CN101329197A - Method for extracting signal under strong noise background - Google Patents

Abstract

The invention relates to a signal extracting method under high-noise background, which solves the problem that signal extraction that is implemented directly with existing models on the basis of the stochastic resonance principle has larger limitation. The signal extracting method from high-noise background comprises the following concrete steps: a noise-containing input signal s(t) is amplified by K times and taken as an input signal S(t) to be processed; the input signal S(t) to be processed is processed by using a piecewise linear mathematical model; the values of real parameters a and b are adjusted; the value of a real parameter c is adjusted so as to reach the aim that frequency f of an input signal H(t) can be distinguished by using a processed output signal x(t); if the frequency f of the input signal H(t) cannot be distinguished, the value of K is reset in the domain of K. With the piecewise model, the signal extracting method of the invention has relatively independent influence of the parameters to system feature values and easy parameter adjustment, is easy to achieve optimal working state of the system by adjusting the parameters, and can extract signals from the high-noise background.

Description

A kind of method of under strong noise background, extracting signal

Technical field

The invention belongs to input and processing technology field, especially belong to input and squelch field based on the accidental resonance principle, related to based on a kind of new piecewise-linear system model, utilized the accidental resonance principle under strong noise background, to extract the method for useful signal and inhibition noise.

Background technology

The phenomenon of accidental resonance is found by scientists such as Benzi at first, that is: when a non-linear continuous bistable system model is imported faint periodic signal and noise signal simultaneously, under the suitable parameters condition, when noise is strengthened to a certain intensity, signal to noise ratio (S/N ratio) not only can not reduce, the phase inverted output signal can significantly be strengthened, and this phenomenon is called as " accidental resonance " phenomenon.Being found to be of this phenomenon utilized the accidental resonance principle to extract useful signal under strong noise background and opened up a new way.

Input based on the accidental resonance principle is non-linear continuous bistable system model with handling the system model that uses at present, claims Lang Zhiwan (Langevin) equation again, and this equation is seen formula (1):

$\stackrel{\·}{x}=\mathrm{\μx}-x^3+H\left(t\right)+\mathrm{\η}\left(t\right)---\left(1\right)$

Wherein H (t) represents input signal, and η (t) represents noise signal, μ＞0th, systematic parameter.

Its potential function is described below:

$U_l\left(x\right)=-\frac{\mathrm{\μ}}{2}{x}^2+\frac{1}{4}{x}^4---\left(2\right)$

Bright ten thousand (Langevin) equation also can be written as:

$\stackrel{\·}{x}=\mathrm{ax}-b{x}^3+H\left(t\right)+\mathrm{\η}\left(t\right)---\left(3\right)$

Wherein, parameter a＞0, b＞0, its potential function then is written as:

$U_l\left(x\right)=-\frac{a}{2}{x}^2+\frac{b}{4}{x}^4---\left(4\right)$

Up to now, be core normally based on accidental resonance (SR) input that principle proposed or extracting method with above-mentioned non-linear continuous bistable system model.

The shortcoming of this class model is: 1. in signal frequency f to be detected＜＜1 o'clock, system can produce accidental resonance, and when signal frequency f to be detected＞1, system is difficult to produce accidental resonance.Thereby, directly realize that in the accidental resonance principle signal extraction under the noise background has bigger limitation with above-mentioned model-based.Because the signal frequency in most of practical applications all can be greater than 1.A kind of preferably at present improving one's methods is earlier with signal process double sampling or transformation of scale.But this has increased the complicacy that realizes, also is unfavorable for the processing to live signal.

2. the parameter of non-linear continuous bistable system model and the configuration of system, feature are closely related.The change of parameter can influence the total system characteristic, so in use, choosing and regulating of parameter is relatively more difficult, and it usually is that conflict is arranged mutually that parameter regulation requires.

Summary of the invention

The objective of the invention is at the deficiencies in the prior art, a kind of method that can extract useful signal under strong noise background is provided.

Concrete grammar of the present invention is:

1. will contain noise input signal s (t) and amplify K doubly as pending input signal S (t), S (t)=Ks (t), wherein, and s (t)=H (t)+η (t), H (t) represents input signal, η (t) represents noise signal; The K value is set according to the frequency f of input signal H (t): f＜1 o'clock, K=1; F 〉=1 o'clock, K=nf, 2≤n≤100.

2. pending input signal S (t) is handled, the mathematical model of processing is the piecewise linearity mathematical model, is expressed as:

Wherein,

Expression x (t) differentiates, and x (t) is the output signal after handling, and a, b, c are real parameter, and a＞b＞0, c＞0;

3. regulate the value of real parameter a and b, concrete grammar is:

At first set 0＜b＜10;

In b＜a≤2b scope, regulate the value of real parameter a then.

