CN109243483B - Method for separating convolution blind source of noisy frequency domain - Google Patents

Method for separating convolution blind source of noisy frequency domain Download PDF

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CN109243483B
CN109243483B CN201811211078.2A CN201811211078A CN109243483B CN 109243483 B CN109243483 B CN 109243483B CN 201811211078 A CN201811211078 A CN 201811211078A CN 109243483 B CN109243483 B CN 109243483B
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CN109243483A (en
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成玮
加正正
陈雪峰
倪晶磊
朱岩
陆建涛
周光辉
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Xian Jiaotong University
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Abstract

The invention discloses a method for separating a convolution blind source of a frequency domain containing noise, which comprises the steps of smoothing a mixed signal by utilizing a thin plate spline model for a convolution mixed signal with additive Gaussian noise, estimating the variance of the additive Gaussian noise in the mixed signal by utilizing a generalized cross verification method, converting the signal from a time domain to a frequency domain by short-time Fourier transform, estimating a separation matrix on each frequency band by utilizing a noise complex value independent component analysis method based on a deviation removal technology, and further obtaining a separation signal of each frequency band; then, sequencing correction and amplitude correction are respectively carried out on the separation signals by using a sequencing algorithm and a minimum distortion method; and finally, carrying out short-time inverse Fourier transform on the corrected signal to restore a separated signal. The method and the device utilize the deviation removing technology to carry out the deviation removing processing on the observation signals, improve the estimation precision of the mixing matrix and the source signals, and avoid the influence of the noise reduction processing on the separation effect. Simulation tests show that the method can still maintain good separation performance under low signal-to-noise ratio.

Description

Method for separating convolution blind source of noisy frequency domain
Technical Field
The invention relates to the field of processing of mechanical vibration signals and acoustic radiation signals, in particular to a method for separating a convolution blind source of a noisy frequency domain.
Background
The radiation noise of the submarine poses serious threat to the concealment of the submarine, and directly influences the operational performance and the viability of the submarine. Therefore, how to find the submarine vibration noise source and further take measures to reduce the influence of the submarine vibration noise source is very important. The monitoring signal of the submarine is often the result of each vibration source signal through a complex mixing process, so that the responses of a plurality of excitation sources are mutually interfered, the transmission paths are various, an accurate model is difficult to establish, and the difficulty is brought to the identification of the vibration source.
Blind source separation is a method for estimating an original signal from an observed mixed signal under the condition that a source signal and a mixing process are unknown, and provides a good solution for separating and identifying a noise source. The instantaneous mixture is the simplest model in blind source separation, and although many efficient independent component analysis algorithms have been proposed for this model, the instantaneous mixture model is rarely met in engineering practice, such as the mixture of submarine mechanical vibration sources or noise sources. For a multi-input multi-output mechanical system, an observation point receives superposition of signals of a vibration source after passing through a complex transmission path, and if non-linear factors are not considered, each transmission path can be approximately represented by a filter in a time domain; similarly, the acoustic signal measured by the microphone is the result of the superposition of several delayed, reflected sound sources in space. Therefore, the research on the separation of the convolution mixed blind source has important engineering significance and value for the vibration and noise source identification.
For the problem of blind separation of convolution, two types of algorithms mainly exist at present: the first is a time domain separation algorithm and the second is a frequency domain separation algorithm. Compared with a time domain blind source separation algorithm, the frequency domain blind separation algorithm of the mixed signal can overcome the problem of difficult estimation of a long filter in time domain blind deconvolution due to smaller calculated amount and good separation performance, and therefore has more engineering application value. In the frequency domain convolution blind source separation algorithm, the Independent Component Analysis (ICA) is the key to the success or failure of frequency domain blind source separation, which is the natural popularization of real-valued ICA.
Over the years, the noise-free real value ICA algorithm using the likelihood, non-gaussian property, etc. of signals as an independence criterion has matured. In recent years, some progress has been made with respect to complex-form signal noiseless ICA processing methods, such as joint approximation feature diagonal matrix method (JADE) and negative entropy-based fast stationary complex algorithm (C-FastICA).
