CN104569586A - High-precision phase difference measuring method based on CRIO platform - Google Patents

Abstract

The invention discloses a high-precision phase difference measuring method based on a CRIO platform. For the method, a four-order Blackman-Harris window is selected to truncate a signal in a data analysis module, so that the frequency spectrum leakage is inhibited better, and the frequency spectrum discretization causes lower frequency resolution; a specific value correction method is introduced to correct the frequency spectrum to improve the frequency resolution; when a signal contains harmonic wave, the window function frequency spectrum energy of the selected our-order Blackman-Harris window is centralized into a main lobe; the interval between a fundamental wave and any harmonic component frequency in the signal is far greater than the width of the window function frequency spectrum main lobe, and the lowest frequency is far greater than a half of the main lobe width, so that the influence of the harmonic component and negative frequency component of the fundamental wave on the fundamental wave is extremely small, and can be ignored. According to the invention, the implementation is simple, the calculated amount is smaller, the precision is high, and higher harmonic and noise can be better inhibited.

Description

A kind of difference of the high-precision phase position based on CRIO platform meter method

Technical field

The present invention is a kind of high-precision phase position based on CRIO platform difference meter method.

Background technology

Compact RIO is a reconfigurable embedded Control and acquisition system, comprise built-in embedded controller, FPGA able to programme and small-sized, firm and hot swappable industry I/O module, help scientific research personnel to realize the self-definition design of measurement and control system, prototype and issue fast.In addition, it is by NI Lab VIEW figureshape programming tool accepts programming, utilizes the I/O function that Lab VIEW FPGA is basic, and user directly can access the imput output circuit of each I/O module of Compact RIO hardware.All I/O modules all comprise built-in interface (as bolt terminal, BNC or DSUB connector), signal condition, change-over circuit (as ADC or DAC), and the Isolated Shield that can match.This design makes the framework of low cost have opening, and user can have access to the hardware resource of bottom.Exactly because good antijamming capability, firm structure and stable performance, Compact RIO platform is widely used in engineering measurement and control area.

In electrical engineering application, have a lot of aspect to need to measure the phase differential relation with frequently between alternating voltage, current signal, and the measurement of phase differential is different from the measurement of traditional voltage, current signal or thing position, Temperature Quantity.First, phase signal depends in voltage, current signal, how to reject voltage, electric current, the impact of frequency change on phase difference measurement be an aspect very important in phase difference measurement; Secondly, phase differential is a comparative quantity, and the phase differential measured between two paths of signals not only needs to ensure that the frequency of two paths of signals is identical, and it is inconsistent and on measuring the impact caused to get rid of the other factors such as amplitude, harmonic wave, noise due to two paths of signals.

Propose the method for multiple phase difference measurement in recent years, be mainly divided into two kinds: the hard ware measure based on hardware circuit and the software measurement method based on alternating data acquisition process.Based in the measuring system of virtual instrument, nearly all function can realize by the method for software, conventional process side method masterhave: zero-crossing method, correlation method, Spectral Analysis Method etc.Zero crossing ratio juris is: determine two moment being all the homogenous frequency signal zero crossing of downtrending (or ascendant trend) respectively, calculate its mistiming, then calculate phase differential according to the time.Correlation method utilizes two with frequency sinusoidal signal at time delay τ ₌ ⁰time the cross-correlation function value principle that is directly proportional to the cosine value of its phase differential obtain phase differential.FFT Spectral Analysis Method asks phase differential, namely carries out spectrum analysis by discrete Fourier method to detected signal, thus obtains the phase-frequency characteristic of signal, then calculates the phase difference value of two signals at predominant frequency place.