4. the value of regulating real parameter c is to utilizing the output signal x (t) after handling can offer an explanation out the frequency f of input signal H (t), and concrete control method is: the frequency f according to input signal H (t) is regulated: when f＜1, c regulates in the scope of 0＜c≤1; When f 〉=1, c regulates in the scope of 1＜c≤2000, and frequency f is high more, and the c value is big more.

5. if can not offer an explanation out the frequency f of input signal H (t) by step 4, return step 1, in the span of K, reset K value, repeating step 1～4.

Among the present invention, after obtaining the output signal x (t) of system, if the parameter of piecewise-linear system is adjusted in suitable value, then noise signal is weakened greatly, make and mainly contain input signal H (t) information among the x (t), thereby reach the purpose that from noise, extracts useful signal; If the parameter of piecewise-linear system is not adjusted in suitable value, then noise signal can not be weakened, and useful signal can not be extracted out, then can solve by the method that above-mentioned parameter is repeatedly revised.

The present invention proposes a kind of new piecewise-linear system model, it is different that this model and continuous nonlinear model have essence, and its model is described by 4 linear equation segmentations.With this model is the method for the present invention's proposition of core, not only can detect the signal of frequency f＜＜1 under very noisy, and can detect the signal of frequency f＞＞1 under very noisy.

Because the segmenting of model, parameter is relatively independent to the influence of system features value, and then parameter is easy to regulate, thereby, be easier to make system reach optimum Working by regulating parameter.

Be subjected to noise pollution signal detection with no matter extract in military field, industrial circle and civil area all extensively exist, and go back neither one the best way at present, so the present invention has excellent application value.

Description of drawings

Fig. 1 is first kind of situation of the embodiment of the invention, the result of frequency f=0.01 of input signal H (t);

Fig. 2 is second kind of situation of the embodiment of the invention, the result of frequency f=100 of input signal H (t);

Fig. 3 is the third situation of the embodiment of the invention, the result of frequency f=1000 of input signal H (t).

Embodiment

Effect of the present invention for convenience of explanation.Embodiment gets input signal H (t)=A ₀Cos2 π ft, wherein, A ₀Be signal amplitude, t represents the time, f representation signal frequency.Noise signal D η (t) is the white Gaussian noise of zero-mean, and D is a noise intensity.The number of winning the confidence frequency f=0.01, three kinds of situations of f=100, f=1000 realize with method of the present invention respectively.Specific implementation is to realize with numerical computation method.

First kind of situation: f=0.01, D=2, A ₀=0.5, noise intensity D is signal amplitude A as can be seen ₀4 times.

1. will contain noise input signal s (t) and amplify K doubly as pending input signal S (t), S (t)=Ks (t), the K value is set at K=1;

2. pending input signal S (t) is handled, handling used mathematical model is piecewise linearity mathematical model of the present invention, is expressed as:

Above-mentioned mathematical model has adopted the numerical computation method euler algorithm when concrete calculating.

3. regulate the value of real parameter a and b, at first set b=1, regulate real parameter a=2 then.

4. regulate the value of real parameter c to c=0.25.

5. after parameter regulation was determined, this model calculated through the euler algorithm recursion, and noise signal is weakened greatly among the time dependent output signal x (t) after obtaining handling, x (t), and mainly contained the information of input signal H (t), referring to shown in Figure 1.Fig. 1 among Fig. 1 (a) is the time-domain diagram of input signal s (t), and Fig. 1 (c) is the time-domain diagram of output signal x (t).From Fig. 1 (a) as can be seen, signal H (t) is flooded by noise fully, can't distinguish.Contrast Fig. 1 (a) and Fig. 1 (c) as can be seen, noise is eliminated greatly after treatment, and signal can be distinguished.Fig. 1 (b) is the frequency domain figure of input signal s (t), and Fig. 1 (d) is the frequency domain figure of output signal x (t), and also as can be seen, noise signal is weakened greatly from the frequency domain figure, and the useful signal at the f=0.01 place is highlighted.

Second kind of situation: f=100, D=16, A ₀=1, noise intensity D is signal amplitude A ₀16 times, noise is very strong.

1. will contain noise input signal s (t) and amplify K doubly as pending input signal S (t), S (t)=Ks (t), the K value is set at K=2000;

2. pending input signal S (t) is handled, handling used mathematical model is piecewise linearity mathematical model of the present invention, is expressed as:

Above-mentioned mathematical model has adopted the numerical computation method euler algorithm when concrete calculating.