However, the actual signal is generally a mixed signal containing noise, and if the mixed signal is subjected to noise reduction processing first, the effective signal is damaged to some extent, which affects the estimation accuracy of the subsequent separation matrix. However, by directly estimating the separation matrix using the conventional noise-free ICA model, the performance of the algorithm is degraded quickly when the noise is large and even the separation fails. The existing noisy independent component analysis algorithm can be roughly divided into three types, namely a high-order cumulative quantity method, a deviation removal algorithm and an algorithm based on signal time characteristics. Among them, the offset removal technique is a method that is much studied and corrects a general (noiseless) ICA method to remove or reduce an offset due to noise. Such ICA algorithms require that the noise variance is known, or even that each mixed signal has the same noise variance, which in practice means that some additional methods or a priori knowledge need to be used to estimate the model covariance matrix, which methods are to some extent independent of the method of estimation of the mixing matrix. How to acquire the covariance matrix of the noise is an important factor affecting the separation accuracy. Under the condition of noisy convolution mixing, a traditional method generally does not consider a noise item, but directly uses a noiseless model to separate a mixed signal, and the separation precision cannot be ensured because the convolution model is complex.
Disclosure of Invention
The invention aims to provide a method for separating a convolution blind source of a noisy frequency domain so as to overcome the defects of the prior art.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for separating a convolution blind source of a frequency domain containing noise comprises the following steps,
step 1), establishing a thin plate spline smoothing model for an observation signal x to be analyzed, and estimating smoothing parameters in the thin plate spline smoothing model by using GCV (generalized regression vector) so as to obtain a covariance matrix sigma of noise in a mixed signal;
step 2), carrying out short-time Fourier transform on an observation signal X to be analyzed to obtain a corresponding time-frequency domain complex matrix X;
step 3), forming an observation data matrix by the time-frequency points with the frequency band of k in the time-frequency domain complex matrix X
Figure BDA0001832468370000031
Estimating a separation matrix by using a noise complex value ICA method based on kurtosis depolarization, and further preliminarily obtaining a separation data matrix
Figure BDA0001832468370000032
Step 4), using a sorting algorithm and a minimum distortion method to respectively separate data
Figure BDA0001832468370000033
Carrying out sequencing correction and amplitude correction to obtain YkAnd then, the separated data of all frequency bands form a time-frequency domain complex matrix Y corresponding to the separated signals, and finally, the separated signals are restored to a time domain by short-time Fourier inversion so as to obtain the separated signals Y.
Further, step 1) for each observation signal x to be analyzedi(t) establishing a thin-plate spline smoothing model, and then estimating smoothing parameters in the model by using GCV (generalized regression curve) so as to obtain a covariance matrix sigma of noise in the mixed signal, wherein x (t) [ x ]1(t) x2(t) … xm(t)]TFor all observed signals, xi(T) denotes the ith observation signal of x (T), m denotes the number of observation signals, and T denotes a transpose operator; the ith observation signal x to be analyzedi(t)＝[xi1 xi2 … xiN]TWhere i is 1,2, …, m, N indicates the number of sample points.
Further, in step 1), i observation signals x to be analyzed are analyzedi(t) establishing a thin-plate spline smoothing model, and making x equal to xi(t); suppose that
Figure BDA0001832468370000041
Where ε is the mean 0 and the variance σ2The unknown gaussian noise is a function of the noise,
Figure BDA0001832468370000042
is a noiseless observation signal, and calculates the noise variance sigma2The following objective function is constructed:
Figure BDA0001832468370000043
wherein s is>0 is a smoothing parameter which is set to 0,
Figure BDA0001832468370000044
is composed of
Figure BDA0001832468370000045
In the form of a second order difference of (c),
Figure BDA0001832468370000046
is the square of the two norms; minimizing the above objective function can be obtained
Figure BDA0001832468370000047
Wherein INIs an N-dimensional unit square matrix.
