CN102608553A - Weak signal extracting method based on self-adaptive stochastic resonance - Google Patents

Abstract

Translated fromChinese

本发明公开了一种基于自适应随机共振的微弱信号提取方法，具体通过调节二次采样的尺度变换因子，可以很好地把微弱信号的频率调整到易于产生自适应随机共振的频率范围内，从而充分的利用了自适应随机共振的优良性能，可以很好的把微弱信号在极低信噪比下提取出来，有效地解决了现有的微弱信号处理方法在极低信噪比下表现不佳甚至失效的问题；同时在不知道微弱信号频率的情况下通过反馈的自动调节尺度变换因子使微弱信号经过二次采样后的信号频率能够匹配自适应随机共振系统并产生随机共振，从而能够很好地提取出微弱信号的特征。

The invention discloses a weak signal extraction method based on adaptive stochastic resonance. Specifically, by adjusting the scale conversion factor of secondary sampling, the frequency of the weak signal can be well adjusted to a frequency range that is easy to generate adaptive stochastic resonance. Therefore, the excellent performance of adaptive stochastic resonance can be fully utilized, and weak signals can be extracted well under extremely low signal-to-noise ratios, which effectively solves the problem that existing weak signal processing methods do not perform well under extremely low signal-to-noise ratios. At the same time, when the frequency of the weak signal is not known, the scale conversion factor can be automatically adjusted through feedback so that the signal frequency of the weak signal after resampling can match the adaptive stochastic resonance system and generate stochastic resonance, so that it can be easily It can extract the features of weak signals well.

Description

A kind of feeble signal method for distilling based on self-adapting random resonant

Technical field

The invention belongs to signal Processing and communication technical field, be specifically related to the extraction of feeble signal.

Background technology

Detection of Weak Signals occupies an important position at high-technology field, is prerequisite and basis that a lot of technology are applied.Generally be called feeble signal to the low-yield signal that is submerged in the strong background noise; Processing for feeble signal generally is that technology such as utilization modern signal processing method and electronics suppress noise; And then from strong background noise, extract feeble signal; But all there is certain limitation in existing method; (signal-to-noise ratio, SNR) higher relatively, the extraction effect of the feeble signal under extremely low SNR can not be expired actual demand mainly to show as the required signal to noise ratio (S/N ratio) of the detected feeble signal of ability.

Discover that (Stochastic Resonance, SR) principle is applied to obtain in the Detection of weak effect preferably to an accidental resonance.SR is a kind of nonlinear physical phenomenon; When having certain coupling between input signal, noise and the NLS; Noise energy can shift to signal energy; Making the signal to noise ratio (S/N ratio) of output signal ratio input signal increase, is that signal has obtained enhancing through the method for utilizing noise rather than inhibition noise like this.Yet the feeble signal of handling generally is not low especially; The SR system is not fine to the reinforced effects of big frequency signal; Though can lower the signal frequency of input SR system through methods such as double samplings; But under the situation of not knowing the feeble signal frequency, be not easy to confirm the coefficient factor of change of scale, and the SR system of preset parameter can not be real-time is complementary with noise and signal and has further weakened the humidification to signal.

Do an explanation in the face of the ultimate principle of double sampling down.

The ultimate principle of double sampling is: be transformed into high-frequency signal the low frequency signal that is complementary with stochastic resonance system through the change of scale factor R.The action principle of R is: the signal indication after the sampling is handled for

then as follows:

Like this R Δ t as new sampling time interval; Be applied to this new SI in the calculating of accidental resonance; Be equivalent to new signal frequency converting for f/R, be called the double sampling change of scale factor to R here, signal frequency has obtained reduction under the situation of visible R＞1; The concrete grammar of double sampling can reference: cold firm forever, and Wang Taiyong. double sampling is used for accidental resonance extracts weak signal from very noisy numerical value research. Acta Physica Sinica, 2003,52 (10): 2432～2437.But under the situation of the feeble signal frequency of not knowing to extract, be not easy to confirm the value of R; Still can not be when the R value is improper like this frequency adjustment of faint letter to being easy to produce in the scope of accidental resonance; Feeble signal can not get strengthening; So feeble signal still is submerged under the strong background noise, can't extract feeble signal.

