CN102608553B - Weak signal extracting method based on self-adaptive stochastic resonance - Google Patents

Abstract

The invention discloses a weak signal extracting method based on self-adaptive stochastic resonance. Particularly, a frequency of a weak signal can be well adjusted to a frequency range easily generating the self-adaptive stochastic resonance through adjusting a scale changing factor which is secondarily sampled, so that the good performance of the self-adaptive stochastic resonance can be sufficiently utilized, the weak signal can be well extracted at a super-low signal to noise ratio, and the problem that the conventional weak signal processing method represents to be poor, even be invalid, at the super-low signal to noise ratio can be effectively solved; and meanwhile, a signal frequency of the weak signal which is secondarily sampled can be matched with a self-adaptive stochastic resonance system and can generate stochastic resonance through a fed-back automatic adjusting scale conversion factor under the condition of not knowing the frequency of the weak signal, so that the characteristic of the weak signal can be better extracted.

Description

A kind of weak signal extraction based on self-adapting random resonant

Technical field

The invention belongs to signal and process 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 the low-yield signal be submerged in strong background noise is called to feeble signal, processing for feeble signal is generally to use the technology such as modern signal processing method and electronics to suppress noise, and then feeble signal is extracted from strong background noise, but existing method all has some limitations, feeble signal required signal to noise ratio (S/N ratio) (the signal-to-noise ratio of main manifestations for detecting, SNR) relatively high, the extraction effect of the feeble signal under extremely low SNR can not be expired actual demand.

Research is found accidental resonance (Stochastic Resonance, SR) application of principle has been obtained to effect preferably in the detection of feeble signal.SR is a kind of nonlinear physical phenomenon, when having certain coupling between input signal, noise and nonlinear system, noise energy can be shifted 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 by the method for utilizing noise rather than inhibition noise like this.Yet feeble signal to be processed is not generally low especially, the SR system is not fine to the enhancing effect of large frequency signal, though can lower the signal frequency of input SR system by methods such as double samplings, but in the situation that do not know that the feeble signal frequency is not easy to determine the coefficient factor of change of scale, and the SR system of preset parameter can not be real-time with noise and signal, is complementary and has further weakened the humidification to signal.

Below the ultimate principle of double sampling is described.

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

then be handled as follows:

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

Summary of the invention

The objective of the invention is the problem that in order to solve under extremely low SNR, can not meet demand in practical application to the extraction of the detection of feeble signal and signal characteristic.

Technical solution of the present invention is as follows: a kind of weak signal extraction based on self-adapting random resonant comprises the following steps:

S1. initiation parameter: described 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 Δ f; Zero-frequency calculates offset Δ f ₀; Spectrum amplitude coefficient of comparisons m;

S2. determine SR systematic parameter b: described SR system is by the langevin equation

be described, wherein,

s (t) is feeble signal; N (t) is that average is that zero variance is

noise.Obtain noise variance according to receiving signal r (t) wherein, r (t)=s (t)+n (t), then by a and

value determine parameter b;

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

S4. signal W (t) obtains signal X (t) by the langevin Solving Equations;

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

S6. ask [f _ref-Δ f, f _ref+ Δ f] or [f _ref-Δ f ,-f _ref+ Δ f] maximal value of Z (f) in scope, be designated as A _ref, ask [Δ f ₀, Δ f ₀] maximal value of Z (f) in scope, be designated as A ₀;

If A S7. _ref>=m * A ₀, X (t) is the echo signal that comprises the feeble signal feature of extraction, otherwise by change of scale factor R assignment be R and Δ R and, R=R+ Δ R, forward step S3 to.

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

The accompanying drawing explanation

The structured flowchart that Fig. 1 is weak signal extraction of the present invention.

Fig. 2 is weak signal extraction schematic flow sheet of the present invention.

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

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

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

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

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

Fig. 8 is the feeble signal amplitude spectrum after processing by system of the present invention.

Embodiment

Below in conjunction with Fig. 1, to Fig. 8, weak signal extraction of the present invention is set forth, the structured flowchart that Fig. 1 is weak signal extraction of the present invention, Fig. 2 is weak signal extraction schematic flow sheet of the present invention, specifically comprises the following steps:

S1. initiation parameter: described 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 Δ f; Zero-frequency calculates offset Δ f ₀; Spectrum amplitude coefficient of comparisons m.

Below the value of initial parameter is described in detail:

F _refvalue be the frequency values that the self-adapting random resonant system is easy to produce accidental resonance, research finds that the input signal of 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 to be [5 * 10 ^-4, 3 * 10 ^-3] the interior value of scope, can value be generally: f _ref=0.001Hz.

Δ f means f _refthe calculating side-play amount, 0<Δ f<f _ref, due to f _refvalue less, so general Δ f value is f _refnear/2.

Δ f ₀mean that zero-frequency calculates side-play amount, 0<Δ f ₀<f _ref, general value is f _refnear/2, and meet Δ f+ Δ f ₀≤ f _ref.

A is the intrinsic parameter of stochastic resonance system, in order to meet the adiabatic approximation theory, require a>>π f _s, wherein, f _sfor the frequency input signal of stochastic resonance system, input signal reference frequency f that herein can be when producing accidental resonance _refcome to determine, a>>π f _ref.

First estimate the minimum frequency f that feeble signal is possible _min, and then determine the initial value of R, the initial value of R is f _min/ f _ref.As a preferred mode, the initial value of R can be R=1, and Δ R can determine a suitable value according to iterations.

By Fig. 7 and Fig. 8 contrast, can be found, producing in the situation of accidental resonance the energy of noise can transfer to feeble signal and get on, thereby near spectrum amplitude zero-frequency can be far smaller than near the feeble signal range value frequency of place after the double sampling change of scale, when if resonance effect is very poor just in time on the contrary as shown in Figure 7, the self-adapting random resonant system produces under the accidental resonance good situations, near the value that the ratio of the spectrum amplitude value of noise can be used as m the spectrum amplitude value of resonance place frequency and zero-frequency according to, m should be minimum value possible in this ratio, because so this ratio is larger value m>>1, in order between the accuracy at computation complexity and extraction signal, to reach balance, generally get 5≤m≤20.

S2. determine SR systematic parameter b: described SR system is by the langevin equation

be described, wherein,

s (t) is feeble signal; N (t) is that average is that zero variance is

noise.Obtain noise variance according to receiving signal r (t)

wherein, r (t)=s (t)+n (t), then by a and

value determine parameter b;

The concrete deterministic process of parameter b is as follows:

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

${\mathrm{SNR}}_o=\left(\frac{\sqrt{2}a{A}_m^2{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="DEST\_PATH\_HDA0000158313880000021.png,DEST\_PATH\_HDA0000158313880000023.png"\; state="\{\{state\}\}">c</figure-callout>}}^2}{{\mathrm{\&sigma;}}_n^4}{e}^{-{2\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="DEST\_PATH\_HDA0000158313880000022.png,DEST\_PATH\_HDA0000158313880000024.png"\; state="\{\{state\}\}">U</figure-callout>}}_0/{\mathrm{\&sigma;}}_n^2}\right){(1-\frac{\frac{{4a}^2{A}_m^2{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="DEST\_PATH\_HDA0000158313880000021.png,DEST\_PATH\_HDA0000158313880000023.png"\; state="\{\{state\}\}">c</figure-callout>}}^2}{{\mathrm{\&pi;}}^2{\mathrm{\&sigma;}}_n^2}{e}^{-4{\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="DEST\_PATH\_HDA0000158313880000022.png,DEST\_PATH\_HDA0000158313880000024.png"\; state="\{\{state\}\}">U</figure-callout>}}_0/{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="DEST\_PATH\_HDA0000158313880000021.png,DEST\_PATH\_HDA0000158313880000023.png"\; state="\{\{state\}\}">n</figure-callout>}}^2}}{\frac{{2a}^2}{{\mathrm{\&pi;}}^2}{e}^{-4{\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="DEST\_PATH\_HDA0000158313880000022.png,DEST\_PATH\_HDA0000158313880000024.png"\; state="\{\{state\}\}">U</figure-callout>}}_0/{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="DEST\_PATH\_HDA0000158313880000021.png,DEST\_PATH\_HDA0000158313880000023.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\; id="2"\; label="c"\; filenames="DEST\_PATH\_HDA0000158313880000021.png,DEST\_PATH\_HDA0000158313880000023.png"\; state="\{\{state\}\}">c</figure-callout>}}^2}{{\mathrm{\&sigma;}}_n^4}{e}^{-2{\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="DEST\_PATH\_HDA0000158313880000022.png,DEST\_PATH\_HDA0000158313880000024.png"\; state="\{\{state\}\}">U</figure-callout>}}_0/{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="DEST\_PATH\_HDA0000158313880000021.png,DEST\_PATH\_HDA0000158313880000023.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,

the variance of strong noise, U ₀=a ²/ (4b) be to work as A _mthe barrier height of the bistable state SR system of=0 o'clock.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 occurs, the output signal-to-noise ratio gain of reception signal r (t) after bistable state SR system is: make k=a ²/ b, obviously have k>0,

be given noise variance, the output signal SNR η that gains _sNRit is the nonlinear function of systematic parameter k.

η _sNRsecond derivative to k is:

therefore, in order to make η _sNRbe the lower concave function about k, in order to obtain unique maximum value, require: so the value that maximizes the optimum k of SNR gain meets: $\left\{\begin{array}{c}{k}_{\mathrm{op}}=\underset{k}{\arg \max }{\mathrm{\&eta;}}_{\mathrm{SNR}}\\ s.t.0<k<{4\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="DEST\_PATH\_HDA0000158313880000021.png,DEST\_PATH\_HDA0000158313880000023.png"\; state="\{\{state\}\}">n</figure-callout>}}^2\end{array}\right.,$ Solving above formula can obtain:

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

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

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

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

S4. signal W (t) obtains signal X (t) by the langevin Solving Equations.

Be specially: solve the langevin equation by the fourth order Runge-Kutta numerical computation method, the output signal that the solution of trying to achieve is the self-adapting random resonant system is designated as X (t);

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

S6. ask [f _ref-Δ f, f _ref+ Δ f] or [f _ref-Δ f ,-f _ref+ Δ f] maximal value of Z (f) in scope, be designated as A _ref, ask [Δ f ₀, Δ f ₀] maximal value of Z (f) in scope, be designated as A ₀;

Δ f means f herein _refthe calculating side-play amount, because R is the value of series of discrete after iteration, thus the feeble signal of input through after discrete R value carries out change of scale, the frequency of feeble signal also can only be got discrete value, can not get optional frequency, establish a less scope [f to reference frequency like this _ref-Δ f, f _ref+ Δ f] or [f _ref-Δ f ,-f _ref+ Δ f], as long as falling in this scope, the feeble signal after change of scale just can produce accidental resonance, after Fourier transform, the maximal value A in this scope _refthe frequency at place is the frequency at actual generation accidental resonance place.So effectively avoided given f _ref, but because the input signal after change of scale is not just in time got f _refthis frequency, and the phenomenon of the iteration failure of R is occurred, be also the condition of having relaxed of choosing of Δ R simultaneously, make choosing of Δ R convenient.

Δ f ₀mean that zero-frequency calculates side-play amount, the signal of finding after deliberation stochastic resonance system output after Fourier transform sometimes in the situation that do not produce accidental resonance, the range value at possible zero-frequency point place is very little, but near range value is very large, so set a scope [Δ f ₀, Δ f ₀], get the maximal value A of spectrum amplitude in this scope ₀represent that near spectrum amplitude value zero-frequency is used for and A _refcompare.So effectively avoided the actual accidental resonance that do not produce still to be mistaken for the phenomenon generation that produces accidental resonance.

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

If A S7. _ref>=m * A ₀, X (t) is the echo signal that comprises the feeble signal feature of extraction, otherwise by change of scale factor R assignment be R and Δ R and, R=R+ Δ R, forward step S3 to.

Below the inventive method is carried out to emulation testing.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 f ₀=f _ref/ 2, R=1, Δ R=1, m=10.

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

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

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

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

Fig. 7 is that SNR is-20dB, feeble signal is that the sine wave that frequency is 0.01Hz receives signal r (t) by the spectrogram after the self-adapting random resonant system, although it is very large to observe the amplitude at zero-frequency place, but the noise amplitude at other frequency place very I to ignore, so overall large not as in Fig. 6 on the impact of waveform, also observe near the spectrum amplitude much larger than the corresponding frequency place in Fig. 6 of spectrum amplitude 0.01Hz in Fig. 7 simultaneously, that is to say that the feeble signal in Fig. 7 has obtained more noise energy, thereby make the waveform of time domain seem more better.Also illustrated that the self-adapting random resonant system has the performance of better enhancing feeble signal.The feeble signal s (t) comprised in input signal r (t) now is 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 self-adapting random resonant system now as shown in Figure 7, do not obtain good waveform.

Fig. 8 is that SNR is-20dB, feeble signal is that the frequency sine wave that is 0.1Hz receives the spectrogram of signal r (t) after by system of the present invention, the frequency of the signal W (t) of feeble signal s (t) after double sampling is 0.001Hz as seen from the figure, the self-adapting random resonant system just in time dropped on now produces in the scope of accidental resonance, so feeble signal has obtained enough energy, noise has obtained maximum inhibition simultaneously.Can observe except near near other frequency place spectrum amplitudes frequency of feeble signal place and zero-frequency very little, can ignore, and near spectrum amplitude zero-frequency is much smaller than near spectrum amplitude 0.001Hz, so noise has been reduced to minimum to the impact of feeble signal, by the time domain waveform figure after the present invention as shown in Figure 5, 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 in conjunction with output.

Emulation shows: the change of scale factor of regulating double sampling by feedback system, can adjust to the frequency of feeble signal to be easy to produce in the frequency range of self-adapting random resonant well, thereby utilized fully the premium properties of self-adapting random resonant, can well extract feeble signal under utmost point low signal-to-noise ratio, effectively solve the problem that existing feeble signal disposal route is performed poor and even lost efficacy under utmost point low signal-to-noise ratio.Simultaneously in the situation that do not know that the feeble signal frequency is by the change of scale factor R of the automatic adjusting double sampling of feedback, make the signal frequency of feeble signal after double sampling can mate the self-adapting random resonant system and produce accidental resonance, thereby can extract well the feature of feeble signal.

One of ordinary skill in the art will appreciate that, realize that all or part of step in above-described embodiment method is to come the hardware that instruction is relevant to complete by program, described program can be stored in readable storage medium storing program for executing, such as ROM (read-only memory), random access memory, disk, CD etc.

The above; be only the present invention's embodiment preferably, but protection scope of the present invention is not limited to this, anyly is familiar with in technical scope that those skilled in the art disclose in the present invention; the variation that can expect easily or replacement, within all should being encompassed in 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)

1. the weak signal extraction based on self-adapting random resonant comprises the following steps:

S1. initiation parameter: described 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 Δ f; Zero-frequency calculates offset Δ f ₀; Spectrum amplitude coefficient of comparisons m;

S2. determine SR systematic parameter b: described SR system is by the langevin equation

be described, wherein,

s (t) is feeble signal; N (t) is that average is that zero variance is

noise; Obtain noise variance according to receiving signal r (t)

wherein, r (t)=s (t)+n (t), then by a and

value determine parameter b;

It is characterized in that, further comprising the steps of,

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

S4. signal W (t) obtains signal X (t) by the langevin Solving Equations;

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

S6. ask [f _ref-Δ f, f _ref+ Δ f] or [f _ref-Δ f ,-f _ref+ Δ f] maximal value of Z (f) in scope, be designated as A _ref, ask [Δ f ₀, Δ f ₀] maximal value of Z (f) in scope, be designated as A ₀;

If A S7. _ref>=m * A ₀, X (t) is the echo signal that comprises the feeble signal feature of extraction, otherwise by change of scale factor R assignment be R and Δ R and, R=R+ Δ R, forward step S3 to.

2. weak signal extraction according to claim 1, is characterized in that, the double sampling change of scale factor R described in step S1=1.

3. weak signal extraction according to claim 1, is characterized in that, step S2 described by a and the definite parameter of value

wherein, h is adjustment factor.

4. weak signal extraction according to claim 1, is characterized in that, the span of the spectrum amplitude coefficient of comparisons m described in step S1 is 5≤m≤20.

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