Preferably, the Discrete Fourier transform operation of the block sampling mode is：
Wherein,For intermediate result, aiAnd biThe respectively cosine coefficient and sinusoidal coefficients of ith harmonic wave, yn,mFor
The sampled data that measurement signal obtains, h are the sampling interval, and N is the sum of measurement signal even group-division in a cycle, and n is
The deck label of measurement signal, m are the sampled data label of every group of measurement signal equal intervals, and [0, s-1] and [t+1, M-1] are scarce
Data label range is lost, [s, t] is retention data label range, and M is the complete of the sampled data of every group of measurement signal equal intervals
Portion's quantity.
Preferably, influence matrix is：
Wherein, aa (i, j) is the element of cosine and cosine interaction matrix AA, and bb (i, j) is sinusoidal mutual with sine
Acting matrix BB element, ab (i, j) are the elements of cosine and sinusoidal interaction matrix AB.
Preferably, as t+s=M, influence matrix AB all elements are zero, and matrix A A is decomposed into three class depression of order squares
Battle array：Ak, A0.5N, and AN, influence matrix BB is decomposed into three class degree reduction matrixes：Bk, B0.5N, and BN。
Preferably, the cosine result of the final frequency spectrum data is：
Wherein, akIt is that frequency is kf1Frequency spectrum final result cosine coefficient, (Ak)-1,(A0.5N)-1, (AN)-1It is matrix A A
Three price reduction inverse of a matrix matrixes.
Preferably, the sinusoidal result of the final frequency spectrum data is：
Wherein, bkIt is that frequency is kf1Frequency spectrum final result sinusoidal coefficients, (Bk)-1,(B0.5N)-1, (BN)-1It is matrix B B
Three price reduction inverse of a matrix matrixes.
Preferably, signal spectral analysis method when fractional-sample data rule lacks is applied to the quantum of spectrum analysis
In measurement.
A kind of according to another aspect of the invention, it is proposed that signal spectral analysis during fractional-sample data rule missing
System, it can include：Memory, it is stored with computer executable instructions, and the signal sample data of excalation；Processing
Device, the computer executable instructions in processor run memory, perform following steps：Lacked for fractional-sample data rule
The measurement signal of mistake, classical Discrete Fourier transform operation is carried out using block sampling mode, obtained in measurement signal frequency spectrum
Between result；The rule presented from orthogonality of trigonometric function in the case of missing data, influence matrix corresponding to calculating, and then obtain
Obtain multiple degree reduction matrixes；Calculate the inverse matrix of degree reduction matrix；Based on inverse matrix, intermediate result is converted into final frequency spectrum data.
Preferably, the measurement signal of fractional-sample data rule missing is：Appearance lacks and lacks quantity phase at equal intervals
Same measurement signal.
Methods and apparatus of the present invention has other characteristics and advantage, and these characteristics and advantage are attached from what is be incorporated herein
It will be apparent in figure and subsequent embodiment, or by the accompanying drawing being incorporated herein and subsequent specific reality
Apply in mode and stated in detail, these the drawings and specific embodiments are provided commonly for explaining the certain principles of the present invention.
Brief description of the drawings
Exemplary embodiment of the present is described in more detail in conjunction with the accompanying drawings, of the invention is above-mentioned and other
Purpose, feature and advantage will be apparent, wherein, in exemplary embodiments of the present invention, identical reference number is usual
Represent same parts.
Fig. 1 shows the step of signal spectral analysis method when being lacked according to the fractional-sample data rule of the present invention
Flow chart.
Fig. 2 shows the step of signal spectral analysis method when being lacked according to the fractional-sample data rule of the present invention
Explanatory diagram.
Fig. 3 a, Fig. 3 b and Fig. 3 c respectively illustrate measurement signal curve according to an embodiment of the invention, all adopted
Sample data, the schematic diagram for lacking post-sampling data.
Fig. 4 shows the schematic diagram of staircase waveform aliasing effect according to an embodiment of the invention.
Fig. 5 shows the difference measurement of the non-sine periodic signal according to an embodiment of the invention based on staircase waveform
In, the alignment schematic diagram of two signals.
