CN104408025A - Over-determined blind signal separation method based on spectrum correction and device of over-determined blind signal separation method - Google Patents

Abstract

The invention discloses an over-determined blind signal separation method based on spectrum correction and a device of the over-determined blind signal separation method. The method comprises the following steps: obtaining a vector comprising N frequency values and an amplitude matrix; gradually detecting whether frequency components in a frequency vector are contained in an ith path of frequency vector, and performing deassign on the amplitude matrix if so; normalizing and clustering all lines of the amplitude matrix subjected to deassign to obtain a clustered amplitude matrix; according to the clustered amplitude matrix, estimating a jth source signal. The device comprises a DSP (Digital Signal Processor) device, wherein multiple paths of observation signals are sampled by an analog-digital converter to obtain a sample sequence, then, the obtained sample sequence enters the DSP device in a digital input way and is processed by an internal algorithm of the DSP device to obtain a signal separation result; finally, the separated source signal is displayed by an output driver and the display module thereof. According to the method, blind separation accuracy is improved, the method and the device have a high application value in a vibration signal processing field, and the separation device has enough anti-noise performance.

Description

Based on overdetermination Blind Signal Separation method and the device thereof of Spectrum Correction

Technical field

The present invention relates to digital signal processing technique field, particularly relate to a kind of overdetermination Blind Signal Separation method based on Spectrum Correction and device thereof.Be specifically related to the Blind Signal Separation occasion for being greater than source signal number (i.e. overdetermination situation) at observation signal number, only process according to having periodic observation signal and recover the problem of institute's active signal.

Background technology

Blind Signal Separation ^[1](Blind Source Separation is called for short BSS) refers to that the observation signal only received sensor processes and realizes the recovery of source signal when source signal and transmission channel the unknown.Blind Signal Separation requires between source signal separate, and thus this usual realistic requirement of engineering is the hot subject of current demand signal process educational circles, is also communication ^[2], biomedical ^[3], computer science, Speech processing ^[4,5]and mechanical fault diagnosis ^[6]the technology promoted is badly in need of Deng engineering field.Thus the blind separation technology of migration fractionation signal has very high researching value.

Obviously, the connection tie of source signal and observation signal is exactly transmission channel, and thus in blind separation, the identification of transmission channel is crucial.And blind separating method, linear instantaneous mixing, linear convolution mixing and non-linear mixing three class is also divided into because of the difference of the hybrid mode of transmission channel; What the present invention solved is the blind separation problem of linear instantaneous mixture model.

In addition, blind separation can also according to classifying by the relative number of source signal and observation signal, be called overdetermination blind separation when observation signal number is greater than source signal number, when both are equal, be called positive definite blind separation, be called when observation signal number is less than source signal number and owe to determine blind separation.Wherein overdetermination and positive definite blind separation are due to after knowing hybrid matrix A, all to this matrix inversion, and source signal recovery can be realized, therefore usually the two is collectively referred to as overdetermination blind separation problem, the present invention does not consider to owe to determine separation case, this kind of just overdetermination blind separation problem of solution.

Usually there are two uncertainties: the uncertainty that (1) sorts in the process that blind separation recovers source signal.Due to hybrid matrix A and source signal s (t) the unknown, when column vector position corresponding both exchanging simultaneously, observation signal x (t) obtained is constant, thus cannot learn the original alignment order of each vector of source signal; (2) uncertainty of amplitude.This is owing to exchanging a fixing scale factor between certain component of source signal s (t) and the row of hybrid matrix A corresponding with it.But this does not hinder the principal character information that source signal comprises.

Typical overdetermination Blind Signal Separation method has joint approximate diagonalization method ^[6]-JADE method (as document [6] is applied in mechanical fault diagnosis), (comprise the neural network algorithm based on information maximization based on the fast neuronal algorithm-FastICA algorithm of fixed-point iteration ^[7], based on the Blind Signal Separation algorithm of negentropy ^[8,9], based on kurtosis or based on maximum likelihood etc.), based on the blind separating method of fraction Fourier conversion, based on the Blind Signal Separation algorithm of power spectrum ^[10]deng.Its Literature ^[4,11,12]theoretical according to ICA, first the preprocessing process such as albefaction, centralization must be carried out to observation signal, again by the Learning Step of setting neural network, repeatedly iterative learning is carried out according to different iterative formulas, until find optimum weight matrix A, finally try to achieve each isolated component, thus reach the object of Blind Signal Separation.Document ^[10,13]the identifying source method based on power spectrum density proposed, is by the ratio of observation signal power spectral density function, obtains power spectral density matrix, then estimate the source number of the uncorrelated source of frequency field or independent source by each column vector of comparator matrix.