Summary of the invention

The objective of the invention is the problem that can not satisfy demand in the practical application to the extraction of Detection of weak and signal characteristic in order to solve under the extremely low SNR.

Technical scheme of the present invention is following: a kind of feeble signal method for distilling based on self-adapting random resonant may further comprise the steps:

S1. initiation parameter: said parameter specifically comprises, double sampling change of scale factor R, the increase step delta R of the change of scale factor; The intrinsic parameter a of accidental resonance, the reference frequency f of generation accidental resonance_Ref, f_RefCalculating offset f; Zero-frequency calculates offset f₀Spectrum amplitude coefficient of comparisons m;

S2. confirm SR systematic parameter b: said SR system is described through langevin equation

; Wherein,

s (t) is a feeble signal; N (t) is that average is the noise of zero variance for

.Obtain noise variance

wherein according to receiving signal r (t); R (t)=s (t)+n (t) confirms parameter b by the value of a and

then;

S3. the signal r (t) that receives is carried out the double sampling that the change of scale factor is R, obtain signal W (t);

S4. signal W (t) tries to achieve signal X (t) through the langevin equation;

S5. X (t) is done Fourier transform, obtain Z (f), f is a frequency values, and Z (f) promptly is to be the spectrum amplitude value at f place in frequency;

S6. ask [f_Ref-Δ f, f_Ref+ Δ f] perhaps [f_Ref-Δ f ,-f_Ref+ Δ f] the maximal value of Z (f) in the scope, be designated as A_Ref, ask [Δ f₀, Δ f₀] the maximal value of Z (f) in the scope, be designated as A₀

If A S7._Ref>=m * A₀, then X (t) is the echo signal that comprises the feeble signal characteristic of extraction, otherwise with change of scale factor R assignment be R and Δ R with, promptly R=R+ Δ R forwards step S3 to.

Beneficial effect of the present invention: the present invention regulates the change of scale factor R of double sampling through the feedback of spectrum amplitude value; Thereby transform to the frequency that the self-adapting random resonant system is easy to produce accidental resonance to the feeble signal of input; And the combining adaptive stochastic resonance system can produce the superperformance of best resonance effect to feeble signal under extremely low SNR; Feeble signal has been realized that the optimum under the extremely low SNR extracts; Can clearly observe the characteristic of input feeble signal, well solve the problem that the feeble signal under the extremely low SNR is extracted.

Description of drawings

Fig. 1 is the structured flowchart of feeble signal method for distilling of the present invention.

Fig. 2 extracts schematic flow sheet for feeble signal of the present invention.

Fig. 3 is through the time domain plethysmographic signal figure after the preset parameter SR system.

Fig. 4 is through the time domain plethysmographic signal figure after the self-adaptation SR system.

Fig. 5 is through the feeble signal time domain waveform figure after the system handles of the present invention.

Fig. 6 is through the feeble signal amplitude spectrum after the preset parameter SR system.

Fig. 7 is through the feeble signal amplitude spectrum after the self-adaptation SR system.

Fig. 8 is through the feeble signal amplitude spectrum after the system handles of the present invention.

Embodiment

Feeble signal method for distilling of the present invention is set forth to Fig. 8 below in conjunction with Fig. 1, Fig. 1 is the structured flowchart of feeble signal method for distilling of the present invention, and Fig. 2 extracts schematic flow sheet for feeble signal of the present invention, specifically may further comprise the steps:

S1. initiation parameter: said parameter specifically comprises, double sampling change of scale factor R, the increase step delta R of the change of scale factor; The intrinsic parameter a of accidental resonance, the reference frequency f of generation accidental resonance_Ref, f_RefCalculating offset f; Zero-frequency calculates offset f₀Spectrum amplitude coefficient of comparisons m.