Further, in step 1), the optimal smoothing parameters in the model are estimated by using a GCV method, that is:
Figure BDA0001832468370000048
where tr (-) is the operation to solve for the matrix trace;
wherein,
Figure BDA0001832468370000049
then the noise variance σ is obtained while the optimum s is obtained2Finally, the covariance matrix of m noises is obtainedMatrix of
Figure BDA00018324683700000410
Further, the i-th observation signal x to be analyzed in step 2)i(t) carrying out short-time Fourier transform to obtain a corresponding time-frequency domain complex matrix Xi＝[Xi，1 Xi，2 … Xi,J]At XiIn, the line represents frequency, the column represents time, Xi,jRepresents XiJ ═ 1,2, …, J; transforming all observed signals by short-time Fourier transform matrix XiCombined into a three-dimensional matrix X ═ Xijk]In the time-frequency domain complex matrix X, the rows represent the observed signal numbers, the columns represent the time, the pages represent the frequency, the row number of X is the observed signal number m, and the column number and the page number respectively correspond to XiColumn number and row number in (1).
Further, the observation data matrix in the step 3)
Figure BDA00018324683700000411
The data points obtained from page k of the three-dimensional matrix X, i.e. with frequency band k, constitute the observation matrix
Figure BDA00018324683700000412
In that
Figure BDA00018324683700000413
In which the rows represent the observed signal sequence numbers, the columns represent the times,
Figure BDA00018324683700000414
to represent
Figure BDA00018324683700000415
J is 1,2, …, J.
Further, in step 3), for each observation data to be analyzed
Figure BDA00018324683700000416
Combining the covariance matrix sigma of the noise obtained in step 1) with the observed data
Figure BDA0001832468370000051
Performing quasi-whitening operation, using covariance matrix C of noiseless data in whiteningk-∑，CkIs composed of
Figure BDA0001832468370000052
To obtain quasi-whitened data
Figure BDA0001832468370000053
Using the kurtosis of complex value as target function to find local maximum value of absolute value of kurtosis and obtain primary separated data matrix
Figure BDA0001832468370000054
Further, in the step 4), all the separated data matrixes are subjected to the correlation coefficient method and the minimum distortion method
Figure BDA0001832468370000055
Carrying out sequencing correction and amplitude correction to obtain accurate separation data matrix Yk。
Further, the separated data matrix Y of all frequency bands in step 4)kForming a time-frequency domain complex matrix Y corresponding to the separation signal, and restoring the separation signal to a time domain by using short-time Fourier inversion to obtain:
y(t)＝[y1(t) y2(t) … yn(t)]Tand n represents the number of observed signals.
Further, the maximum value of the cross-correlation function normalized by the source signal and the separation signal is used:
ρsy＝max Csy(τ)/σsσy
wherein C issy(τ) is the cross-correlation function, σ, of the original signal with the separated signalsIs the standard deviation, σ, of the source signalyIs the standard deviation of the separated signals.
Compared with the prior art, the invention has the following beneficial technical effects:
the invention discloses a method for separating a convolution blind source of a frequency domain containing noise, which comprises the steps of smoothing a mixed signal by utilizing a thin plate spline model for a convolution mixed signal with additive Gaussian noise, estimating the variance of the additive Gaussian noise in the mixed signal by utilizing a generalized cross verification method, converting the signal from a time domain to a frequency domain by short-time Fourier transform, estimating a separation matrix on each frequency band by utilizing a noise complex value independent component analysis method based on a deviation removal technology, further obtaining a separation signal of each frequency band, and ensuring the separation precision; then, sequencing correction and amplitude correction are respectively carried out on the separation signals by using a sequencing algorithm and a minimum distortion method; and finally, carrying out short-time inverse Fourier transform on the corrected signal to restore a separation signal, thereby obtaining the separation signal with high separation precision. Simulation tests show that the method can still maintain good separation performance under low signal-to-noise ratio.
Further, the estimated independent components are noisy, and therefore the isolated signal waveform has a glitch compared to the source signal, which is different from estimating the noise-free independent components, and the denoising of the independent components is another problem.