In order to the measuring accuracy of these three kinds of algorithms most in use of com-parison and analysis, above-mentioned three kinds of algorithms are used following two signals to be carried out to the l-G simulation test of measurement two signal phase difference respectively:

$x_1\left(t\right)=\underset{k=1}{\overset{p}{\mathrm{\Σ}}}{A}_k\cos (2\mathrm{\πk}{f}_{k}t+{\mathrm{\α}}_k)+e_1\left(t\right)---\left(1\right)$

$x_2\left(t\right)=\underset{k=1}{\overset{p}{\mathrm{\Σ}}}{B}_k\cos (2\mathrm{\πk}{f}_{k}t+{\mathrm{\β}}_k)+e_2\left(t\right)---\left(2\right)$

If signal fundamental frequency f ₁=50Hz, two signal phase differences are 30 °.The each harmonic parameter of two signals in formula as table 1shown in:

Form 1 liang of signal harmonic parameter

Ignore the quantization error in data acquisition and other errors, if the sample frequency of data acquisition system (DAS) is 5000Hz, consider in the ideal case, conventional several algorithm measurement precision of phase differential of asking are all very high, therefore be not discussed at this, l-G simulation test mainly carries out in following 4 kinds of situations:

1) interference of harmonic wave is only considered;

2) consider the interference of noise and harmonic wave, adding in realistic model in harmonic wave situation whitely has noise to carry out test simulation again, and Signal-to-Noise is 60db;

3) consider the interference of harmonic wave and the fluctuation of frequency, signalization frequency jitter is to 50.3Hz;

4) consider harmonic wave and the interference of noise and the fluctuation of frequency, signal frequency fluctuates 50.3Hz, and Signal-to-Noise is 60db.

In above 4 kinds of situations, use zero-crossing method, correlation method respectively, FFT spectrum analysis test, the simulation result of algorithms of different measure phase difference as following table instituteshow, wherein

Phase difference measurement simulation result under form 2 algorithms of different

Can find out zero-crossing method and correlation method by harmonic influence very greatly by simulation result, precision is all lower; Simple FFT spectral analysis algorithm, can also keep higher precision when having harmonic wave and noise, but when frequency generation fluctuation causes non-integer-period sampled, measuring error just raises rapidly.

Because DFT algorithm requires very high to synchronized sampling, otherwise the spectral leakage of time domain brachymemma introducing and fence effect can make frequency analysis occur error.Domestic conventional windowed interpolation DFT algorithm is all by using different window functions and interpolation algorithm to revise the spectral line after DFT conversion, arithmetic accuracy can be improved to a certain extent, conventional window has Hanning window, Hamming, Blackman window, Blackman-Harris window, but there are following 2 deficiencies in it:

(1) the window function side lobe performance of signal brachymemma use is poor, effectively can not overcome spectral leakage;

(2) Discrete spectrum causes frequency resolution lower.

Summary of the invention

The present invention for the technical matters that solves for providing a kind of high-precision phase position based on CRIO platform difference meter method, solve problems of the prior art, it effectively can measure the phase differential of two-way voltage or current signal, its data analysis module can solve spectral leakage that the brachymemma of DFT algorithm time domain introduces and fence effect and spectrum analysis can be made to occur improving compared with the technical matters of big error and its 2 deficiencies that interpolation method exists: the window function side lobe performance that (1) signal brachymemma uses is poor, effectively can not overcome spectral leakage; (2) Discrete spectrum causes frequency resolution lower.

Technical solution problem of the present invention adopts following technical scheme:

Based on a high-precision phase position difference meter method for CRIO platform, the technical scheme following steps that it adopts:

The first step, data acquisition module comprises digital data acquisition module and analogue collection module, can gather voltage (electric current) signal and the digital quantity being converted to certain format also can gather SV message, FT in digital transformer substation ₃message.

Second step, the digital quantity of the set form that data collecting module collected is uploaded by data resolution module or SV message, FT ₃packet parsing is can for data analysis module digital quantity signal directly.

3rd step, the data analysis that data analysis module is uploaded data resolution module.Concrete point of following three aspects.