Value in the face of initial parameter is described in detail down:

f_RefValue be easy to produce the frequency values of accidental resonance for the self-adapting random resonant system, the input signal of discovering the self-adapting random resonant system is 5 * 10^-4Hz～3 * 10^-3Be easy to produce accidental resonance in the time of in the Hz scope, so f_RefNeed be [5 * 10^-4, 3 * 10^-3] the interior value of scope, generally can value be: f_Ref=0.001Hz.

Δ f representes f_RefThe calculating side-play amount, 0＜Δ f＜f_Ref, because f_RefValue less, so general Δ f value is f_RefNear/2.

Δ f₀The expression zero-frequency calculates side-play amount, 0＜Δ f₀＜f_Ref, general value is f_RefNear/2, and satisfy Δ f+ Δ f₀≤f_Ref

A is the intrinsic parameter of stochastic resonance system, in order to satisfy the adiabatic approximation theory, require a＞＞π f_s, wherein, f_sBe the frequency input signal of stochastic resonance system, input signal reference frequency f that can be when producing accidental resonance here_RefCome to confirm, promptly a＞＞π f_Ref

Estimate the possible minimum frequency f of feeble signal earlier_Min, and then confirm the initial value of R, the initial value of R is f_Min/ f_RefAs a preferred mode, the initial value of R can be R=1, and Δ R can confirm a suitable value according to iterations.

Can find by Fig. 7 and Fig. 8 contrast; Producing under the situation of accidental resonance the energy of noise can transfer to feeble signal and get on; Thereby near the spectrum amplitude the zero-frequency can be far smaller than near the range value of feeble signal place frequency behind the double sampling change of scale; Just in time as shown in Figure 7 on the contrary when if resonance effect is very poor, the self-adapting random resonant system produces under the accidental resonance good situations, and the value that near the ratio of the spectrum amplitude value of the noise of the spectrum amplitude value of resonance place frequency and zero-frequency can be used as m accordings to; M should be a minimum value possible in this ratio; So,, generally get 5≤m≤20 in order between the accuracy of computation complexity and extraction signal, to reach balance because this ratio is bigger value m＞＞1.

S2. confirm SR systematic parameter b: said SR system is described through langevin equation

; Wherein, s (t) is a feeble signal; N (t) is that average is the noise of zero variance for

.Obtain noise variance

wherein according to receiving signal r (t); R (t)=s (t)+n (t) confirms parameter b by the value of a and

then;

The concrete deterministic process of parameter b is following:

Utilize adiabatic approximation (Adiabatic Approximation) theory, when signal r (t)=s (t)+n (t) passed through the bistable state SR system of langevin equation definition, the SNR of output signal x (t) was:

${\mathrm{SNR}}_o=\left(\frac{\sqrt{2}a{A}_m^2{\mathrm{<figure-callout\; label="c"\; filenames="HDA0000144237740000021.png,HDA0000144237740000023.png"\; state="\{\{state\}\}">c</figure-callout>}}^2}{{\mathrm{\&sigma;}}_n^4}{e}^{-{2\mathrm{<figure-callout\; label="U"\; filenames="HDA0000144237740000021.png,HDA0000144237740000023.png"\; state="\{\{state\}\}">U</figure-callout>}}_0/{\mathrm{\&sigma;}}_n^2}\right){(1-\frac{\frac{{4a}^2{A}_m^2{\mathrm{<figure-callout\; label="c"\; filenames="HDA0000144237740000021.png,HDA0000144237740000023.png"\; state="\{\{state\}\}">c</figure-callout>}}^2}{{\mathrm{\&pi;}}^2{\mathrm{\&sigma;}}_n^2}{e}^{-4{\mathrm{<figure-callout\; label="U"\; filenames="HDA0000144237740000021.png,HDA0000144237740000023.png"\; state="\{\{state\}\}">U</figure-callout>}}_0/{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; label="n"\; filenames="HDA0000144237740000021.png,HDA0000144237740000023.png"\; state="\{\{state\}\}">n</figure-callout>}}^2}}{\frac{{2a}^2}{{\mathrm{\&pi;}}^2}{e}^{-4{\mathrm{<figure-callout\; label="U"\; filenames="HDA0000144237740000021.png,HDA0000144237740000023.png"\; state="\{\{state\}\}">U</figure-callout>}}_0/{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; label="n"\; filenames="HDA0000144237740000021.png,HDA0000144237740000023.png"\; state="\{\{state\}\}">n</figure-callout>}}^2}+{\left({2\mathrm{\&pi;f}}_s\right)}^2})}^{-1}\&ap;\frac{\sqrt{2}a{A}_m^2{\mathrm{<figure-callout\; label="c"\; filenames="HDA0000144237740000021.png,HDA0000144237740000023.png"\; state="\{\{state\}\}">c</figure-callout>}}^2}{{\mathrm{\&sigma;}}_n^4}{e}^{-2{\mathrm{<figure-callout\; label="U"\; filenames="HDA0000144237740000021.png,HDA0000144237740000023.png"\; state="\{\{state\}\}">U</figure-callout>}}_0/{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; label="n"\; filenames="HDA0000144237740000021.png,HDA0000144237740000023.png"\; state="\{\{state\}\}">n</figure-callout>}}^2}$