Drawings
FIG. 1 is a block diagram of the algorithm flow of the method of the present invention;
FIG. 2 is a waveform diagram of a simulation signal according to example 1 of the present invention; (ii) a
FIG. 3 is a comparison graph of variance estimation performance as described in example 1 of the present invention;
FIG. 4 is a source signal waveform and spectrum as described in example 2 of the present invention;
FIG. 5 is a waveform diagram of a hybrid filter according to example 2 of the present invention;
FIG. 6 is a waveform and spectrum of a mixed signal with a signal-to-noise ratio of 10dB according to example 2 of the present invention;
FIG. 7 is a waveform and spectrum of a separated signal obtained by the present invention as described in example 2 of the present invention;
FIG. 8 is a waveform and a spectrum of a separated signal obtained by the conventional invention described in example 2 of the present invention;
FIG. 9 is a graph comparing the separation performance described in example 2 of the present invention.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings:
a method for separating a convolution blind source of a frequency domain containing noise by using a convolution mixed model with additive Gaussian noise to separate a convolution mixed observation signal with noise comprises the following steps,
step 1), establishing a thin plate spline smoothing model for an observation signal x to be analyzed, and estimating smoothing parameters in the model by using GCV (generalized regression curve) so as to obtain a covariance matrix sigma of noise in a mixed signal;
step 2), carrying out short-time Fourier transform on an observation signal X to be analyzed to obtain a corresponding time-frequency domain complex matrix X;
step 3), forming an observation data matrix by the time-frequency points with the frequency band of k in the time-frequency domain complex matrix X
Figure BDA0001832468370000071
The separation matrix is estimated by using a noise complex value ICA method based on kurtosis depolarization, the estimation precision of the separation matrix is improved, and a separation data matrix is obtained preliminarily
Figure BDA0001832468370000072
Step 4), using a sorting algorithm and a minimum distortion method to respectively separate data
Figure BDA0001832468370000073
Carrying out sequencing correction and amplitude correction to obtain YkAnd then, the separated data of all frequency bands form a time-frequency domain complex matrix Y corresponding to the separated signals, and finally, the separated signals are restored to a time domain by short-time Fourier inversion to obtain Y.
For each observation signal x to be analyzed in step 1)i(t) establishing a thin plate spline smoothing model, and then estimating smoothing parameters in the model by using GCV (generalized regression curve) so as to obtain noise in the mixed signalCovariance matrix sigma, where x (t) x1(t) x2(t) … xm(t)]TFor all observed signals, xi(T) denotes the ith observation signal of x (T), m denotes the number of observation signals, and T denotes a transpose operator; the ith observation signal x to be analyzedi(t)＝[xi1 xi2 … xiN]TWhere i is 1,2, …, m, N indicates the number of sample points.
In step 1), i observation signals x to be analyzedi(t) establishing a thin-plate spline smoothing model, and making x equal to xi(t); suppose that
Figure BDA0001832468370000074
Where ε is the mean 0 and the variance σ2The unknown gaussian noise is a function of the noise,
Figure BDA0001832468370000075
is a noiseless observation signal, and calculates the noise variance sigma2The following objective function is constructed:
Figure BDA0001832468370000076
wherein s is>0 is a smoothing parameter which is set to 0,
Figure BDA0001832468370000077
is composed of
Figure BDA0001832468370000078
In the form of a second order difference of (c),
Figure BDA0001832468370000079
is the square of the two norms. Minimizing the above objective function can be obtained
Figure BDA00018324683700000710
Wherein INIs an N-dimensional unit square matrix.