In above-mentioned several algorithm, JADE ^[6]rule needs the diagonalization of High Order Moment, and calculated amount is very large.Based on the neural network algorithm of information maximization ^[7]need the probability density function of source signal, but when source signal the unknown, need to make estimation to probability density function, have impact on the separation accuracy of fanaticism number.Document [4,8,9,11,12] the ICA algorithm in all realizes based on different Learning Step iteration, and when when the Learning Step set is less, error is larger, iteration parameter needs could restrain for a long time, can affect the effect of blind source separating, there is the deficiency being easily absorbed in local minimum point in blind source separating BP network model; In addition, first FastICA method needs to carry out the pretreatment operation such as centralization to signal, also can strengthen the calculated amount of algorithm.And based on the Blind Signal Separation of power spectrum ^[10,13]require the aspect ratio between observation signal, this easily produces infinitely-great value and inconvenient computer disposal, simultaneously due to spectrum leakage, the frequency at the spectrum peak place obtained when carrying out Fourier transform to observation signal and amplitude are all coarse, and these all have impact on last separating effect.

Summary of the invention

The invention provides a kind of overdetermination Blind Signal Separation method based on Spectrum Correction and device thereof, present invention reduces the complexity of algorithm, improve the precision of separation, described below:

Based on an overdetermination Blind Signal Separation method for Spectrum Correction, said method comprising the steps of:

(1) according to frequency deviation estimated value, the frequency estimation after the p bunch of spectral line correction on the i-th tunnel and Amplitude Estimation value is obtained;

(2) acquisition comprises the vector of N number of frequency values, the amplitude matrix of n × N dimension; Check whether the frequency component in frequency vector is included in the frequency vector on the i-th tunnel, if comprise, then carries out assignment again to amplitude matrix one by one;

(3) each row of the amplitude matrix after assignment are normalized and clustering processing, obtain the amplitude matrix after cluster;

(4) according to the amplitude Matrix Estimation Chuj road source signal after cluster.

Before step (1), described method also comprises:

Obtain Ni bunch of spectral line of each road observation signal; Record the position of the highest spectral line of every bunch of spectral line one by one;

The frequency deviation estimated value of every bunch of spectral line is upgraded according to the position acquisition of the highest spectral line.

Frequency estimation is

f _i,p＝k _i,p+Δk _i,pi＝1,2,...,n,p＝1,2,...,N _i

Amplitude Estimation value is

B _i,p＝2πΔk _i,p×(1-Δk _i,p ²)/sin(πΔk _i,p)×|X _i(k _i,p)|i＝1,2,...,n,p＝1,2,...,N _i

Wherein, k _i,pfor the highest position of spectral line; Δ k _i,pfor frequency deviation estimated value; | X _i(k _i,p) | for correcting the amplitude of p bunch of spectral line of front i-th tunnel observation; N _iit is the number of clusters of peak value spectral line in the i-th road observation signal.

Based on an overdetermination Blind Signal Separation device for Spectrum Correction, described device comprises: DSP device,

Multichannel observation signal obtains sample sequence through the sampling of analog-to-digital conversion device, enters described DSP device, through the internal algorithm process of DSP device, obtain the separating resulting of signal with the form of Parallel Digital input; Finally demonstrate isolated source signal by output driving and display module thereof.

The beneficial effect of technical scheme provided by the invention is: ensure that the complexity of separation algorithm is lower by the frequency of each composition of signal and the quick estimation of magnitude parameters, have higher actual effect; Corrected and the measure of K-mean cluster by spectrum, improve the accuracy of blind separation, in vibration signal processing field, there is very high using value, and this tripping device possesses enough noise robustness; And by verification experimental verification, demonstrate correctness and the terseness of separation method and tripping device thereof, have very important using value to engineering fields such as biomedical applications, Speech processing and mechanical fault diagnosis.

