CN103970716A - Signal decomposition and reconstruction method based on independent sub elements - Google Patents

Abstract

The invention discloses a signal decomposition and reconstruction method based on independent sub elements. The independent sub elements are used for decomposing and reconstructing any signals. One signal can be converted to linear superposition of a series of the independent sub elements, the conversion can be regarded as the process that n-dimensional time domain space data are projected to an m-dimensional independent sub space, irrelevance originally hidden in the signals can be highlighted through independent element analysis, and data of a new space have statistics independence. The new method is used for processing the signals in a statistics domain, the signals are converted to the statistics domain for representation, a plurality of advantages of the linear conversion are inherited, the statistics independent features of the signals are highlighted, and the independent sub elements are used for decomposing and reconstructing any signals.

Description

A kind of based on first signal decomposition and the reconstructing method of independent son

Technical field

The present invention relates to a kind of signal decomposition and reconstructing method, belong to signal processing technology field in communication engineering.

Background technology

Normally time series of signal in Practical Project, but researchist interested be the feature of detection signal, these features are often not necessarily obvious in time series.In order to highlight some physical features of signal, time-domain signal is transformed to other transform domains and play vital effect, modal FFT, wavelet transformation, Huang, time-frequency combination analysis (JTFA), Multi-channel signal analysis etc.

FFT is the fast algorithm of discrete Fourier transform (DFT), a signal can be transformed to frequency domain.What feature some signal is difficult to find out in time domain, if but after transforming to frequency domain, be just easy to find out feature.Here it is, and a lot of signal analysis adopt the reason of FFT conversion.

Wavelet analysis is a kind of emerging branch of mathematics, and it is the most perfect crystallization of functional, Fourier analysis, harmonic analysis, numerical analysis; In application, particularly in signal processing, image processing, speech processes and numerous nonlinear science field, it is considered to the another effective Time-Frequency Analysis Method after Fourier analyzes.Wavelet transformation is compared with Fourier conversion, be a time and frequency domain local conversion thereby can information extraction from signal effectively, by calculation functions such as flexible and translations, function or signal are carried out to multiscale analysis (Multiscale Analysis), solved the indeterminable many difficult problems of Fourier conversion.

1998, the people such as Norden E.Huang have proposed empirical mode decomposition method, and the concept of Hilbert spectrum and the method for Hilbert analysis of spectrum are introduced, American National aviation and NASA (NASA) are by this method called after Hilbert-HuangTransform, be called for short HHT, i.e. Hilbert-Huang transform.Fourier transform, short time discrete Fourier transform, wavelet transformation have a common feature, are exactly to select in advance basis function, and its account form is by producing with the convolution of basis function.HHT is different from these methods, and it converts and try to achieve phase function by Hilbert, then phase function differentiate is produced to instantaneous frequency.The instantaneous frequency of obtaining is like this locality, and the frequency of Fourier transform is of overall importance, and the frequency of wavelet transformation is zonal.

For time-domain signal, the many components composition possibility that adopts conventional transform method linear transformation to obtain is irrelevant, but conventionally can not meet the independently feature of adding up, and effectively avoids the redundancy of feature.

Summary of the invention

Technical matters to be solved by this invention is to provide a kind of based on first signal decomposition and the reconstructing method of independent son, utilizes independently son unit realization to decompose and reconstruct arbitrary signal.A signal can be transformed into the first linear superposition of a series of independent son, this conversion can be regarded as the problem of n dimension time domain spatial data to the projection of m dimension Independent subspace, highlight and be originally hidden in those irrelevances in signal by ICA, make the data in new space there is statistical independence.This method has not only been inherited the plurality of advantages of linear transformation, and has realized the statistics territory sign of signal, can complete the surely blind separation of owing without priori.