In step 1), in order to reduce the influence of the smoothing parameter s, the optimal smoothing parameter in the model is estimated by using the GCV method, i.e. the optimal smoothing parameter is
Figure BDA00018324683700000711
Where tr (-) is the operation of finding matrix traces. Due to the fact that
Figure BDA00018324683700000712
The noise variance σ while the optimum s is obtained2Can also be obtained; because the noises are independent from each other, finally obtaining the covariance matrix of m noises
Figure BDA0001832468370000081
For the ith observation signal x to be analyzed in step 2)i(t) carrying out short-time Fourier transform to obtain a corresponding time-frequency domain complex matrix Xi＝[Xi，1 Xi，2 … Xi,J]At XiIn, the line represents frequency, the column represents time, Xi,jRepresents XiJ is 1,2, …, J. For each observation signal x to be analyzedi(t) performing the above operations in sequence, transforming the short-time Fourier transform matrix X of all the observed signalsiCombined into a three-dimensional matrix X ═ Xijk]In X, the row represents the number of observed signals, the column represents time, the page represents frequency, the row number of X is the number m of observed signals, and the column number and the page number are respectively corresponding to XiColumn number and row number in (1).
Observation data matrix in step 3)
Figure BDA0001832468370000082
Is obtained through the k page of the three-dimensional matrix X in the step 2), namely, the data points with the frequency band k form an observation matrix
Figure BDA0001832468370000083
In that
Figure BDA0001832468370000084
In which the rows represent the observed signal sequence numbers, the columns represent the times,
Figure BDA0001832468370000085
to represent
Figure BDA0001832468370000086
J is 1,2, …, J.
For each observation data to be analyzed in step 3)
Figure BDA0001832468370000087
Sequentially performing the operation of step 3), where K is 1,2, …, K indicates the number of frequency bands, and combining the covariance matrix Σ of the noise obtained in step 1) with the observation data
Figure BDA0001832468370000088
Performing quasi-whitening operation, using covariance matrix C of noiseless data in whiteningk-∑，CkIs composed of
Figure BDA0001832468370000089
To obtain quasi-whitened data
Figure BDA00018324683700000810
The local maximum of the kurtosis absolute value is found by taking the kurtosis of the complex value as a target function, the separation matrix is accurately and effectively estimated, and a preliminary separation data matrix is further obtained
Figure BDA00018324683700000811
Obtaining a separation data matrix in step 3)
Figure BDA00018324683700000812
There are sequence inconsistency and amplitude inconsistency, and the correlation coefficient method and the minimum distortion method are used in step 4 for all the signals
Figure BDA00018324683700000813
Carrying out sequencing correction and amplitude correction to obtain accurate separation data matrix Yk。
Step 4) separating data Y of all frequency bandskForming a time-frequency domain complex matrix Y corresponding to the separation signals, and separating the signals by short-time Fourier inversionThe signal is restored to the time domain to obtain:
y(t)＝[y1(t) y2(t) … yn(t)]Tand n represents the number of observed signals.
In step 4), in order to evaluate the performance of the method for estimating the separation signal, the maximum value of the normalized cross-correlation function of the source signal and the separation signal is utilized: rhosy＝max Csy(τ)/σsσyIn which C issy(τ) is the cross-correlation function, σ, of the original signal with the separated signalsIs the standard deviation, σ, of the source signalyIs the standard deviation of the separated signals.
The volume mixing model used in the invention is:
Figure BDA0001832468370000091
wherein the observation signal vector x (t) ═ x1(t),…,xm(t)]TSource signal vector s (t) ═ s1(t),…,sn(t)]TZero mean, unknown variance gaussian noise signal vector e (t) ═ e1(t),…,em(t)]T(the superscript "T" denotes transpose), L is the length of the FIR filter, AlThe dimension of the first coefficient matrix of filter a (t) is m × n (n source signals, m observed signals, where m is n in the present invention), and t is the discrete time index. To obtain a noise signal ei(t) the variance, i ═ 1, 2.. times, m, is modeled by a smooth spline nonparametric regression analysis method, and the variance of the noise in the noisy signal is obtained by a generalized cross-validation method
Figure BDA0001832468370000092
Because of mutual independence between noises, a covariance matrix of a noise signal vector e (t) is obtained
Figure BDA0001832468370000093
The goal for blind separation of multi-channel deconvolution is to find a length LτDeconvoluting to obtain y (t), which is expressed in matrix form