(1) use 4 rank Blackman-Harris window weightings to the digital quantity signal received, 4 rank B-H windows are defined as 4 reconvolutions of B-H window, can obtain its time-domain expression as follows:

w _4B-H(n)＝w _B-H(n)*w _B-H(n)*w _B-H(n)*w _B-H(n) (1)

Wherein $w_{B-H}\left(n\right)=a_0-a_1\cos \frac{2\mathrm{\πn}}{N}+a_2\cos \frac{4\mathrm{n\π}}{N}-a_3\cos \frac{6\mathrm{n\π}}{N},$ a ₀＝0.35875，a ₁＝0.48829，a ₂＝0.14128，a ₃＝0.01168。According to the 4 rank Blackman-Harris windows that formula (1) structure length is N, to signal x (n) windowing, obtain burst x ' (n) after windowing=x (n) w _4B-H(n);

(2) FFT frequency spectrum calculates;

If be respectively x (t), y (t) for two periodic signals of measure phase difference, for the sake of simplicity, first do not consider the harmonic component in signal, namely suppose that they are unifrequency periodic signal.Suppose that two signals obtained by Data Analysis link can be expressed as simultaneously

In formula: T is signal x ₁and x ₂cycle; A _1m, A _2mbe respectively x ₁, x ₂amplitude; be respectively x ₁, x ₂initial phase; T _sfor sampling interval.

Make X ₁k the real part of () is Re [X ₁(k)], imaginary part is Im [X ₁(k)], then by the X obtained that samples ₁k (), shared by the fundamental frequency in real system, component is maximum, and the amplitude of corresponding frequency spectrum is also maximum, therefore can search the sequence number k corresponding to maximum spectral line in frequency spectrum _m, obtaining frequency spectrum shared by first-harmonic is X ₁(k _m), its amplitude is A (k _m).

Then can ask and obtain first phase and be:

In like manner, another road signal X can be calculated ₂k the first phase of () is:

Survey phase differential and be:

(3) utilize ratiometric correction method to carry out phase correction, search kth _mtwo spectral lines about root spectral line, obtaining its amplitude is A (k _m-1) and A (k _m+ 1), then correction coefficient is Δ k:

$\mathrm{\&Delta;k}=\left\{\begin{array}{c}\frac{2A(k-1)-A\left(k\right)}{A(k-1)+A\left(k\right)},\frac{A(k-1)}{A(k+1)}>1\\ -\frac{2A(k+1)-A\left(k\right)}{A(k+1)+A\left(k\right)},\frac{A(k-1)}{A(k+1)}<1\end{array}\right.---\left(4\right)$

The corrected value that can solve each signal parameter according to correction coefficient is: phase correction amount fundamental phase after then correcting x can be calculated after the same method ₂fundamental phase k () is calibrated after

Two signal phase differences that finally can record through the correction of ratio revised law are:

Beneficial effect of the present invention is as follows:

4 rank Blackman-Harris windows are selected to carry out brachymemma process to signal in data analysis module of the present invention, the frequency domain distribution feature of 4 rank Blackman-Harris windows is a further reduction sidelobe level, and along with the increase of window exponent number, the rate of decay of secondary lobe increases, better inhibit spectrum leakage, Discrete spectrum causes frequency resolution lower, and introduces ratiometric correction method and correct to improve frequency resolution to frequency spectrum.The present invention is because haveing nothing to do with signal frequency in theory when carrying out phase difference measurements, therefore without the need to tracking measurement signal frequency and integer-period sampled to signal, impact by signal frequency jitter is less, effectively can make up FFT when power system frequency fluctuates among a small circle due to spectrum leakage that non-synchronous sampling causes and bring the measuring error of phase place.When containing harmonic wave in signal, the 4 rank Blackman-Harris window window function spectrum energies selected concentrate in main lobe, in signal, first-harmonic and the spaced far arbitrarily between frequencies of harmonic components are greater than the width of this window function frequency spectrum main lobe, low-limit frequency is much larger than the half of main lobe width, then first-harmonic is minimum, negligible by the impact of harmonic components and the negative frequency components of himself.The present invention realizes simply,

Calculated amount is less, and precision is high, has stronger rejection ability to higher hamonic wave and noise.