Accompanying drawing explanation

Fig. 1 is Blind Signal Separation theory diagram;

Fig. 2 is the tripping device design general flow chart of fanaticism number;

Fig. 3 is time domain waveform and the spectrogram of source signal;

Fig. 4 is without the time domain waveform of observation signal and spectrogram when making an uproar;

Fig. 5 is time domain waveform and the spectrogram (without making an uproar) of signal after being separated;

Fig. 6 is time domain waveform and the spectrogram (without making an uproar) of signal after Fast-ICA method is separated;

Fig. 7 is the time domain waveform and the spectrogram that add mixed signal when making an uproar;

Fig. 8 is time domain waveform and the spectrogram (add and make an uproar) of signal after being separated;

Fig. 9 is time domain waveform and the spectrogram (add and make an uproar) of signal after Fast-ICA method is separated;

Figure 10 is hardware implementation figure of the present invention;

Figure 11 is DSP internal processes flow graph.

Embodiment

For making the object, technical solutions and advantages of the present invention clearly, below embodiment of the present invention is described further in detail.

For improving above method and carrying out simple Blind Signal Separation efficiently, the present invention's proposition is the overdetermination Blind Signal Separation device based on Spectrum Correction of periodic signal for source signal, the frequency that this device is used and amplitude are all through to correct and obtain, eliminate the impact of spectrum leakage as far as possible, thus ensure that the pinpoint accuracy of separation; Different from document [10], this device core algorithm there will not be infinitely-great extreme case, is thus more easily computer disposal; Core of the present invention is the estimation of hybrid matrix, and this matrix only need go out the amplitude of each composition by spectrum correction calculation and obtain amplitude matrix, then can obtain in conjunction with K mean cluster pattern abbreviation, therefore implementation process is simple, without the need to iterating.Experiment demonstrates the feasibility of put forward the methods of the present invention, therefore has very important using value to engineering fields such as biomedical applications, Speech processing and mechanical fault diagnosis.

As shown in Figure 1, in this separation principle figure, S (t) is source signal to Blind Signal Separation System recover principle of the prior art, and A is hybrid matrix, and source signal is through being mixed to get observation signal x (t), by asking for separation matrix C ^-1, finally recover institute's active signal by observation signal, therefore the key of this piece-rate system is for more accurately to estimate separation matrix C ^-1.For this reason, the present invention proposes to estimate this matrix based on the Blind Signal Separation method of Spectrum Correction.

Model of the present invention is linear instantaneous mixture model, and desirable without in situation of making an uproar, its mathematic(al) representation is:

x(t)＝AS(t) (1)

In formula, x (t) is that n ties up observation signal vector, and S (t) is unknown independent source periodic signal vector for m ties up, and A is that n × m ties up unknown hybrid matrix.

For making fanaticism number separable, suppose that source signal is separate here, each frequency component of the frequency component namely between source signal and source signal inside is unequal mutually, and requires source signal number m≤n, then the matrix representation of (1) formula is:

In formula (2), x ₁(t) ~ x _nt () represents n road observation signal, s ₁(t) ~ s _nt () represents the unknown Independent sources signal in m road, a ₁₁~ a _nmfor mixing constant.

Owing to there is spectrum leakage when observation signal being made to analysis of spectrum, make X _if there is deviation in amplitude and the frequency of () each frequency component, now for obtaining accurate amplitude and frequency just needs to correct it, can obtain specific algorithm as follows by Fig. 2:

101: to each road observation signal x _i(t), i=1 ..., n, makes FFT analysis of spectrum and obtains X after adding Hamming window _i(f), and then obtain out N _ibunch spectral line (every bunch of spectral line represents 1 frequency content); And the position of recording the highest spectral line of every bunch of spectral line is one by one

102: the X of access spectrum one by one _ithe highest position of spectral line k of every bunch of spectral line of (f) _i,p, p=1,2 ..., N _i, write down correspondence position spectrum peak (| X _i(k _i,p) |), then obtain spectral line value that in two spectral lines adjacent with every bunch of spectrum peak position, amplitude is larger (be designated as | X _i(k _i,p(secondary high spectrum) |);

And try to achieve both ratio by v _i,pvalue substitution formula (3) tries to achieve the frequency deviation estimated value Δ k of every bunch of spectral line _i,p, namely

Δk _i,p＝(v _i,p-2)/(v _i,p+1) (3)