Figure BDA0001832468370000094
If the window length LwLong enough to contain a significant portion of the impulse response, the convolution mixture model can be approximated as an instantaneous mixture over each frequency band, i.e., over frequency band f, time period t, after a Short Time Fourier Transform (STFT) of the equation
Figure BDA0001832468370000095
The kurtosis of complex value is taken as an objective function, and a m multiplied by n separation matrix W is estimated on each frequency band by utilizing a complex ICA algorithm based on a deviation removal technologyfAnd
Figure BDA0001832468370000096
the order uncertainty problem (persistence algorithm) is an inherent problem of blind source separation algorithms. Since the independent component analysis is performed in each frequency band, the independent components in each frequency band are not in the same order. The order of the individual components of each frequency band needs to be determined before transforming the frequency domain signal into the time domain. The correct permutation matrix P (f) is sought after by using the correlation coefficient method for sorting correction, and W (f) is updated through W (f) → P (f) W (f). Thus, on each frequency band, a sorted separation signal Y (f, t) and a separation matrix W (f) are obtained, and the amplitude uncertainty is solved by using the minimum distortion criterion, i.e., W (f) ← diag (W)-1(f) And (f) finally, performing inverse discrete Fourier transform on the modified signal to obtain a separation signal y (t) on a time domain. The invention does not need to know the prior knowledge of the noise in the signal and presumes that the noise variances in all signal components are consistent, and when the signal-to-noise ratio is lower, the good estimation performance is still kept, and the invention has better robustness. And effective support is provided for the separation of the actual vibration noise source. A frequency domain blind separation process of a noisy frequency domain convolution blind source separation method based on thin-plate spline estimation of noise variance is shown in fig. 1.
The performance of the present invention is illustrated by two-part simulation experiments. A first part estimates a variance of noise in a noisy signal. And in the second part, a blind separation experiment is carried out by adopting a mechanical signal mixed by manual convolution, the separation effect is shown, and a noisy convolution mixing model is used in the experiment.
Example 1, to illustrate the superiority of the smooth spline non-parametric regression analysis method for the estimation of noise variance in noisy signals. An artificial signal is selected, the waveform of which is shown as the smooth curve portion in fig. 2. The simulation signal is a doppler signal and can be directly obtained by a matlab internal function 'woise', the sampling time is 1s, and the sampling frequency is 1024 Hz. Gaussian noise with a variance σ of 0.2 was added to the simulated signal to obtain a red partial curve as shown in fig. 2.
Noise with different variances is added into a pure doppler signal in sequence, the variance of the noise in the noisy signal is estimated by using a smooth spline non-parametric regression analysis method and a median variance estimation method, 10 experiments are performed on each variance value, and finally the average value of the results of the 10 experiments is taken, and the obtained result is shown in fig. 3. Comparing the estimated value and the true value of the two methods in fig. 3 shows that the noise variance estimated by the regression analysis method is statistically more accurate and has less discreteness with respect to the true value.
Example 2 to illustrate the separation performance of the method of the invention, 4 signals were chosen as source signals, which are expressed as follows:
1) impact signal: s1(t) from f0Ss of one cycle1The components of the composition are as follows,
Figure BDA0001832468370000111
wherein f is0＝20Hz，TL＝1/f0，σ1＝0.005，tt＝0:1/Fs:TL，A1＝0.04×(1+randn(1,f0×TL)/4)；
2) Amplitude modulation signal: s2(t)＝sin(2π×100×t)×(1+sin(2π×16×t))；
3) Frequency modulation signal: s3(T) ═ cos (2 pi × 60 × T + randn +4 × cos (10 × + randn)), the sampling frequency and the sampling time are Fs ═ 5000Hz, and T ═ 1s, respectively;
4) sinusoidal signals: s4(t)＝sin(2π×70×t)。
The time domain waveform and the frequency spectrum of the source signal are shown in fig. 4, and four mixed signals are obtained by adding gaussian noise after the source signal is subjected to convolution mixing. The number of observations P is 4 and the number of sources Q is 4. The hybrid filter adopts a single-side oscillation attenuation FIR filter with the order of R being 20, and FIG. 5 is a waveform diagram of the hybrid filter.