Wherein, a is the SR systematic parameter, A_mBe the amplitude of feeble signal s (t), c is the potential well point of bistable state SR system,

Be the variance of strong noise, U₀=a²/ (4b) be to work as A_mThe barrier height of=0 o'clock bistable state SR system.But concrete list of references: McNamara B, Wiesenfeld K.Theory of stochastic resonance, Physical Review A, 1989,39 (9): 4854-4869.

Because the average signal-to-noise ratio of input signal is:

Therefore, when accidental resonance took place, the output signal-to-noise ratio gain after reception signal r (t) the process bistable state SR system was:

Make k=a²/ b obviously has k＞0, then

Be given noise variance, output signal SNR gain η_SNRIt is the nonlinear function of systematic parameter k.

η_SNRSecond derivative to k is:

Therefore, in order to make η_SNRBe following concave function,, require so that obtain unique maximum value about k:

So the value of the optimum k of maximization SNR gain satisfies:$\left\{\begin{array}{c}{k}_{\mathrm{Op}}=\underset{k}{\mathrm{Arg}\mathrm{Max}}{\mathrm{\&eta;}}_{\mathrm{SNR}}\\ s.t.0<k<{4\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; label="n"\; filenames="HDA0000144237740000021.png,HDA0000144237740000023.png"\; state="\{\{state\}\}">n</figure-callout>}}^2\end{array}\right.,$Finding the solution following formula can get:

So the parameter of the bistable state SR system of maximization SNR gain need satisfy$\left\{\begin{array}{c}b=a^2/\left({2\mathrm{\&sigma;}}_n^2\right)\\ a>>\mathrm{\&pi;}{f}_{\mathrm{Ref}}\end{array}\right..$

In the present invention, a that obtains for following formula and the relation of b can be adjusted through an adjustment factor h, promptly$b=h{a}^2/\left({2\mathrm{\&sigma;}}_n^2\right).$

The SR system that dynamically changes parameter b at this this noise parameter according to the outside is called the self-adapting random resonant system.

S3. carry out the double sampling that the change of scale factor is R to the signal r (t) that receives, obtain signal W (t).

S4. signal W (t) tries to achieve signal X (t) through the langevin equation.