Obtain Δ k _i,pafter, compare spectrum peak k _i,pthe spectral line amplitude of both sides, if the spectral line amplitude in left side is greater than the spectral line amplitude on right side, by Δ k _i,pvalue be updated to Δ k _i,p-1, peak value spectral line k simultaneously _i,pvalue be updated to k _i,p-1;

103: according to Δ k _i,pfrequency deviation estimated value, obtains the frequency estimation f after the p bunch of spectral line correction on the i-th tunnel _i,pfor

f _i,p＝k _i,p+Δk _i,pi＝1,2,...,n,p＝1,2,...,N _i(4)

Correspondingly, the Amplitude Estimation value obtained after p bunch of spectral line correction of the i-th tunnel observation is

B _i,p＝2πΔk _i,p×(1-Δk _i,p ²)/sin(πΔk _i,p)×|X _i(k _i,p)|i＝1,2,...,n,p＝1,2,...,N _i

(5)

In formula (5) | X _i(k _i,p) | represent the amplitude of the p bunch of spectral line correcting front i-th tunnel observation, N _iit is the number of clusters of peak value spectral line in the i-th road observation signal.

Thus obtain comprising the vector f that all Frequency Estimation results are observed on the i-th tunnel _iwith the vectorial B of Amplitude Estimation result _i, namely

$f_i=\left[\begin{array}{ccc}{f}_{i,1}& f_{i,2}& f_{i,3}\·\·\·f_{i{,N}_i}\end{array}\right],B_i=\left[\begin{array}{ccc}{B}_{i,1}& B_{i,2}& B_{i,3}\·\·\·\end{array},B_{i,N_i}\right]---\left(6\right)$

Similarly, the amplitude of other each road observation signal and the step of frequency correction the same, thus obtain n frequency vector f ₁~ f _nwith n amplitude vector B ₁~ B _n;

104: n observing frequency Vector Groups is combined together, form the longer frequency vector f containing redundancy frequency _r, that is:

$f_r=\{\left[\begin{array}{ccc}{f}_{\mathrm{1,1}}& f_{\mathrm{1,2}}& ,\·\·\·,f_{1,N_1}\end{array}\right],\·\·\·,\left[\begin{array}{ccc}{f}_{n,1}& f_{n,2}& ,\·\·\·,f_{n,N_n}\end{array}\right]\}---\left(7\right)$

The all frequencies comprised formula (7) vector are by sequence from small to large and multiple frequencies nearer for spacing are merged into its average, and then the vectorial F obtaining comprising N number of frequency values is

F＝[F ₁F ₂,…,F _N] (8)

Because composite vector F is come by frequency vector de-redundancy combination corresponding to each observation signal, therefore obviously there is N>=N _i;

The amplitude matrix B of 105: structure n × N dimension _m,

$B_m=\left[\begin{array}{ccc}{B}_{\mathrm{1,1}}\left(f_1\right)& B_{\mathrm{1,2}}\left(f_2\right)& \·\·\·B_{1,N}\left(f_N\right)\\ B_{2.1}\left(f_1\right)& B_{2.2}\left(f_2\right)& \·\·\·B_{2,N}\left(f_N\right)\\ \·\·\·& \·\·\·& \·\·\·\\ B_{n,1}\left(f_1\right)& B_{n,2}\left(f_2\right)& \·\·\·B_{n,N}\left(f_N\right)\end{array}\right]---\left(9\right)$

And by this matrix B _mall elements is initialized as 0; Check frequency vector F=[F one by one again ₁f ₂..., F _n] in frequency component F _j, j=1 ..., whether N, be included in the frequency vector f on the i-th tunnel _i=[f _{i, 1}f _{i, 2}f _{i, 3}f _i, N _i] in, if comprise, then by B _i,jvalue assignment is to B _i,j(f _j), namely

$B_{i,j}\left(f_j\right)=\left\{\begin{array}{cc}{B}_{i,j}& ,F_j\∈f_i\\ 0& ,F_j\∉f_i\end{array}\right.---\left(10\right)$

106: by B _meach row carry out 2 norm normalizeds, each column vector as being 1 pattern, then use K means Method by B _min N number of pattern be polymerized to m class, the amplitude matrix after cluster can be obtained for

107: obtain source signal according to the following formula and estimate namely

$\hat{S}\left(t\right)={\hat{C}}^{-1}x\left(t\right)---\left(12\right)$

Wherein, in formula (12) for amplitude matrix pseudoinverse.