Embodiment
The present invention is more fully described below with reference to accompanying drawings.Although showing the preferred embodiments of the present invention in accompanying drawing,
However, it is to be appreciated that the present invention is may be realized in various forms without should be limited by embodiments set forth here.Conversely, there is provided
These embodiments are in order that the present invention is more thorough and complete, and can will fully convey the scope of the invention to ability
The technical staff in domain.
Fig. 1 shows the step of signal spectral analysis method when being lacked according to the fractional-sample data rule of the present invention
Flow chart.
Fig. 2 shows the step of signal spectral analysis method when being lacked according to the fractional-sample data rule of the present invention
Explanatory diagram.
In this embodiment, signal spectral analysis method when being lacked according to the fractional-sample data rule of the present invention can
With including：
Step 101, for the measurement signal of fractional-sample data rule missing, using discrete Fu of block sampling mode
Vertical leaf transformation computing, obtain the intermediate result of measurement signal frequency spectrum；
Step 102, the rule presented from orthogonality of trigonometric function in the case of missing data, corresponding influence square is calculated
Battle array, and then obtain multiple degree reduction matrixes；
Step 103, the inverse matrix of degree reduction matrix is calculated；
Step 104, based on inverse matrix, intermediate result is converted into final frequency spectrum data.
In one example, the measurement signal of fractional-sample data rule missing is：Appearance is lacked and lacked at equal intervals
Quantity identical measurement signal.
In one example, the Discrete Fourier transform operation of block sampling mode is：
Wherein,For the PRELIMINARY RESULTS of signal spectrum, aiAnd biThe respectively cosine coefficient and sine of ith harmonic wave
Coefficient, yn,mThe sampled data obtained for measurement signal, h are the sampling interval, and N is measurement signal even group-division in a cycle
Sum, n is the deck label of measurement signal, and m is the sampled data label of every group of measurement signal equal intervals, [0, s-1] and [t+
1, M-1] it is missing data label range, [s, t] is retention data label range, and M is adopting for every group of measurement signal equal intervals
The entire quantity of sample data.
In one example, influence matrix is：
Wherein, aa (i, j) is the element of cosine and cosine interaction matrix AA, and bb (i, j) is sinusoidal mutual with sine
Acting matrix BB element, ab (i, j) are the elements of cosine and sinusoidal interaction matrix AB.
In one example, as t+s=M, influence matrix AB all elements are zero, and matrix A A is decomposed into three classes drop
Rank matrix：Ak, A0.5N, and AN, influence matrix BB is decomposed into three class degree reduction matrixes：Bk, B0.5N, and BN。
In one example, the cosine result of final frequency spectrum data is：
Wherein, akIt is that frequency is kf1Frequency spectrum final result cosine coefficient, (Ak)-1,(A0.5N)-1, (AN)-1It is matrix A A
Three price reduction inverse of a matrix matrixes.
In one example, the sinusoidal result of final frequency spectrum data is：
Wherein, bkIt is that frequency is kf1Frequency spectrum final result sinusoidal coefficients, (Bk)-1,(B0.5N)-1, (BN)-1It is matrix B B
Three price reduction inverse of a matrix matrixes.
Specifically, the measurement signal based on fractional-sample data rule missing, using discrete Fu of block sampling mode
Vertical leaf transformation computing, obtain the intermediate result of the frequency spectrum of measurement signal；The systematicness missing of this data is probably derived from artificial
Processing, such as delete some data intentionally to overcome the influence of transient process in ladder wave measurement, deposited in these data
In transient process, it is impossible to accurately reflect original signal, actual conditions can be preferably reflected after deletion；It may also derive from non-
Artificial process, such as loss of the signal during (or communication) is transmitted, although this lose is often random, having can
The systematicness missing of description can be present, or by converting, turn into the situation of systematicness.Fractional-sample data rule
Missing can be further depicted as, and the sampled data of a cycle is divided into N groups, deck label n=0,1,2 ..., N-1；Every group of tool
There are M equally spaced sampled datas, every group of data are marked as m=0,1,2 ..., M-1；Identical missing is produced in every group of data,
The data of missing are marked as m=0,1,2 ..., s-1 and m=t+1, t+2 ..., and M-1, remaining data label is from s to t, i.e. m=
S, s+1 ..., t, shared (t-s+1) is individual, typically there is 0 ＜ s ＜ 0.5M ＜ t ＜ M-1.In order to describe conveniently, it is referred to as segmentation and adopts
Sample, (s, t-s+1, M-1-t) is designated as, includes DFT and only middle remaining (t-s+1) individual sampled data is entered
Capable implication.In the foregoing description, missing in the case of missing is not or not both sides, is not difficult to pass through positioned at the both sides of every group of data
The starting point in cycle is reselected, the both sides that missing is arranged into one group of data are gone, therefore, fractional-sample data rule missing
Measurement signal there is wide applicability.
Measurement signal is：
Wherein, y is measurement signal, aiAnd biThe respectively cosine coefficient and sinusoidal coefficients of ith harmonic wave, f1It is fundamental wave frequency
Rate, ω are circular frequency, use block sampling mode to carry out classical Discrete Fourier transform operation as formula (2), wherein, between sampling
Formula (6) is divided into, and then obtains intermediate result,
H=2 π/(NM) (6).
The rule presented from orthogonality of trigonometric function in the case of missing data, influence matrix corresponding to calculating are formula
(3).As t+s=M, influence matrix AB all elements are zero；As t+s=M, influence matrix AA is decomposed into three class depression of orders
Matrix：Ak, A0.5N, and AN；As t+s=M, influence matrix BB is decomposed into three class degree reduction matrixes：Bk, B0.5N, and BN。
Fig. 4 shows the schematic diagram of staircase waveform aliasing effect according to an embodiment of the invention.
Wherein, degree reduction matrix Ak(BkEqually) be original matrix AA (BB) a part, be that line label is k, N- in original matrix
K, N+k, 2N-k, 2N+k ... and row label is also k, N-k, N+k, 2N-k, 2N+k ... element composition, wherein final line
Label (row label) is by requiring that the highest order of analysis determines.If last line label (row label) is designated as wN-k (or wN+
K), 2 ω≤(t-s+1) ＜ M should typically be met.Degree reduction matrix Ak(Bk) diagonal element be 1.Work as k=1,2 ..., 0.During 5N-1,
All Ak(BkEqually) there is identical form, in Fig. 4, these matrixes correspond to set out from k=1,2 ..., 0.5N-1 points
Dotted line.
Wherein, degree reduction matrix A0.5N(B0.5NEqually) be original matrix AA (BB) a part, be that line label is in original matrix
0.5N, 1.5N ... and row label is also 0.5N, 1.5N ... element composition, the same depression of order of requirement of final line label (row label)
Matrix Ak, in Fig. 4, this matrix corresponds to from point 0.5N, positioned at the line (not shown) of rightmost.
Wherein, degree reduction matrix AN(BNEqually) be original matrix AA (BB) a part, be that line label is N in original matrix,
2N ... and row label is also N, 2N ... element composition, the requirement of final line label (row label) is the same as degree reduction matrix Ak, in Fig. 4
In, this matrix corresponded to from 0 (the N)s, positioned at leftmost line (not shown) of point.
Respective inverse matrix is calculated by each degree reduction matrix：(Ak)-1, (A0.5N)-1, and (AN)-1；(Bk)-1, (B0.5N)-1, and
(BN)-1, those skilled in the art can calculate inverse matrix as the case may be.
Based on inverse matrix, intermediate result is converted into final frequency spectrum data.By taking cosine coefficient as an example, first by intermediate result
Press relation of plane and be divided into three class column vectors：And then obtain the cosine knot of final frequency spectrum data
Fruit is formula (4), and sinusoidal result is formula (5).
Signal spectral analysis method is expanded to new scope by this method, has relatively low operand and higher accurate
Degree.
For ease of understanding the scheme of the embodiment of the present invention and its effect, two concrete application examples given below.This area
It should be understood to the one skilled in the art that the example, only for the purposes of understanding the present invention, its any detail is not intended to be limited in any way
The system present invention.
Using example 1
Fig. 3 a, Fig. 3 b and Fig. 3 c respectively illustrate measurement signal curve according to an embodiment of the invention, all adopted
Sample data, the schematic diagram for lacking post-sampling data.
Table 1 gives the arranges value of a primary signal, including the amplitude of each frequency component and phase angle.The shape of its curve
Shape is as shown in Figure 3 a.From Fig. 3 a, for curve within ± 1V, this is easy to subsequent calculations error, and obtained absolute error is right
For 1V, therefore relative error can also be considered as.
Table 1
| Primary signal arranges value | 1 | 3 | 4 | 15 | 24 |
| Amplitude | 0.800 | -0.320 | 0.200 | -0.045 | 0.023 |
| Phase angle | -π/5 | π/3 | 0 | -π/2.3 | π/10 |
This signal is done into uniform sampling, a cycle branch 960, is divided into 20 groups, every group of 48 samplings；Open in each group
12 to begin, and last 11 data are deleted and not had to, and middle 25 data retain, and do subsequent arithmetic.Each cycle is participated in
The sampling of computing has 500.Therefore 250 subharmonic can be at most analyzed, agreement highest harmonic wave is 60 times.
N=20, M=48, block sampling are designated as (12,25,11), s=12, t=36, meet s+t=M condition.According to
Formula (2) carries out being segmented DFT computings to sampling.The intermediate result of signal spectrum is obtained, as shown in table 2.
Fig. 4 shows the schematic diagram of staircase waveform aliasing effect according to an embodiment of the invention.When the frequency of analysis
During less than 0.5N, classical Fourier transformation can obtain accurate result without difficulty, when the frequency of analysis is more than or equal to
0.5N and when being less than 0.5N (t-s+1), should use the present invention to obtain accurate result.
Then influence matrix is calculated according to formula (3), they are：
AkIt is 6 × 6 matrixes, row (column) is marked as (k, 20-k, 20+k, 40-k, 40+k, 60-k), matrix
A10It is 3 × 3 matrixes, row (column) is marked as (10,30,50), matrix
A20It is 3 × 3 matrixes, row (column) is marked as (20,40,60), matrix
BkFor
B10For
B20For
Their inverse matrix is respectively：
(Ak)-1For
(A10)-1For
(A20)-1For
(Bk)-1For
(B10)-1For
(B20)-1For
Finally, using these inverse matrixs, recovery processing is done to the intermediate result obtained in the first step, obtains final spectrum number
According to as shown in table 2.Two row errors of rightmost are the differences of final frequency spectrum data and original arranges value in table.As before, due to measurement
Signal maximum amplitude is close to 1V, so the result can be considered as relative value.
Table 2
As seen from Table 2, the deviation of intermediate result and original arranges value is larger, and this is that block sampling carries out classical direct computation of DFT
The result of leaf transformation；But pass through after inverse matrix recovery, the difference of final result and arranges value is 10-9Magnitude, substantially count
Calculation error caused by the limited setting of the numerical digit of calculation machine in itself.(data are given to after decimal point 7 in table, but actual calculate does not have
Restricted numerical digit, so 10 can be obtained-9The error of magnitude).
From the principle, influence matrix of the invention is actually relevant with orthogonality of trigonometric function, block sampling
Deviation caused by classical discrete Fourier transform is exactly as caused by these influence matrixs.Its inverse matrix is then extensive by baseline results
Come again.Due to the systematicness of shortage of data in time, therefore as the basic function being related in classical discrete Fourier transform,
I.e. trigonometric function can directly write out, and in other words, this measurement pattern can design in advance, or determine afterwards
, therefore the present invention is with a wide range of applications.
Present embodiment shows that possessed ability of the present invention, compared with general classics discrete Fourier transform method
Compared with the case where sampled data lacks because of temporal regularity, when highest harmonic wave is primary demand as 60 times, it is necessary to ask
The influence matrix and its inverse matrix, workload of solution 120 × 120 are very huge.But using the present invention, it is only necessary to 26 × 6 matrixes,
The calculating of 43 × 3 matrixes and invert, compare under, amount of calculation is simultaneously uncomplicated, but the degree of accuracy obtained is very high.
Using example 2
In one example, signal spectral analysis method when fractional-sample data rule lacks is applied to spectrum analysis
Quantum measurement in.
The lecture experiment of the difference measurement of non-sine periodic signal of this example based on staircase waveform, actual presentation frequency analysis
Quantum measuring method.
The non-sine periodic signal of measurement is provided by signal source, the signal and quantum ladder ripple signal (in lecture experiment by
DAC exports in general stairstep signal) do difference sampling, sampled value and quantum ladder ripple signal into analog-digital converter (ADC)
Known step value is added (obtaining these step values by ADC measurements in lecture experiment), is then classical discrete Fu of block sampling
Vertical leaf transformation, its result are recovered by the inverse matrix of correlation, obtain the fourier coefficient of each harmonic of measurement signal.
Here what the step data for first having to solve staircase waveform come from, and this is related to the alignment issues of two waveforms.It is former
Then the step data of upper staircase waveform should follow the sampled data of measurement signal.It should specifically carry out as follows.
Measurement signal is sampled by ADC.If by description of the present invention to being lacked by temporal regularity, a cycle N groups
Sampling, every group of M sampled data, sampling interval should be taken as measurement signal and adopted by formula (6) expression, then the step value of the n-th step
That sampled data among sample n-th group, i.e.,：
zn=y (nMh+Mh/2) (7)
Fig. 5 shows the difference measurement of the non-sine periodic signal according to an embodiment of the invention based on staircase waveform
In, the alignment schematic diagram of two signals.
The alignment of two signal waveforms is as shown in Figure 5.So make the crosspoint of two waveforms among every group, when
When abandoning the data on every group of both sides, less difference value is positioned at centre, required for this is difference measurement.
The parameter of lecture experiment is as follows, and ladder wave frequency rate is 1.0416kHz, 20 steps, per the μ s of step width 48；It is anon-normal
The frequency component arranges value of string periodic signal is identical with table 1, and fundamental frequency is also 1.0416kHz；Sample frequency is 1MHz, because
This each step (or there be not group) has sampling M=48, and each cycle is sampled as 960；Block sampling selects (12,25,11)；Synchronous letter
Non-sine periodic signal source number is derived from, controls DAC and ADC synchronous operations.
ADC has two input ports A and B, and staircase waveform and non-sine periodic signal are respectively connected into input port A and B.
Measured first under Mo ShiA ＆B, i.e., measure two waveforms respectively.Step is obtained by the sampled data of staircase waveform
Value, by the sampled data of non-sine periodic signal, the frequency spectrum of measurement signal is obtained by common classical DFT,
Data i.e. in a cycle all participate in calculating, do not abandon the situation of data, it is not required that the help of inverse matrix, this result
Calculating as error below refers to, and resulting error is exactly of the invention to do ratio with common classical DFT
Compared with.
Then measured under Mode A-B, obtain difference sampled value, become according to the classical discrete Fourier of block sampling
Swap-in row calculates, and obtains the intermediate result of signal spectrum, then the recovery by inverse matrix, obtains the final result of frequency spectrum.
In order to overcome the difference between common-mode rejection ratio present in difference measurement (CMRR), and two passages, in experiment,
Two signal exchanges are connected to input port A and B, and do multiple measurement.
Table 3 illustrates the result of experiment, and error is the final result of the present invention and the common discrete Fourier of classics in table
The difference of leaf transformation result, because measurement signal maximum amplitude is close to 1V, so the result can be considered as error relative value.
Table 3
As frequency fi/f1When=20,40,60, often there is larger error, in fi/f1When=10,30,50, sometimes
Larger error occurs.These errors are not included in table.Preliminary experiment shows, two in table block sampling pattern
Under, error is within ± 40 μ V/V.
Lecture experiment shows that error reaches 10-6Magnitude, much larger than the analog result 10 of application example 1-9Magnitude.This is real
Caused by the noise tested, this noise is typically 10-5Magnitude, the average effect of classical DFT make result in table
Reach 10-6Magnitude is rational.See simultaneously, in the case of N=20M=48, (12,25,11), error is up to ± 40.0
μ V/V, this is due to that the classical DFT of block sampling can be interpreted as roughly from the process for partly knowing entirety,
Similar to extrapolation, commonly greater than 1, this has been showed the design factor of presentation in above-mentioned inverse matrix.From such understanding,
We can increase sampling utilization rate, i.e. part and the ratio of entirety, reach the purpose for reducing this error.
Another block sampling is have selected for this, its pattern N=20M=100, (15,71,14), wherein s=15, t=
85, meet s+t=100=M condition, it is (71/100) now to sample utilization rate, more than (25/48) of former pattern.It is real
Test result to show, under this pattern, error is within ± 4.0 μ V/V on most of Frequency point, hence it is evident that smaller than former pattern.
It is additionally observed that in lecture experiment, frequency fi/f1When=20,40,60, often occur larger error, and frequency
fi/f1When=10,30,50, it sometimes appear that larger error, preliminary experiment shows, in above two block sampling pattern
Under, this error is up to ± 40 μ V/V.The reason for this error is due to frequency fi/f1=20,40,60 with step number (or point
Group number) N=20 is relevant.If similar noise be present on each step, it will produce error on these Frequency points；As for
fi/f1When=10,30,50, situation is substantially similar.But contribution of these noise profiles to other Frequency points, will be due to offsetting
Effect and error is diminished.
In actual measurement, this kind of error can be overcome by changing segments N.
In the quantum measurement of frequency analysis, in lecture experiment DAC produce that staircase waveform this link is changed to directly input can
Quantum voltage is programmed, for ADC also without the sampled measurements for being Mo ShiA ＆B, final result should be uncertainty, rather than error,
The level of uncertainty data and quantum voltage, the level with ADC are relevant with the method for measurement to be assessed, it is necessary to make a concrete analysis of
Go out.
In summary, signal spectral analysis method is expanded to new scope by the present invention, have relatively low operand and compared with
The high degree of accuracy.
It will be understood by those skilled in the art that the purpose of the description to embodiments of the invention is only for exemplarily saying above
The beneficial effect of bright embodiments of the invention, it is not intended to limit embodiments of the invention to given any example.
According to an embodiment of the invention, there is provided signal spectral analysis system during a kind of fractional-sample data rule missing
System, can include：Memory, it is stored with computer executable instructions, and the signal sample data of excalation；Processor,
Computer executable instructions in processor run memory, perform following steps：Lacked for fractional-sample data rule
Measurement signal, using the Discrete Fourier transform operation of block sampling mode, obtain the intermediate result of measurement signal frequency spectrum；From
The rule that orthogonality of trigonometric function is presented in the case of missing data, influence matrix corresponding to calculating, and then obtain multiple drops
Rank matrix；Calculate the inverse matrix of degree reduction matrix；Based on inverse matrix, intermediate result is converted into final frequency spectrum data.
In one example, the measurement signal of fractional-sample data rule missing is：Appearance is lacked and lacked at equal intervals
Quantity identical measurement signal.
Signal spectral analysis method is expanded to new scope by the present invention, has relatively low operand and higher accurate
Degree.
It will be understood by those skilled in the art that the purpose of the description to embodiments of the invention is only for exemplarily saying above
The beneficial effect of bright embodiments of the invention, it is not intended to limit embodiments of the invention to given any example.
It is described above various embodiments of the present invention, described above is exemplary, and non-exclusive, and
It is not limited to disclosed each embodiment.In the case of without departing from the scope and spirit of illustrated each embodiment, for this skill
Many modifications and changes will be apparent from for the those of ordinary skill in art field.
Claims (10)
1. a kind of signal spectral analysis method during fractional-sample data rule missing, including：
For the measurement signal of fractional-sample data rule missing, transported using the DFT of block sampling mode
Calculate, obtain the intermediate result of the measurement signal frequency spectrum；
The rule presented from orthogonality of trigonometric function in the case of missing data, influence matrix corresponding to calculating, and then obtain
Multiple degree reduction matrixes；
Calculate the inverse matrix of the degree reduction matrix；
Based on the inverse matrix, the intermediate result is converted into final frequency spectrum data.
2. signal spectral analysis method during fractional-sample data rule missing according to claim 1, wherein, it is described
Fractional-sample data rule missing measurement signal be：Appearance lacks and lacks quantity identical measurement signal at equal intervals.