Accompanying drawing explanation

figure1 is phasometer theory structure figure.

figure2 (a) is time domain waveform in data analysis figure;

figure2 (b) is data analysis frequency domain waveform figure.

figure3 (a) is phase difference measurement relative error error statistics when adding Blackman-Harris window in data analysis figure;

figure3 (b) is phase difference measurement relative error error statistics when adding 4 rank Blackman-Harris window in data analysis figure;

figure3 (c) is phase difference measurement relative error statistics when adding 4 rank Blackman-Harris windows in data analysis and revise figure.

figure4 is phase difference measurement relative error statistics when adding 4 rank Blackman-Harris windows under white noise interference and revise figure.

Embodiment

The technological means realized to make the present invention, character of innovation, reach object and effect is easy to understand, below in conjunction with specifically figureshow, set forth the present invention further.

The present invention is gathered to measured signal by its data acquisition module, data resolution module receives the signal of data collecting module collected, and resolve to and can directly carry out for data analysis module the digital quantity signal analyzed, analyze finally by data analysis module, its data analysis module carries out truncation by structure 4 rank Blackman-Harris window to through discrete sample signals, and FFT spectrum analysis is carried out to the signal after windowing, extract first-harmonic parameter, calculate the initial phase angle of measured signal respectively, then the phase place at the useful frequency spectrum place of Discrete Spectrum Correcting Method correction is utilized, thus calculate phase differential.

Data analysis module of the present invention introduces one of knowing clearly novelwindow function---4Blackman-Harris, 4 rank Blackman-Harris windows improve the rejection ability of spectral leakage and use discrete spectrum alignment technique to correct accurately spectral line and improve frequency resolution, on this basis, this invention can realize the high-acruracy survey of phase differential.The specific implementation method of the method is as follows:

If be respectively x (t) for two periodic signals of measure phase difference, y (t), for the sake of simplicity, does not first consider the harmonic component in signal, namely suppose that they are unifrequency periodic signal, suppose that two signals obtained by data acquisition link can be expressed as simultaneously

In formula: T is signal x ₁and x ₂cycle; A _1m, A _2mbe respectively x ₁, x ₂amplitude; be respectively x ₁, x ₂initial phase; T _sfor sampling interval.

The first step, use 4 rank Blackman-Harris window weightings, 4 rank B-H windows are defined as 4 reconvolutions of B-H window, can obtain its time-domain expression as follows:

w _4B-H(n)＝w _B-H(n)*w _B-H(n)*w _B-H(n)*w _B-H(n) (1)

Wherein $w_{B-H}\left(n\right)=a_0-a_1\cos \frac{2\mathrm{\&pi;n}}{N}+a_2\cos \frac{4\mathrm{n\&pi;}}{N}-a_3\cos \frac{6\mathrm{n\&pi;}}{N},$ a ₀＝0.35875，a ₁＝0.48829，a ₂＝0.14128，a ₃＝0.01168。According to the 4 rank Blackman-Harris windows that formula (1) structure length is N, to signal x (n) windowing, obtain burst x ' (n) after windowing=x (n) w _4B-H(n);

Second step, FFT frequency spectrum calculates;

To the sequence x obtained ₁' (n) carries out FFT computing, directly calculates the first phase of first-harmonic, thus calculates the phase differential of two signals, and computation process is as follows:

$X_1\left(k\right)=\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{x}_1^{\&prime;}\left(n\right)W_N^{\mathrm{kn}}=\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{x}_1^{\&prime;}\left(n\right)[\cos (2\mathrm{\&pi;nk}/N)-j\sin (2\mathrm{\&pi;nk}/N)],k=\mathrm{0,1},...N-1---\left(2\right)$

In formula, represent twiddle factor; N is sampling number; N is the n-th sampled point; K is overtone order, selects first-harmonic here, i.e. k=1.