Fig. 6 shows the waveform and spectrum of the mixed signal at a signal-to-noise ratio of 10 dB. Taking L as window length of time-short Fourier transform of separation signalw Frame shifting S40 w5. The normalized maximum cross-correlation coefficient is used to measure the waveform similarity of the two signals in the delay sense. The cross-covariance function of the two signals x (t) and y (t) is:
Figure BDA0001832468370000112
in the formula uxAnd uyThe mean values of x (t) and y (t), respectively.
In practice the cross-correlation coefficient (i.e. normalized or normalized cross-correlation function) of two signals
Figure BDA0001832468370000113
In the formula, Cxy(τ) is a cross-covariance function, σxIs the standard deviation of x (t) (. sigma.)yIs the standard deviation of y (t).
The waveform and spectrum of the separated signal obtained by the method of the invention are shown in fig. 6, and the cross correlation coefficient of the separated signal and the source signal is as follows:
Figure BDA0001832468370000121
the waveform and spectrum of the separated signal obtained by the conventional method without considering the influence of noise are shown in fig. 7, and the cross-correlation coefficient matrix of the separated signal and the source signal is:
Figure BDA0001832468370000122
it can be preliminarily seen that, when the signal-to-noise ratio is low, three source signals can be basically estimated by the conventional method, but the other source signal fails to be separated, and for the method, four source signals can be well estimated, so that a good separation effect can be achieved. It is noted that the estimated independent components are noisy and therefore the isolated signal waveform has a spur compared to the source signal, which is to be distinguished from the estimation of noise-free independent components, the denoising of which is another problem.
In order to objectively illustrate the separation performance of the method, a traditional method is used as a contrast, noise with different signal-to-noise ratios is added into a convolution mixed signal, and the separation parameters are as follows: window length L w40, frame shift S w5. FIG. 9 is a graph comparing the correlation coefficients of the source signal and the isolated signal under different SNR conditions in the method and the conventional method in example 2, wherein each data is an average value obtained by repeating 10 times under the same parameters. The four graphs in fig. 9 show the curves of the correlation coefficients of the four source signals and the separated signal at different signal-to-noise ratios. It can be seen from the figure that under the condition of low signal-to-noise ratio, the separation performance of the method is better compared with that of the traditional method, and when the signal-to-noise ratio is higher, the separation performance of the two methods is basically consistent, which shows that the method has better robustness to noise.

Claims (7)

1. A method for separating a convolution blind source of a frequency domain containing noise is characterized by comprising the following steps,
step 1), establishing a thin plate spline smoothing model for an observation signal x to be analyzed, and estimating smoothing parameters in the thin plate spline smoothing model by using GCV (generalized regression vector) so as to obtain a covariance matrix sigma of noise in a mixed signal; for each observation signal x to be analyzedi(t) establishing a thin-plate spline smoothing model, and then estimating smoothing parameters in the model by using GCV (generalized regression curve) so as to obtain a covariance matrix sigma of noise in the mixed signal, wherein x (t) [ x ]1(t) x2(t) … xm(t)]TFor all observed signals, xi(t) denotes the ith observation signal of x (t), and m denotes an observation signalThe number of the numbers, T, represents a transposition operator; the ith observation signal x to be analyzedi(t)＝[xi1 xi2 … xiN]TWherein i is 1,2, …, m, N represents the number of sampling points;
for i observation signals x to be analyzedi(t) establishing a thin-plate spline smoothing model, and making x equal to xi(t); suppose that
Figure FDA0003422184040000011
Where ε is the mean 0 and the variance σ2The unknown gaussian noise is a function of the noise,
Figure FDA0003422184040000012
is a noiseless observation signal, and calculates the noise variance sigma2The following objective function is constructed:
Figure FDA0003422184040000013
wherein s > 0 is a smoothing parameter,
Figure FDA0003422184040000014
is composed of
Figure FDA0003422184040000015
In the form of a second order difference of (c),
Figure FDA0003422184040000016
is the square of the two norms; minimizing the above objective function can be obtained
Figure FDA0003422184040000017
Wherein INIs an N-dimensional unit square matrix;
and (3) estimating the optimal smoothing parameters in the model by using a GCV method, namely:
Figure FDA0003422184040000018
where tr (-) is the operation to solve for the matrix trace;
wherein,
Figure FDA0003422184040000019
then the noise variance σ is obtained while the optimum s is obtained2Finally, the covariance matrix of m noises is obtained
Figure FDA00034221840400000110
Step 2), carrying out short-time Fourier transform on an observation signal X to be analyzed to obtain a corresponding time-frequency domain complex matrix X;
step 3), forming an observation data matrix by the time-frequency points with the frequency band of k in the time-frequency domain complex matrix X
Figure FDA0003422184040000021
Estimating a separation matrix by using a noise complex value ICA method based on kurtosis depolarization, and further preliminarily obtaining a separation data matrix
Figure FDA0003422184040000022
Step 4), using a sorting algorithm and a minimum distortion method to respectively separate data
Figure FDA0003422184040000023
Carrying out sequencing correction and amplitude correction to obtain YkAnd then, the separated data of all frequency bands form a time-frequency domain complex matrix Y corresponding to the separated signals, and finally, the separated signals are restored to a time domain by short-time Fourier inversion so as to obtain the separated signals Y.