3. signal spectral analysis method during fractional-sample data rule missing according to claim 1, wherein, segmentation
The Discrete Fourier transform operation of sample mode is：
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Wherein,For intermediate result, aiAnd biThe respectively cosine coefficient and sinusoidal coefficients of ith harmonic wave, yn,mBelieve for measurement
Number obtained sampled data, h are the sampling interval, and N is the sum of measurement signal even group-division in a cycle, and n believes for measurement
Number deck label, m is the sampled data label of every group of measurement signal equal intervals, and [0, s-1] and [t+1, M-1] are missing data
Label range, [s, t] are retention data label range, and M is the entire quantity of the sampled data of every group of measurement signal equal intervals.
4. signal spectral analysis method during fractional-sample data rule missing according to claim 3, wherein, it is described
Influence matrix is：
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Wherein, aa (i, j) is the element of cosine and cosine interaction matrix AA, and bb (i, j) is sinusoidal and sinusoidal interaction
Matrix B B element, ab (i, j) are the elements of cosine and sinusoidal interaction matrix AB.
5. signal spectral analysis method during fractional-sample data rule missing according to claim 4, wherein, work as t+
During s=M, influence matrix AB all elements are zero, and matrix A A is decomposed into three class degree reduction matrixes：Ak, A0.5N, and AN, influence square
Battle array BB is decomposed into three class degree reduction matrixes：Bk, B0.5N, and BN。
6. signal spectral analysis method during fractional-sample data rule missing according to claim 1, wherein, it is described
Finally the cosine result of frequency spectrum data is：
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Individual price reduction inverse of a matrix matrix.
7. signal spectral analysis method during fractional-sample data rule missing according to claim 1, wherein, it is described
Finally the sinusoidal result of frequency spectrum data is：
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<mtd>
<mrow>
<msub>
<msup>
<mi>b</mi>
<mi>P</mi>
</msup>
<mrow>
<mn>0.5</mn>
<mi>N</mi>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<msup>
<mi>b</mi>
<mi>P</mi>
</msup>
<mrow>
<mn>1.5</mn>
<mi>N</mi>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>...</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mfenced open = "|" close = "|">
<mtable>
<mtr>
<mtd>
<msub>
<mi>b</mi>
<mi>N</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>b</mi>
<mrow>
<mn>2</mn>
<mi>N</mi>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>...</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>=</mo>
<msup>
<mrow>
<mo>(</mo>
<msup>
<mi>B</mi>
<mi>N</mi>
</msup>
<mo>)</mo>
</mrow>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msup>
<mfenced open = "|" close = "|">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<msup>
<mi>b</mi>
<mi>P</mi>
</msup>
<mi>N</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<msup>
<mi>b</mi>
<mi>P</mi>
</msup>
<mrow>
<mn>2</mn>
<mi>N</mi>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>...</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>5</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, bkIt is that frequency is kf1Frequency spectrum final result sinusoidal coefficients, (Bk)-1,(B0.5N)-1, (BN)-1It is the three of matrix B B
Individual price reduction inverse of a matrix matrix.
Signal spectral analysis method when 8. the fractional-sample data rule in claim 1-7 described in any one lacks,
Applied in the quantum measurement of spectrum analysis.
9. signal spectral analysis system during a kind of fractional-sample data rule missing, it is characterised in that the system includes：
Memory, it is stored with computer executable instructions, and the signal sample data of excalation；
Processor, the processor run the computer executable instructions in the memory, perform following steps：
For the measurement signal of fractional-sample data rule missing, classical discrete Fourier change is carried out using block sampling mode
Computing is changed, obtains the intermediate result of the measurement signal frequency spectrum；
The rule presented from orthogonality of trigonometric function in the case of missing data, influence matrix corresponding to calculating, and then obtain
Multiple degree reduction matrixes；
Calculate the inverse matrix of the degree reduction matrix；
Based on the inverse matrix, the intermediate result is converted into final frequency spectrum data.
10. signal spectral analysis system during fractional-sample data rule missing according to claim 9, wherein, institute
Stating the measurement signal that fractional-sample data rule lacks is：Appearance lacks and lacks quantity identical measurement signal at equal intervals.
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