Formula (2) is DFT algorithm, directly calculates by this, and its operand is N ²secondary taking advantage of again is added with N (N-1) is secondary.When N is very large, operand is just suitable large, adopts fast fourier algorithm (FFT) for this reason, utilizes the inherent symmetry and periodically of the butterfly-type factor, the DFT of long sequence is decomposed into the DFT of short data records, to accelerate arithmetic speed.The design adopts decimation in time (DIT) fft algorithm.Its principle is as follows:

$\begin{array}{c}{X}_1\left(k\right)=\underset{n=0}{\overset{N/2-1}{\mathrm{\&Sigma;}}}{x}_1^{\&prime;}\left(2n\right)W_N^{2\mathrm{nk}}+\underset{n=0}{\overset{N/2-1}{\mathrm{\&Sigma;}}}{x}_1^{\&prime;}(2n+1)W_N^{(2n+1)k}\\ =\underset{n=0}{\overset{N/2-1}{\mathrm{\&Sigma;}}}{x}_1^{\&prime;}\left(2n\right)W_{N/2}^{2\mathrm{nk}}+W_N^k\underset{n=0}{\overset{N/2-1}{\mathrm{\&Sigma;}}}{x}_1^{\&prime;}(2n+1)W_{N/2}^{\mathrm{nk}}\end{array}---\left(3\right)$

Order $Y\left(k\right)=x_1^{\&prime;}\left(2n\right)W_{N/2}^{2\mathrm{nk}},Z\left(k\right)=x_1^{\&prime;}(2n+1)W_{N/2}^{2\mathrm{nk}},$ Then formula (3) is variable is changed to:

$X_1\left(k\right)=Y\left(k\right)+W_N^{k}Z\left(k\right)$

Because the cycle of Y (k) and Z (k) is N/2, then the scope of above formula k is 0 ~ N/2-1, then utilizes when calculating k=N/2 ~ N-1 characteristic, can obtain:

X ₁(k+N/2)＝Y(k)

Utilize formula (2), (3) calculate the X (k) of k=0 ~ N/2-1 and k=N/2 ~ N-1 respectively.Extract further in the same way, just can obtain the DFT of N/4 point, repeat this extraction process, the butterfly-unit that just can realize base 2-DIT-FFT calculates X (k).

Make X ₁k the real part of () is Re [X ₁(k)], imaginary part is Im [X ₁(k)], then by the X obtained that samples ₁k (), shared by the fundamental frequency in real system, component is maximum, and the amplitude of corresponding frequency spectrum is also maximum, therefore can search the sequence number k corresponding to maximum spectral line in frequency spectrum _m, obtaining frequency spectrum shared by first-harmonic is X ₁(k _m), its amplitude is A (k _m).

Then can ask and obtain first phase and be:

In like manner, another road signal X can be calculated ₂k the first phase of () is:

Survey phase differential and be:

3rd step, utilizes ratiometric correction method to carry out phase correction, searches kth _mtwo spectral lines about root spectral line, obtaining its amplitude is A (k _m-1) and A (k _m+ 1), then correction coefficient is Δ k:

$\mathrm{\&Delta;k}=\left\{\begin{array}{c}\frac{2A(k-1)-A\left(k\right)}{A(k-1)+A\left(k\right)},\frac{A(k-1)}{A(k+1)}>1\\ -\frac{2A(k+1)-A\left(k\right)}{A(k+1)+A\left(k\right)},\frac{A(k-1)}{A(k+1)}<1\end{array}\right.---\left(6\right)$

The corrected value that can solve each signal parameter according to correction coefficient is: phase correction amount fundamental phase after then correcting x can be calculated after the same method ₂fundamental phase k () is calibrated after

Two signal phase differences that finally can record through the correction of ratio revised law are:

Adopt the data analysis module in this phasometer to carry out measurement two signal to following two signals below and carry out a series of emulation experiment:

$x_1\left(t\right)=\underset{k=1}{\overset{p}{\mathrm{\&Sigma;}}}{A}_k\cos (2\mathrm{\&pi;k}{f}_{k}t+{\mathrm{\&alpha;}}_k)+e_1\left(t\right)---\left(10\right)$

$x_2\left(t\right)=\underset{k=1}{\overset{p}{\mathrm{\&Sigma;}}}{B}_k\cos (2\mathrm{\&pi;k}{f}_{k}t+{\mathrm{\&beta;}}_k)+e_2\left(t\right)---\left(11\right)$

If signal fundamental frequency f ₁=50Hz, two signal phase differences are 30 °, each harmonic parameter of two signals in formula as table 1shown in:

Form 1 liang of signal harmonic parameter

Experiment one, is first constructed the 4 rank Blackman-Harris windows of length N=64, does simulation comparison, construct the Hanning window of same length, Hamming, Blackman window, Blackman-Harris window, each window normalization time domain waveform by formula (1) figurewith normalization frequency-domain waveform respectively as figure2 (a) and figureshown in 2 (b).

From figurein can find out, although Blackman-Harris window adds main lobe bandwidth (being 12 π/N) compared to other windows, the resolution of spectral line is caused to decline to some extent, but its sidelobe level is also low than other windows, and side lobe attenuation slope is also steeper, thus, Blackman-Harris window is revealed suppressed sidelobes can play better effect, and the frequency domain distribution feature of 4 rank Blackman-Harris windows is a further reduction sidelobe level, and along with the increase of window exponent number, the rate of decay of secondary lobe increases, and better inhibits spectrum leakage.

Experiment two, the emulation of the data sampling asynchronous that frequency jitter causes.Utilize under identical same sample add Blackman-Harris window DFT, add 4 rank Blackman-Harris window DFT and introduction ratiometric correction algorithm in this paper add 4 rank Blackman-Harris (B-H) window fft algorithms, obtain two signal phase difference measurements relative errors respectively as figure3 (a), figure3 (b) and figureshown in 3 (c);

Can find out, in the humorous wave interference of consideration, do not have ideally noisy, time integer-period sampled, error is all 0.This is because integer-period sampled time, add Blackman-Harris window and improve window 4 rank Blackman-Harris window time, each harmonic frequency spectrum on first-harmonic without impact.Non-integer-period sampled, influence from harmonic error increases, and at this moment adds different windows, different to the inhibition of harmonic wave.When frequency fluctuates in the scope of 49.5Hz ~ 50.5Hz, Blackman-Harris window phase differential maximum error absolute value is 5.47519e-5rad, 4 rank Blackman-Harris window phase differential maximum error absolute values are 5.0968048e-7rad, the use ratiometric correction algorithm proposed in this method to add 4 rank Blackman-Harris (B-H) window fft algorithm maximum error absolute values be 3.967801e-7rad, and what use ratiometric correction method adds 4 rank Blackman-Harris (B-H) window fft algorithms when frequency jitter scope is less, maximum error absolute value is 9.64454e-8rad, the DFT algorithm comparing direct windowing 4 rank Blackman-Harris window improves an order of magnitude.

Experiment three, the state lower frequency having white noise to disturb fluctuates the emulation of the data sampling asynchronous caused.In actual measurement, the interference of harmonic wave and random noise are inevitable, and adding in realistic model under considering harmonic wave situation whitely has noise to carry out test simulation again.Signal fundamental frequency 50.3Hz in emulation experiment, select fixed sampling frequency 5000Hz, input signal signal to noise ratio (S/N ratio) change between 30dB ~ 140dB use respectively add introduction ratiometric correction algorithm that 4 rank Blackman-Harris window DFT and this method propose add 4 rank Blackman-Harris (B-H) window fft algorithms, complete the phase differential absolute error that emulation experiment obtains when there is white noise as figureshown in 4.