The present invention is for solving the problems of the technologies described above by the following technical solutions:

Based on first signal decomposition and the reconstructing method of independent son, wherein, described signal is n dimension finite energy signal, and making this signal is x (t), comprises following concrete steps:

Step 1, according to layering principle, adopts wavelet-decomposing method by signal x (t), resolves into multilayer signal y=y _j, wherein, y _jfor hierarchical signal, j=1,2 ..., m, m is independent wavelet number; Specific as follows:

When φ (t) is Orthogonal Scaling Function function, ψ (t) is mutually orthogonal small echo, and the result of the wavelet transformation of x (t) can be expressed as so:

$x_k\left(t\right)=\underset{n=-\∞}{\overset{\∞}{\mathrm{\Σ}}}{v}_{k,n}\mathrm{\φ}(2^{k}t-n)$

$g_k\left(t\right)=\underset{n=-\∞}{\overset{\∞}{\mathrm{\Σ}}}{d}_{k,n}\mathrm{\ψ}(2^{k}t-n)$

In formula, x _k(t) be the wavelet transformation form of Orthogonal Scaling Function function, g _k(t) be the variation of mutually orthogonal small echo, c _k,nand d _k,nwavelet conversion coefficient, 2 ^kbe yardstick or the contraction-expansion factor of discrete digital representation, n is shift factor;

Making y is the set of above-mentioned linear transform coefficient vector, is small echo hierarchical signal:

y＝[c _k,n,d _k,n] ^T；

Described layering principle is as follows:

A. between hierarchical signal, answer As soon as possible Promising Policy mutually orthogonal, show that the effect of signal layering is equivalent to projection on one group of orthogonal basis, this orthogonality of hierarchical signal is conducive to carry out next step independent component analysis, obtains independent son first;

B. the certain restructural of hierarchical signal goes out original signal, has shown that signal layering should have reconfigurability;

C. hierarchical signal should have identical length with original signal, makes hierarchical signal meet the pacing items that blind source separates, and the length between each source signal is identical;

Step 2, carries out independent component analysis to y, the sub first b=b of independence of picked up signal x (t) _j, wherein, b _jfor corresponding hierarchical signal y _jindependent son unit; Be specially:

The covariance matrix of hierarchical signal y is c _x=E{y, y ^t, E=(e ₁... ..e _m) be with c _xunit norm proper vector be example matrix, D=diag (d ₁... ..d _m) be with c _xthe eigenwert diagonal matrix that is diagonal element, order:

Y＝(D ^-1/2E ^T)y；

For the new data Y after albefaction, can find a kind of combination b=wY, in order to make b=b _j(j=1,2 ..., m) independent as much as possible, data y is carried out to independent component analysis, obtain inverse matrix w;

Step 3, is reconstructed signal x (t), and reconstruction formula is: wherein, Cj is reconstruction coefficients.

As further prioritization scheme of the present invention, the method for described in step 2, y being carried out to independent component analysis comprises fast independent component analysis (FastICA) or cosine independent component analysis or expansion independent component analysis.

As further prioritization scheme of the present invention, the C of reconstruction coefficients described in step 4 _jvalue is 1.

The present invention adopts above technical scheme, compared with existing FFT, wavelet transformation, Huang, time-frequency combination analysis (JTFA), Multi-channel signal analysis etc., the new method that provides a kind of signal to process in statistics territory, signal is transformed into statistics territory to be characterized, highlight the statistics independent characteristic of signal, realized and utilized independent sub-unit to decompose and reconstruct arbitrary signal.On the one hand, the feature of utilizing independent sub-unit to remove characterization signal, making between these features is to add up independently, avoids its redundancy; On the other hand, realize and do not need to utilize any training data just can from single channel non-stationary aliasing signal, isolate the blind separation of multiple source signals, complete the surely blind separation of owing without priori.

Wherein, this area common technology term the present invention relates to, as shown in the table.

Technical term	Chinese
		FFT	Fast Fourier Transform (FFT)
JTFA	Time-frequency combination is analyzed
		ICA	Independent component analysis
FastICA	Fast independent component analysis

Brief description of the drawings

Fig. 1 is process flow diagram of the present invention.

Fig. 2 is the schematic diagram of one-period cardiechema signals.

Fig. 3 is one-period cardiechema signals hierarchical signal schematic diagram.

Fig. 4 is one-period cardiechema signals hierarchical signal schematic diagram.

Fig. 5 is hierarchical signal the corresponding first schematic diagram of independent son.

Fig. 6 is hierarchical signal the corresponding first schematic diagram of independent son.

Fig. 7 is the schematic diagram of the one-period cardiechema signals of reconstruct.

Embodiment

Describe embodiments of the present invention below in detail, the example of described embodiment is shown in the drawings, and wherein same or similar label represents same or similar element or has the element of identical or similar functions from start to finish.Be exemplary below by the embodiment being described with reference to the drawings, only for explaining the present invention, and can not be interpreted as limitation of the present invention.

Those skilled in the art of the present technique are understandable that, unless specially statement, singulative used herein " ", " one ", " described " and " being somebody's turn to do " also can comprise plural form.Should be further understood that, the wording using in instructions of the present invention " comprises " and refers to and have described feature, integer, step, operation, element and/or assembly, exists or adds one or more other features, integer, step, operation, element, assembly and/or their group but do not get rid of.Should be appreciated that, when we claim element to be " connected " or " coupling " when another element, it can be directly connected or coupled to other elements, or also can have intermediary element.In addition, " connection " used herein or " coupling " can comprise wireless connections or couple.Wording "and/or" used herein comprises arbitrary unit of listing item and all combinations that one or more is associated.

Those skilled in the art of the present technique are understandable that, unless otherwise defined, all terms used herein (comprising technical term and scientific terminology) have with the present invention under the identical meaning of the general understanding of those of ordinary skill in field.Should also be understood that such as those terms that define in general dictionary and should be understood to have the meaning consistent with meaning in the context of prior art, unless and definition as here, can not explain by idealized or too formal implication.

Below in conjunction with accompanying drawing, technical scheme of the present invention is described in further detail:

The present invention designs a kind of signal decomposition and reconstructing method based on independent sub-unit, and wherein, described signal is finite energy signal, and making signal is x (t), as shown in Figure 1, comprises following concrete steps:

Step 1, according to layering principle, adopts wavelet-decomposing method by signal x (t), resolves into multilayer signal y=y _j, wherein, y _jfor hierarchical signal, j=1,2 ..., m, m is independent wavelet number;

Step 2, carries out independent component analysis to y, the sub first b=b of independence of picked up signal x (t) _j, wherein, b _jfor corresponding hierarchical signal y _jindependent son unit;

Step 3, is reconstructed signal x (t), and reconstruction formula is: wherein, C _jfor reconstruction coefficients.

Below by a specific embodiment, technical scheme of the present invention is further elaborated:

Hear sounds is a kind of natural sign of human body, is the external reflection of human heart physiologic information, possesses ubiquity, unique and collection property.Cardiechema signals is carried out to the research of denoising, feature extraction and sorting technique, aspect hear sounds intelligence auscultation and hear sounds identification, there is positive meaning.

The cardiechema signals of one-period can be described as:

$s_T\left(t\right)=\underset{t=1}{\overset{T}{\mathrm{\Σ}}}(c_1{s}_1\left(t\right)+c_2{s}_2\left(t\right)+c_3{s}_3\left(t\right)+c_4{s}_4\left(t\right)+c_5{s}_5\left(t\right))$

Wherein, s ₁(t), s ₂(t) be first and second cardiechema signals, s ₃(t), s ₄(t) be third and fourth weak hear sounds, s ₅(t) be hear sounds noise, c ₁, c ₂, c ₃, c ₄, c ₅for composite coefficient.

Cardiechema signals obviously can be transformed into the first linear superposition of a series of independent son, therefore, and according to calculating the independently general step of son unit, first to single channel monocycle cardiechema signals s _t(t) carry out layering processing, by s _t(t) be decomposed into the combination of a series of hierarchical signals that meet certain requirements: and then it is carried out to independent component analysis, obtain the independent son of hear sounds unit, and can reconstruct s by the independent sub-unit of these hear sounds _t(t).

Obviously, wavelet transformation meets foregoing layering principle, can obtain Q layer coefficients vector with the wavelet transformation bag model of standard, has utilize method of interpolation to make Z _qfor isometric, then Z is carried out to independent component analysis, have:

$\underset{q=1}{\overset{Q}{\mathrm{\Σ}}}{b}_q=\underset{p=1,q=1}{\overset{P,Q}{\mathrm{\Σ}}}{C}_{p,q}{Z}_q$

Wherein, C _p,qfor wavelet conversion coefficient.

Adopt fast independent component analysis (FastICA) to process to above formula, obtain the independent sub first b of one group of hear sounds _q.

According to reconstruction formula, have: wherein d _qfor reconstruction coefficients.

The cardiechema signals s of one-period _t(t) as shown in Figure 2, according to signal layering principle, carry out 2 layers of layering based on method of wavelet packet, available with wherein, as shown in Figure 3, as shown in Figure 4; Again based on fast independent component analysis (FastICA) method pair carry out independent component analysis, can obtain the independent sub first b of 2 hear sounds ₁and b ₂, wherein, b ₁as shown in Figure 5, as shown in Figure 6; According to reconstruction formula, can obtain the cardiechema signals s of the one-period of reconstruct _t(t) as shown in Figure 7.

According to s _t(t) periodicity, the s in any one cycle _t(t) should comprise the principal character of people's cardiechema signals, the independent sub first b of hear sounds in obvious some cycles _qit is exactly a kind of forms of characterization of this feature.By independent hear sounds first b _qas a kind of biological characteristic, order for standard group, be identified for tested group, the different distance that defines them is:

$d_k=1-\frac{\left|\underset{t=1}{\overset{M}{\mathrm{\Σ}}}{b}_q^i\left(t\right)b_q^i\left(t\right)\right|}{\sqrt{\underset{t=1}{\overset{M}{\mathrm{\Σ}}}{b}_q^{i2}\left(t\right)\underset{t=1}{\overset{M}{\mathrm{\Σ}}}{b}_q^{j2}\left(t\right)}}$

, d _kit is less, with more similar, when with when identical, d _k=0.

By first independent tested group of hear sounds with the independent son of standard group hear sounds unit carry out one by one pattern match, can hear sounds be identified and be classified by different range formula.

Following table is the average dissimilarity distance that the independent son of same person different time sections hear sounds unit has, because their different distance is not undergone mutation, so should there is not obvious pathology in this human heart organ, and the annual conventional physical examination of this people also proves that this conclusion is correct yet.

d k	ST2	2011	2012	2013
					S T3	0.0014	0.1413	0.1750	0.1638

The above; it is only the embodiment in the present invention; but protection scope of the present invention is not limited to this; any people who is familiar with this technology is in the disclosed technical scope of the present invention; can understand conversion or the replacement expected; all should be encompassed in of the present invention comprise scope within, therefore, protection scope of the present invention should be as the criterion with the protection domain of claims.

Claims (4)

1. based on first signal decomposition and the reconstructing method of independent son, wherein, described signal is finite energy signal, and making this signal is x (t), it is characterized in that, the method comprises following concrete steps:

Step 1, according to layering principle, adopts wavelet-decomposing method by signal x (t), resolves into multilayer signal y=y _j, wherein, y _jfor hierarchical signal, j=1,2 ..., m, m is independent wavelet number;

Step 2, carries out independent component analysis to y, the sub first b=b of independence of picked up signal x (t) _j, wherein, b _jfor corresponding hierarchical signal y _jindependent son unit;

Step 3, is reconstructed signal x (t), and reconstruction formula is: wherein, C _jfor reconstruction coefficients.

2. a kind of signal decomposition and reconstructing method based on independent sub-unit according to claim 1, is characterized in that, the principle of layering described in step 1 is:

A. between hierarchical signal, answer As soon as possible Promising Policy mutually orthogonal;

B. the certain restructural of hierarchical signal goes out original signal;

C. hierarchical signal should have identical length with original signal.

3. according to claim 1 a kind of based on first signal decomposition and the reconstructing method of independent son, it is characterized in that, the method for described in step 2, y being carried out to independent component analysis comprises fast independent component analysis or cosine independent component analysis or expansion Independent Component Analysis.

4. according to claim 1 a kind of based on first signal decomposition and the reconstructing method of independent son, it is characterized in that the C of reconstruction coefficients described in step 3 _jvalue is 1.