Experiment

For verifying correctness of the present invention and validity, blind separating method the present invention proposed carries out performance comparison with conventional Fast-ICA algorithm.

For the performance of quantitative comparison two kinds of algorithms, experiment adopts the similar matrix ξ and performance index PI value that pass judgment on blind signal recuperation quality as criterion.

Similar matrix ξ is the parameter describing estimated signal and source signal similarity, its often row with often arrange and only have the absolute value of an element close to 1, other element is all similar to close to 0, then can think that this algorithm separating effect is ideal.

Performance index PI value is defined as follows:

$\mathrm{PI}=\frac{1}{n(n-1)}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\{(\underset{k=1}{\overset{n}{\mathrm{\Σ}}}\frac{\left|g_{\mathrm{ik}}\right|}{{\max }_j\left|g_{\mathrm{ij}}\right|}-1)+(\underset{k=1}{\overset{n}{\mathrm{\Σ}}}\frac{\left|g_{\mathrm{ki}}\right|}{{\max }_j\left|g_{\mathrm{ji}}\right|}-1)\}---\left(13\right)$

In formula (13), g _ijfor matrix G, (G is actual hybrid matrix A and separation matrix product) element (g in formula _ik, g _jielement in equal representing matrix G, just value is different with the difference of i, j, k); max _j| g _ij| represent the maximal value in the i-th row element absolute value of G; max _j| g _ji| represent the maximal value in the i-th column element absolute value.The PI=0 when isolated signal is identical with source signal waveform.In reality, this value is less, then represent that recovery effects is better.

In addition, in the cluster link of the step 106 of this method, need specification error threshold value to the amplitude matrix B after normalization _mcolumn vector carry out cluster.In an experiment, this error threshold is set as 5%, even these two column vectors are then polymerized to a class by the relative error of two column vectors within 5%.

For studying the noise immunity of the inventive method, experiment being divided into and discussing respectively without make an uproar situation and noisy situation.

1, without making an uproar situation

First the separation case of fanaticism number under noiseless disturbed condition be discussed.Supposing the system sampling rate F _s=310 sample points/second, N=1024 sample, then the frequency resolution Δ f=F of FFT are collected in every road _s/ N=0.3027 Hz.

Known following 4 periodic source signals and hybrid matrix A:

s ₁(t)＝cos(2π70t)

s ₂(t)＝sin(2π30t+27)

s ₃(t)＝sin(2π60t+6sin(2π20t)) (14)

s ₄(t)＝sin(2π10t+12)sin(2π100t)

$A=\left[\begin{array}{cccc}1.25& 0& 0.83& 0\\ 0.84& 1.06& 1.10& 1.68\\ 0& 0.98& 0& 0.93\\ 2.12& 0& 1.65& 1.47\\ 0.56& 2.89& 0& 2.18\end{array}\right]---\left(15\right)$

For carrying out waveform contrast before and after separation, first as FFT, time domain waveform as shown in Figure 3 and spectrogram are obtained to source signal sample.By source signal s ₁(t) ~ s ₄t () obtains observation signal x by hybrid matrix A ₁(t) ~ x ₅t (), as shown in Figure 4, in Fig. 4, left-half is the source signal recovered for its time domain waveform and spectrogram, and right half part is the corresponding spectrogram of source signal.

The algorithm carried by the present invention, the exact amplitude of each mixed signal on each Frequency point need be obtained, therefore by step 102 and 103, frequency correction and amplitude rectification are carried out to each composition that every road is observed, according to step 104, the frequency after correction is sorted, combined, then frequency vector F and the amplitude vector B of length N=10 can be obtained according to step 105 _m, as shown in table 1:

Table 1 is without amplitude matrix table when making an uproar

More every column vector can be clearly seen that following 4 groups of amplitude column vectors are close, and the combination of frequency of their correspondences is: { 29.9998}{69.9998} { 89.9999,109.9999} { 19.9997,39.9998,99.9999,129.9999,140.0000,150.0000}

By this 4 class frequency known of analysis above respectively from 4 different source signals.Wherein 20.9998Hz and 69.998Hz can not find column vector close with it to deserved column vector, therefore, the source signal of their correspondences should be single source signal, and this and source signal formula (14) are just in time coincide, and other two groups of column vectors also match with source signal formula (14) equally.Namely close column vector is carried out cluster:

Then according to step 106, to B _meach row carry out 2 norm normalizeds, and with K means Method by B _min 10 patterns be polymerized to 4 classes, the hybrid matrix after cluster can be obtained for

$\hat{C}=\left[\begin{array}{cccc}0.0000& 0.4699& 0.0001& 0.3861\\ 0.3283& 0.3159& 0.5290& 0.5117\\ 0.3033& 0.0000& 0.2731& 0.0001\\ 0.0000& 0.7970& 0.4863& 0.7675\\ 0.8945& 0.2105& 0.6401& 0.0001\end{array}\right]---\left(16\right)$

The actual hybrid matrix A of formula (15) is done two norm normalization, and its result is:

$A=\left[\begin{array}{cccc}0.4699& 0.0000& 0.3861& 0.0000\\ 0.3158& 0.3281& 0.5117& 0.5160\\ 0.0000& 0.3034& 0.0000& 0.2856\\ 0.7970& 0.0000& 0.7675& 0.4515\\ 0.2105& 0.8946& 0.0000& 0.6696\end{array}\right]---\left(17\right)$

To in illuminated (16) with each column vector of formula (17), the known sequence except column vector exists except difference, and the error of each column vector is all very little, indicates correctness and the accuracy of algorithm provided by the present invention.

Right according to step 107 again ask pseudoinverse and obtain separation matrix basis again and recovering source signal waveform and frequency spectrum thereof as shown in Figure 5, in Fig. 5, left-half is the source signal recovered, and right half part is the corresponding spectrogram of source signal.

In addition, to same observation signal, according to the Fast-ICA algorithm based on kurtosis, be restored waveform and frequency spectrum thereof as shown in Figure 6.

Comparison diagram 3 and Fig. 5 can significantly see, except difference that put in order except its time domain waveform and spectrum distribution substantially identical, and it is very little to compose leakage; And Fast-ICA method is separated to the source signal (Fig. 6) obtained, be not difficult to find for source s from spectrogram ₂(t), s ₃t () has the situation that obviously spectrum is leaked to occur.

For quantitative target similar matrix and performance index, according to the inventive method and Fast-ICA method, obtain similar matrix ξ and PI value is respectively:

${\mathrm{\ξ}}_{\mathrm{proposed}}=\left[\begin{array}{cccc}0.0005& 1.0000& 0.0002& -0.0008\\ 0.9984& 0.0012& 0.0006& 0.0045\\ 0.0090& -0.0004& 0.0615& 1.0000\\ 0.0569& 0.0037& 1.0000& 0.0531\end{array}\right],{\mathrm{PI}}_{\mathrm{proposed}}=0.0163$

${\mathrm{\ξ}}_{\mathrm{Fast}-\mathrm{ICA}}=\left[\begin{array}{cccc}-0.0013& 0.9999& -0.0023& 0.0128\\ -0.9795& 0.0033& 0.0174& 0.2008\\ -0.0252& -0.0027& -0.9996& -0.0081\\ 0.1988& -0.0122& -0.0745& 0.9771\end{array}\right],{\mathrm{PI}}_{\mathrm{Fast}-\mathrm{ICA}}=0.0922$

Wherein ξ _proposedrepresent the similar matrix adopting the inventive method to try to achieve, ξ _fast-ICAfor the similar matrix adopting Fast-ICA method to try to achieve; In like manner, PI _proposedrepresent the PI value adopting the inventive method to try to achieve, PI _fast-ICAfor the PI value adopting Fast-ICA method to try to achieve.Contrast two kinds of algorithms, can find out without in situation of making an uproar:

1. similar matrix ξ _proposedand ξ _fast-ICAin often row all uniquely exist absolute value close to 1 maximal value, other value is close to 0, and namely two kinds of algorithms all can recover source signal preferably in without situation of making an uproar;

2. comparatively speaking, ξ _proposedcompare ξ _fast-ICAthe absolute value of middle maximal value is closer to 1, and the separation matrix of namely trying to achieve is more accurate

3. from performance index PI value, the PI value that obvious the inventive method is tried to achieve is less of 0, is therefore better than Fast-ICA algorithm.

(2) situation of making an uproar is added

For verifying its recovery effects in noisy situation, provide the experiment added in the situation of making an uproar below.Zero-mean random Gaussian white noise is added to above source signal, adds observation signal x after making an uproar ₁(t) ~ x ₅t () as shown in Figure 7, in Fig. 7, left-half is the source signal recovered, right half part is the corresponding spectrogram of source signal.

Experimental procedure is the same, by step 102 ~ step 105, and the frequency vector F of length N=10 corresponding under can obtaining noisy situation and amplitude vector B _m, as shown in table 2

Table 2 adds amplitude matrix table when making an uproar

Close column vector is carried out cluster:

By matrix B now _mtwo norm normalization obtain hybrid matrix

$\hat{C}=\left[\begin{array}{cccc}0.0000& 0.4699& 0.0001& 0.3911\\ 0.3274& 0.3150& 0.5304& 0.5178\\ 0.3051& 0.0000& 0.2690& 0.0002\\ 0.0000& 0.7979& 0.4819& 0.7608\\ 0.8943& 0.2080& 0.6433& 0.0002\end{array}\right]---\left(18\right)$

Will compare with the hybrid matrix A after two norm normalization, other is substantially equal except sequence difference for each column vector, indicate the present invention when noise exists put forward the correctness of algorithm.

From adding isolated source signal result observation signal of making an uproar, as shown in Figure 8, in Fig. 8, left-half is the source signal recovered, and right half part is the corresponding spectrogram of source signal:

To same observation signal, according to the Fast-ICA algorithm based on kurtosis, be restored waveform and frequency spectrum thereof as shown in Figure 9:

The similar matrix ξ and the PI value that add two kinds of methods in the situation of making an uproar are respectively:

${\mathrm{\ξ}}_{\mathrm{proposed}}=\left[\begin{array}{cccc}0.0020& 1.0000& -0.0029& 0.0040\\ 0.9930& 0.0012& -0.0029& 0.0059\\ 0.0066& 0.0075& 0.0646& 0.9809\\ 0.0541& 0.0020& 0.9820& 0.0529\end{array}\right],{\mathrm{PI}}_{\mathrm{proposed}}=0.0248$

${\mathrm{\ξ}}_{\mathrm{Fast}-\mathrm{ICA}}=\left[\begin{array}{cccc}0.9913& -0.0238& 0.0096& 0.0194\\ -0.0228& -0.9731& -0.0092& 0.1958\\ 0.0118& 0.0053& 0.9822& -0.0086\\ -0.0238& 0.1730& 0.0987& 0.9599\end{array}\right],{\mathrm{PI}}_{\mathrm{Fast}-\mathrm{ICA}}=0.0991$

In situation of making an uproar, comparatively often row maximal value absolute value is closer to 1 in Fast-ICA algorithm can to find out by similar matrix and performance index ξ that the inventive method tries to achieve, and PI value is closer to 0, is therefore better than Fast-ICA algorithm.

By above without make an uproar with add the situation of making an uproar under emulation experiment that overdetermination fanaticism number is separated, demonstrate correctness and the terseness of the Blind Signal Separation collocation method that the present invention is based on Spectrum Correction, have very important using value to engineering fields such as biomedical applications, Speech processing and mechanical fault diagnosis.

See Figure 10, multichannel observation signal x (t) collected is obtained sample sequence x (n) through A/D (analog-to-digital conversion device) sampling, DSP device is entered with the form of Parallel Digital input, through the internal algorithm process of DSP device, obtain the separating resulting of signal; Finally to drive by output and display module demonstrates isolated source signal (image or sound or other useful waveforms).

Wherein, the DSP (Digital Signal Processor, digital signal processor) of Figure 11 is core devices, in Signal parameter estimation process, completes following major function:

(1) call the overdetermination blind separation algorithm of periodic signal, the frequency correction of settling signal and amplitude rectification, obtain correct signal frequency and estimate and Amplitude Estimation;

(2) cluster is carried out to amplitude matrix, obtain corresponding hybrid matrix.

(3) by asking the generalized inverse of hybrid matrix to export source signal restoration result to driving and display module in real time.

Need point out, owing to have employed digitized method of estimation, thus determining the complexity of Figure 10 system, real-time levels and the principal element of degree of stability is not that the periphery of DSP device in Figure 10 is connected, but the kernel estimation algorithm that DSP internal program memory stores.

The internal processes flow process of DSP device as shown in figure 11.

Proposed " Blind Signal Separation based on Spectrum Correction " this kernel estimation algorithm is implanted in DSP device by the present invention, completes high precision, low complex degree, efficiently blind source separating based on this.

Figure 11 flow process is divided into following several step:

(1) first need according to embody rule requirement (the concrete measurement as medical science and military affairs etc. requires), the sampling number N of signalization and the number of times i of duplicate measurements, and setting accuracy requirement according to specific needs.This step proposes real needs from engineering aspect, processes targetedly to make follow-up flow process.

(2) then, CPU primary controller reads sampled data from I/O port, enters internal RAM.

(3) follow-up " DC processing " is the impact in order to eliminate the flip-flop in measured signal.Otherwise the existence of flip-flop, can reduce measuring accuracy.Flip-flop is easy to measure, and only needs the mean value calculating sampling point to obtain.

(4) carrying out Blind Signal Separation by Fig. 2 processing procedure of the present invention is the most crucial part of DSP algorithm, after running this algorithm, quick and precisely can try to achieve separation matrix, finally recover source signal.

(5) judge whether the inventive method meets engineering demand, if do not meet, program returns, and again sets sample frequency as requested and carries out Blind Signal Separation, repeat above detachment process i time.

(6) export outside display drive device to by the output bus of DSP, isolated for institute source signal is carried out difference display, as advantageous form such as sound, image, ecg wave forms.

Need point out, realize owing to have employed DSP, make whole parameter estimation operation become more flexible, the concrete condition of the various components that can comprise according to signal, the inner parameter being changed algorithm by flexible in programming is arranged, as sampling number N, and sample rate f _sdeng.

List of references

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The embodiment of the present invention is to the model of each device except doing specified otherwise, and the model of other devices does not limit, as long as can complete the device of above-mentioned functions.

It will be appreciated by those skilled in the art that accompanying drawing is the schematic diagram of a preferred embodiment, the invention described above embodiment sequence number, just to describing, does not represent the quality of embodiment.

The foregoing is only preferred embodiment of the present invention, not in order to limit the present invention, within the spirit and principles in the present invention all, any amendment done, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (4)

1., based on an overdetermination Blind Signal Separation method for Spectrum Correction, it is characterized in that, said method comprising the steps of:

(1) according to frequency deviation estimated value, the frequency estimation after the p bunch of spectral line correction on the i-th tunnel and Amplitude Estimation value is obtained;

(2) acquisition comprises the vector of N number of frequency values, the amplitude matrix of n × N dimension; Check whether the frequency component in frequency vector is included in the frequency vector on the i-th tunnel, if comprise, then carries out assignment again to amplitude matrix one by one;

(3) each row of the amplitude matrix after assignment are normalized and clustering processing, obtain the amplitude matrix after cluster;

(4) according to the amplitude Matrix Estimation Chuj road source signal after cluster.

2. a kind of overdetermination Blind Signal Separation method based on Spectrum Correction according to claim 1, it is characterized in that, before step (1), described method also comprises:

Obtain the N of each road observation signal _ibunch spectral line; Record the position of the highest spectral line of every bunch of spectral line one by one;

The frequency deviation estimated value of every bunch of spectral line is upgraded according to the position acquisition of the highest spectral line.

3. a kind of overdetermination Blind Signal Separation method based on Spectrum Correction according to claim 1, is characterized in that,

Frequency estimation is

f _i,p＝k _i,p+Δk _i,pi＝1,2,...,n,p＝1,2,...,N _i

Amplitude Estimation value is

B _i,p＝2πΔk _i,p×(1-Δk _i,p ²)/sin(πΔk _i,p)×|X _i(k _i,p)| i＝1,2,...,n,p＝1,2,...,N _i

Wherein, k _i,pfor the highest position of spectral line; Δ k _{i, p}for frequency deviation estimated value; | X _i(k _i,p) | for correcting the amplitude of p bunch of spectral line of front i-th tunnel observation; N _iit is the number of clusters of peak value spectral line in the i-th road observation signal.

4., based on an overdetermination Blind Signal Separation device for Spectrum Correction, described device comprises: DSP device, is characterized in that,

Multichannel observation signal obtains sample sequence through the sampling of analog-to-digital conversion device, enters described DSP device, through the internal algorithm process of DSP device, obtain the separating resulting of signal with the form of Parallel Digital input; Finally demonstrate isolated source signal by output driving and display module thereof.