Be specially: find the solution the langevin equation through quadravalence Long Gekuta numerical computation method, the output signal that is the self-adapting random resonant system of separating of trying to achieve is designated as X (t);

S5. X (t) is done Fourier transform, obtain Z (f), f is a frequency values, and Z (f) promptly is to be the spectrum amplitude value at f place in frequency;

S6. ask [f_Ref-Δ f, f_Ref+ Δ f] perhaps [f_Ref-Δ f ,-f_Ref+ Δ f] the maximal value of Z (f) in the scope, be designated as A_Ref, ask [Δ f₀, Δ f₀] the maximal value of Z (f) in the scope, be designated as A₀

Δ f representes f here_RefThe calculating side-play amount; Because R is through being the value of series of discrete after the iteration, so the feeble signal of input is carried out after the change of scale through discrete R value, the frequency of feeble signal also can only be got discrete value; Can not get optional frequency, establish a small range [f to reference frequency like this_Ref-Δ f, f_Ref+ Δ f] perhaps [f_Ref-Δ f ,-f_Ref+ Δ f], as long as falling in this scope, the feeble signal behind the change of scale just can produce accidental resonance, through behind the Fourier transform, the maximal value A in this scope_RefThe frequency at place is the frequency at actual generation accidental resonance place.Avoided given f so effectively_Ref, but because the input signal behind the change of scale is not just in time got f_RefThis frequency, and the phenomenon of the iteration failure of R is taken place, also be simultaneously the condition of having relaxed of choosing of Δ R to make choosing of Δ R convenient.

Δ f₀The expression zero-frequency calculates side-play amount; The signal of finding stochastic resonance system output after deliberation through behind the Fourier transform sometimes under the situation that does not produce accidental resonance; The range value at possible zero-frequency point place is very little, but near range value is very big, so set a scope [Δ f₀, Δ f₀], get the maximal value A of spectrum amplitude in this scope₀Represent near the spectrum amplitude value of zero-frequency to be used for and A_RefCompare.Avoided the actual phenomenon that does not produce accidental resonance but judge by accident to take place so effectively to producing accidental resonance.

Improved the precision that judges whether to produce accidental resonance through after the above processing, and guaranteed that the iteration of R under the condition that signal exists can finish well.

If A S7._Ref>=m * A₀, then X (t) is the echo signal that comprises the feeble signal characteristic of extraction, otherwise with change of scale factor R assignment be R and Δ R with, promptly R=R+ Δ R forwards step S3 to.

Carry out emulation testing in the face of the inventive method down.The parameter of emulation is:

1) preset parameter stochastic resonance system: input sinusoidal signal s (t)=A_mSin (2 π ft), amplitude A_m=1, frequency f=0.01Hz, intrinsic parameter a=1, b=2, sampling period Δ t=0.02s, SNR=-20dB.

2) self-adapting random resonant system: input sinusoidal signal s (t)=A_mSin (2 π ft), amplitude A_m=1, frequency f=0.01Hz, a=2.4 * 10^-2, the sampling period is made as Δ t=0.02s, SNR=-20dB.

3) method of the present invention: input sinusoidal signal s (t)=A_mSin (2 π ft), amplitude A_m=1, frequency f=0.1Hz, a=2.4 * 10^-2, f_Ref=0.001Hz, Δ f=f_Ref/ 4, Δ f₀=f_Ref/ 2, R=1, Δ R=1, m=10.

Fig. 3 is that SNR is-20dB; Feeble signal is that frequency is the time domain waveform figure of the signal X (t) that exports after the stochastic resonance system of sine wave signal s (t) through preset parameter of 0.01Hz; Can observe when SNR=-20dB feeble signal and can not well extract, characteristics such as the frequency of signal, phase place are difficult to extract.

Fig. 4 is that SNR is-20dB; Feeble signal is that frequency is the time domain waveform figure of the signal X (t) that exports after through the self-adapting random resonant system of the sine wave signal s (t) of 0.01Hz; Can observe the general shape of feeble signal when SNR=-20dB can differentiate; Than the figure among Fig. 3 the lifting on the very big performance has been arranged, can tell the frequency of feeble signal basically, confirmed but phase place is difficult.

Fig. 5 is that SNR is-20dB; Feeble signal is that frequency is that the sine wave of 0.1Hz becomes 0.001Hz through the double sampling frequency; Double sampling change of scale factor R is 100 the time domain figure of feeble signal s (t) through exporting after the system of the present invention; At first make its frequency be reduced to 0.001Hz and obtain signal W (t) through double sampling; And then through output signal X (t) after the self-adapting random resonant system, X (t) combines with the R value of output and exports the time domain waveform figure that comprises s (t) signal characteristic, can confirm the characteristics of signals such as frequency, phase place of feeble signal s (t) easily through Fig. 5.

Fig. 6 is that SNR is-20dB; Feeble signal is that frequency is that the sine wave of 0.01Hz receives signal r (t) through the spectrogram after the preset parameter stochastic resonance system; Though it is very little to observe under the preset parameter stochastic resonance system near spectrogram range value zero-frequency; But on whole frequency, all there is the noise of can not ignore to exist,, is difficult to extrapolate the characteristic of feeble signal through Fig. 3 so the output time domain plethysmographic signal of preset parameter stochastic resonance system is as shown in Figure 3.

Fig. 7 is that SNR is-20dB; Feeble signal is that frequency is that the sine wave of 0.01Hz receives signal r (t) through the spectrogram after the self-adapting random resonant system; Though it is very big to observe the amplitude at zero-frequency place; But the noise amplitude at other frequency place very I ignoring, so, also observe near the spectrum amplitude at the corresponding frequency place in Fig. 6 of the spectrum amplitude the 0.01Hz among Fig. 7 simultaneously totally to big not as among Fig. 6 of the influence of waveform; That is to say that the feeble signal among Fig. 7 has obtained the more noise energy, thereby make the waveform of time domain seem more better.Explained that also the self-adapting random resonant system has the performance of better enhancing feeble signal.The feeble signal s (t) that comprises among the input signal r (t) of this moment is a periodic drive signal; The frequency of s (t) is not in the optimum resonance frequency range of self-adapting random resonant system; So the time domain waveform of the output signal of the self-adapting random resonant system of this moment is as shown in Figure 7, does not obtain good waveform.

Fig. 8 is that SNR is-20dB; Feeble signal is that frequency is that the sine wave of 0.1Hz receives the spectrogram of signal r (t) after through system of the present invention; Can find out that by figure feeble signal s (t) is 0.001Hz through the frequency of the signal W (t) after the double sampling; The self-adapting random resonant system that just in time drops on this moment produces in the scope of accidental resonance, so feeble signal has obtained enough energy, noise has obtained maximum inhibition simultaneously.Can observe except near the frequency of feeble signal place and near other frequency place spectrum amplitudes the zero-frequency very little; Can ignore; And near the spectrum amplitude the zero-frequency is so noise has been dropped to minimum to the influence of feeble signal, as shown in Figure 5 through the time domain waveform figure behind the present invention much smaller than near the spectrum amplitude the 0.001Hz; The signal characteristics such as frequency, phase place of W (t) can be clearly told, the signal characteristic of feeble signal s (t) can be obtained in the final R value that combines output.

Emulation shows: the change of scale factor of regulating double sampling through feedback system; Can adjust to the frequency of feeble signal well is easy to produce in the frequency range of self-adapting random resonant; Thereby utilized the premium properties of self-adapting random resonant fully; Can well under utmost point low signal-to-noise ratio, extract feeble signal, solved the problem that existing feeble signal disposal route is performed poor even lost efficacy effectively under utmost point low signal-to-noise ratio.Under the situation of not knowing the feeble signal frequency, pass through the change of scale factor R of the automatic adjusting double sampling of feedback simultaneously; Make feeble signal can mate the self-adapting random resonant system and produce accidental resonance, thereby can extract the characteristic of feeble signal well through the signal frequency after the double sampling.

One of ordinary skill in the art will appreciate that; Realize that all or part of step in the foregoing description method is to instruct relevant hardware to accomplish through program; Described program can be stored in the readable storage medium storing program for executing, for example ROM (read-only memory), RAS, disk, CD etc.

The above; Be merely the preferable embodiment of the present invention, but protection scope of the present invention is not limited thereto, any technician who is familiar with the present technique field is in the technical scope that the present invention discloses; The variation that can expect easily or replacement all should be encompassed within protection scope of the present invention.Therefore, protection scope of the present invention should be as the criterion with the protection domain of claim.

Claims (4)

Translated fromChinese

1.一种基于自适应随机共振的微弱信号提取方法，包括以下步骤：1. A weak signal extraction method based on adaptive stochastic resonance, comprising the following steps:S1.初始化参数：所述参数具体包括，二次采样尺度变换因子R，尺度变换因子的增加步长ΔR；随机共振的固有参数a，产生随机共振的参考频率f_ref，f_ref的计算偏移量Δf；零频计算偏移量Δf₀；频谱幅度比较系数m；S1. Initialization parameters: The parameters specifically include, the resampling scale conversion factor R, the increase step size ΔR of the scale conversion factor; the inherent parameter a of stochastic resonance, the reference frequency f_ref for generating stochastic resonance, and the calculated offset of f_ref Quantity Δf; Zero-frequency calculation offset Δf₀ ; Spectrum amplitude comparison coefficient m;S2.确定SR系统参数b：所述SR系统通过langevin方程

进行描述，其中，

s(t)是微弱信号；n(t)是均值为零方差为

的噪声。根据接收信号r(t)获得噪声方差

其中，r(t)＝s(t)+n(t)，然后由a和的值确定参数b；S2. Determine the SR system parameter b: the SR system passes the langevin equation

describe, among them,

s(t) is a weak signal; n(t) is the mean is zero and the variance is

noise. Obtain the noise variance from the received signal r(t)

Among them, r(t)=s(t)+n(t), then by a and The value of determines the parameter b;S3.把接收到的信号r(t)进行尺度变换因子为R的二次采样，得到信号W(t)；S3. Subsampling the received signal r(t) with a scaling factor of R to obtain a signal W(t);S4.信号W(t)通过langevin方程求得信号X(t)；S4. The signal W(t) obtains the signal X(t) through the langevin equation;S5.将X(t)做傅里叶变换，得到Z(f)，f为频率值，Z(f)即是在频率为f处的频谱幅度值；S5. X (t) is done Fourier transform, obtains Z (f), and f is a frequency value, and Z (f) is exactly the frequency spectrum amplitude value at f place at frequency;S6.求[f_ref-Δf，f_ref+Δf]或者[-f_ref-Δf，-f_ref+Δf]范围内的Z(f)的最大值，记为A_ref，求[-Δf₀，Δf₀]范围内的Z(f)的最大值，记为A₀；S6. Find the maximum value of Z(f) within the range of [f_ref -Δf, f_ref +Δf] or [-f_ref -Δf, -f_ref +Δf], denoted as A_ref , and find [-Δf₀ , Δf₀ ] the maximum value of Z(f) within the range, denoted as A₀ ;S7.如果A_ref≥m×A₀，则X(t)即为提取的包含微弱信号特征的目标信号，否则将尺度变换因子R赋值为R与ΔR的和，即R＝R+ΔR，转到步骤S3。S7. If A_ref ≥ m×A₀ , then X(t) is the extracted target signal containing weak signal features, otherwise assign the scaling factor R to the sum of R and ΔR, that is, R=R+ΔR, turn to Go to step S3.2.根据权利要求1所述的微弱信号提取方法，其特征在于，步骤S1中所述的二次采样尺度变换因子R＝1。2. The weak signal extraction method according to claim 1, characterized in that the re-sampling scale conversion factor R=1 described in step S1.3.根据权利要求1所述的微弱信号提取方法，其特征在于，步骤S2所述的由a和的值确定的参数其中，h为调节系数。3. weak signal extracting method according to claim 1, is characterized in that, step S2 described by a and The parameter determined by the value of Among them, h is the adjustment coefficient.4.根据权利要求1所述的微弱信号提取方法，其特征在于，步骤S1中所述的频谱幅度比较系数m的取值范围为5≤m≤20。4. The weak signal extraction method according to claim 1, characterized in that the value range of the spectrum amplitude comparison coefficient m described in step S1 is 5≤m≤20.

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