3. regulate the value of real parameter a and b, at first set b=1, regulate real parameter a=0.05+b then.

4. regulate the value of real parameter c to c=60.

5. after parameter regulation was determined, this model calculated through the euler algorithm recursion, and noise signal is weakened greatly among the time dependent output signal x (t) after obtaining handling, x (t), and mainly contained the information of input signal H (t), referring to shown in Figure 2.Fig. 2 among Fig. 2 (a) is the time-domain diagram of input signal s (t), and Fig. 2 (c) is the time-domain diagram of output signal x (t).From Fig. 2 (a) as can be seen, signal H (t) is flooded by noise fully, can't distinguish.Contrast Fig. 2 (a) and Fig. 2 (c) as can be seen, noise is eliminated greatly after treatment, and signal can be distinguished.Fig. 2 (b) is the frequency domain figure of input signal s (t), and Fig. 2 (d) is the frequency domain figure of output signal x (t), and also as can be seen, noise signal is weakened greatly from the frequency domain figure, and the useful signal at the f=100 place is highlighted.

The third situation: f=1000, D=6, A ₀=0.3, noise intensity D is signal amplitude A ₀20 times, and A ₀Be 0.3 only, illustrate that signal to be extracted compares very faint with noise.To this situation, use additive method, almost can't extract useful signal.

1. will contain noise input signal s (t) and amplify K doubly as pending input signal S (t), S (t)=Ks (t), the K value is set at K=30000;

2. pending input signal S (t) is handled, handling used mathematical model is piecewise linearity mathematical model of the present invention, is expressed as:

Above-mentioned mathematical model has adopted the numerical computation method euler algorithm when concrete calculating.

3. regulate the value of real parameter a and b, at first set b=1, regulate real parameter a=0.01+b then.

4. regulate the value of real parameter c to c=100.

5. after parameter regulation was determined, this model calculated through the euler algorithm recursion, and noise signal is weakened greatly among the time dependent output signal x (t) after obtaining handling, x (t), and mainly contained the information of input signal H (t), referring to shown in Figure 3.Fig. 3 among Fig. 3 (a) is the time-domain diagram of input signal s (t), and Fig. 3 (c) is the time-domain diagram of output signal x (t).From Fig. 3 (a) as can be seen, signal H (t) is flooded by noise fully, can't distinguish.Contrast Fig. 3 (a) and Fig. 3 (c) as can be seen, noise is eliminated greatly after treatment, and signal can be distinguished.Fig. 3 (b) is the frequency domain figure of input signal s (t), and Fig. 3 (d) is the frequency domain figure of output signal x (t), and also as can be seen, noise signal is weakened greatly from the frequency domain figure, and the useful signal at the f=1000 place is highlighted.

For the effect and the advantage of outstanding this method, the foregoing description has all been selected the strong noise background signal.Especially the third situation under so strong noise background, under the condition of f＞＞1, is used this method, can weaken noise widely, has fully shown the superiority of this method.In the reality, general noise can be relatively a little less than.In addition, the signal that this method extracts in the example also contains certain noise, and the needs that this can use according to reality again are through further filtering or smoothing processing.Concerning the person skilled in art, method for subsequent processing is comparative maturity, no longer describes in detail.

Claims (1)

1, a kind of method of extracting signal under strong noise background is characterized in that the step of this method is:

(1) will contain noise input signal s (t) and amplify K doubly as pending input signal S (t), S (t)=Ks (t), wherein, and s (t)=H (t)+η (t), H (t) represents input signal, η (t) represents noise signal; The K value is set according to the frequency f of input signal H (t): f＜1 o'clock, K=1; F 〉=1 o'clock, K=nf, 2≤n≤100;

(2) pending input signal S (t) is handled, the mathematical model of processing is the piecewise linearity mathematical model, is expressed as:

Wherein,

Expression x (t) differentiates, and x (t) is the output signal after handling, and a, b, c are real parameter, and a＞b＞0, c＞0;

(3) value of adjusting real parameter a and b, concrete grammar is:

At first set 0＜b＜10;

In b＜a≤2b scope, regulate the value of real parameter a then;

(4) value of regulating real parameter c is to utilizing the output signal x (t) after handling can offer an explanation out the frequency f of input signal H (t), and concrete control method is: the frequency f according to input signal H (t) is regulated: when f＜1, c regulates in the scope of 0＜c≤1; When f 〉=1, c regulates in the scope of 1＜c≤2000, and frequency f is high more, and the c value is big more;

(5) if can not offer an explanation out the frequency f of input signal H (t), return step (1), in the span of K, reset the K value, repeating step (1)～(4) by step (4).

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