2. The method according to claim 1, wherein the ith observation signal x to be analyzed in step 2) is subjected to convolution blind source separation in a noisy frequency domaini(t) carrying out short-time Fourier transform to obtain a corresponding time-frequency domain complex matrix Xi＝[Xi，1 Xi，2… Xi,J]At XiIn, the line represents frequency, the column represents time, Xi,jRepresents XiJ ═ 1,2, …, J; transforming all observed signals by short-time Fourier transform matrix XiCombined into a three-dimensional matrix X ═ Xijk]In the time-frequency domain complex matrix X, the rows represent the observed signal numbers, the columns represent the time, the pages represent the frequency, the row number of X is the observed signal number m, and the column number and the page number respectively correspond to XiColumn number and row number in (1).
3. The method as claimed in claim 2, wherein the observation data matrix in step 3) is a matrix of the blind sources
Figure FDA0003422184040000024
Obtained from page k of the three-dimensional matrix X, i.e. the data points of band k form the observation matrix
Figure FDA0003422184040000025
In that
Figure FDA0003422184040000026
In which the rows represent the observed signal sequence numbers, the columns represent the times,
Figure FDA0003422184040000027
to represent
Figure FDA0003422184040000028
J is 1,2, …, J.
4. The method as claimed in claim 1, wherein the blind source separation method is performed in step 3) for each observation data to be analyzed
Figure FDA0003422184040000029
Combining the covariance matrix sigma of the noise obtained in step 1) with the observed data
Figure FDA00034221840400000210
Performing quasi-whitening operation, using covariance matrix C of noiseless data in whiteningk-∑，CkIs composed of
Figure FDA0003422184040000031
To obtain quasi-whitened data
Figure FDA0003422184040000032
Using the kurtosis of complex value as target function to find local maximum value of absolute value of kurtosis and obtain primary separated data matrix
Figure FDA0003422184040000033
5. The method as claimed in claim 4, wherein the correlation coefficient method and the minimum distortion method are used in step 4) to separate all the separated data matrices
Figure FDA0003422184040000034
Carrying out sequencing correction and amplitude correction to obtain accurate separation data matrix Yk。
6. The method as claimed in claim 5, wherein the matrix Y of the separated data of all frequency bands in step 4) is obtainedkForming a time-frequency domain complex matrix Y corresponding to the separation signal, and restoring the separation signal to a time domain by using short-time Fourier inversion to obtain:
y(t)＝[y1(t) y2(t) … yn(t)]Tand n represents the number of observed signals.
7. The method according to claim 6, wherein the maximum value of the cross-correlation function of the source signal normalized with the separation signal is used:
ρsy＝max Csy(τ)/σsσy
wherein C issy(τ) is the cross-correlation function, σ, of the original signal with the separated signalsIs the standard deviation, σ, of the source signalyIs the standard deviation of the separated signals.
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