By figure4 can find out when there is white noise when signal to noise ratio (S/N ratio) is less than 80dB, and after adopting the correction of ratiometric correction algorithm, phase differential is definitely better than primal algorithm to error; When signal to noise ratio (S/N ratio) is greater than 80dB, the phase differential absolute error of innovatory algorithm is slightly better than primal algorithm.When noise is larger, this method phase difference measurement error still can remain on 0.005 ° (0.00015rad) below, higher than primal algorithm; When signal to noise ratio (S/N ratio) is less, measuring error significantly drops to 10-7 (rad) order of magnitude, can the impact of effectively harmonic inhabitation and noise, meets engineer applied actual requirement.

More than show and describe ultimate principle of the present invention, principal character and advantage of the present invention.The technician of the industry should understand; the present invention is not restricted to the described embodiments; what describe in above-described embodiment and instructions just illustrates principle of the present invention; without departing from the spirit and scope of the present invention; the present invention also has various changes and modifications, and these changes and improvements all fall in the claimed scope of the invention.Application claims protection domain is defined by appending claims and equivalent thereof.

Claims (1)

1., based on a high-precision phase position difference meter method for CRIO platform, it is characterized in that: its technical scheme adopted comprises the steps:

The first step, data acquisition module comprises digital data acquisition module and analogue collection module, can gather voltage (electric current) signal and the digital quantity being converted to certain format also can gather SV message, FT in digital transformer substation ₃message;

Second step, the digital quantity of the set form that data collecting module collected is uploaded by data resolution module or SV message, FT ₃packet parsing is can for data analysis module digital quantity signal directly.

3rd step, the data analysis that data analysis module is uploaded data resolution module.Concrete point of following three aspects;

(1) use 4 rank Blackman-Harris window weightings to the digital quantity signal received, 4 rank B-H windows are defined as 4 reconvolutions of B-H window, can obtain its time-domain expression as follows:

w _4B-H(n)＝w _B-H(n)*w _B-H(n)*w _B-H(n)*w _B-H(n) (1)

Wherein a ₀=0.35875, a ₁=0.48829, a ₂=0.14128, a ₃=0.01168.According to the 4 rank Blackman-Harris windows that formula (1) structure length is N, to signal x (n) windowing, obtain burst x ' (n) after windowing=x (n) w _4B-H(n);

(2) FFT frequency spectrum calculates;

If be respectively x (t), y (t) for two periodic signals of measure phase difference, for the sake of simplicity, first do not consider the harmonic component in signal, namely suppose that they are unifrequency periodic signal.Suppose that two signals obtained by Data Analysis link can be expressed as simultaneously

In formula: T is signal x ₁and x ₂cycle; A _1m, A _2mbe respectively x ₁, x ₂amplitude; be respectively x ₁, x ₂initial phase; T _sfor sampling interval;

Make X ₁k the real part of () is Re [X ₁(k)], imaginary part is Im [X ₁(k)], then by the X obtained that samples ₁k (), shared by the fundamental frequency in real system, component is maximum, and the amplitude of corresponding frequency spectrum is also maximum, therefore can search the sequence number k corresponding to maximum spectral line in frequency spectrum _m, obtaining frequency spectrum shared by first-harmonic is X ₁(k _m), its amplitude is A (k _m).

Then can ask and obtain first phase and be:

In like manner, another road signal X can be calculated ₂k the first phase of () is:

Survey phase differential and be:

(3) utilize ratiometric correction method to carry out phase correction, search kth _mtwo spectral lines about root spectral line, obtaining its amplitude is A (k _m-1) and A (k _m+ 1), then correction coefficient is Δ k:

The corrected value that can solve each signal parameter according to correction coefficient is: phase correction amount fundamental phase after then correcting x can be calculated after the same method ₂fundamental phase k () is calibrated after

Two signal phase differences that finally can record through the correction of ratio revised law are: