CN105827221B - Based on the smooth noise cancellation technology of recombination Product function waveform - Google Patents
Based on the smooth noise cancellation technology of recombination Product function waveform Download PDFInfo
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Abstract
The invention discloses a kind of noise cancellation technologies smooth based on recombination Product function waveform, which is characterized in that this method comprises the following steps: 1) extraction of instantaneous envelope and pure frequency modulation component；2) building of Product function component；3) identification of Product function noise characteristic；4) band make an uproar Product function Energy distribution analysis；5) band make an uproar high-order Product function component superposition recombination；6) detection of Product function outlier and rejecting；7) it is eliminated and regular processing based on the smooth miniature spike of waveform.The invention has the advantages that method designs reasonable, clear process, de-noising effect is good.
Description
Technical field
The present invention is based on signal processing theory, the height constituted due to the instantaneous envelope of noise polluted signal and pure frequency modulation component
Rank band makes an uproar Product function with significant Dual pulse characteristic, decomposed using multistage local mean value, high-order band Product function component of making an uproar it is folded
Exacerbation group, wild point detection and waveform smoothing technique, eliminate pulse repetition step by step and restore true source signal, be finally reached elimination
The purpose of noise.The noise cancellation technology be solve Testing of Feeble Signals involved in many fields and extraction, signal purification and purification with
And the problems such as noise jamming elimination, has established theoretical basis.
Background technique
" pure " noise signal is passed through in the resulting Product function of local mean value resolution process, particularly high-order Product function component,
Pulse repetition occupies ascendancy, and forms apparent energy and concentrate, " pure " noise each unlike empirical mode decomposition
The energy of intrinsic mode functions component is substantially uniform to be distributed on entire waveform.In addition, the Energy distribution and base of " pure " noise signal
It is significantly different that resulting logarithmic decrement rule is studied in empirical mode decomposition[1], it is clear that it is by the principle of two kinds of Algorithm of Signal Decomposition
Caused by sex differernce.
Although band is made an uproar, the first rank Product function component of observation signal is mainly made of noise contribution, this and empirical mode decomposition
Result it is similar[2], but wherein there is also obvious pulse energy concentrations.This pulse energy collection in high-order Product function
Middle effect becomes readily apparent from.Therefore, under the denoising application background decomposed based on mean value, existing wavelet basis threshold denoising[3]
Or empirical mode decomposition base denoising[4]The amplitude filtering principle relied on is no longer applicable in, need to study new denoising principle or
Method.
Summary of the invention
The purpose of the present invention is to solve the above problems, develop a kind of de-noising smooth based on recombination Product function waveform
Technology.
Realize above-mentioned purpose the technical scheme is that, it is a kind of based on the smooth noise cancellation technology of recombination Product function waveform,
It is characterized in that, this method comprises the following steps:
1) extraction of instantaneous envelope and pure frequency modulation component；
2) building of Product function component；
3) identification of Product function noise characteristic；
4) band make an uproar Product function Energy distribution analysis；
5) band make an uproar high-order Product function component superposition recombination；
6) detection of Product function outlier and rejecting；
7) it is eliminated and regular processing based on the smooth miniature spike of waveform.
The extraction-type of the instantaneous envelope and pure frequency modulation component are as follows:
In formulah ij (t) it is from original noise polluted signalx(t) in removal local mean value after signal,a i (t)
It isiWalk the instantaneous envelope component extracted, also referred to as instantaneous amplitude.s in (t) it is theiWalk the pure frequency modulation component extracted.
The building formula of the Product function component are as follows:
In formulaP i (t) it is theiWalk the Product function component extracted.
The recognition principle of the Product function noise characteristic are as follows:
In formulaE 1nThe first Product function component extracted from " pure " noise signal is decomposed for local mean valueP 1nEnergy
Amount.E i Signal is polluted for raw noisex(t) by local mean value decompose extract theiA Product function componentP i Make an uproar
Acoustic energy estimation.Median () is mediant estimation.
The band is made an uproar Product function Energy distribution analysis mode are as follows:
In formulaCFor constant.Ê i It isiRank Product function componentP i Estimation of noise energy.E 1nFor the first rank
" pure " noise Product function componentP 1nEnergy.For some specific local mean value decomposable process, parameterWithIt is main
To depend on the number of iterations that local mean value is decomposed.
The band make an uproar high-order Product function component superposition recombination calculating formula are as follows:
In formulaiThe series decomposed for multistage local mean value.To the high-order Product function point of the second-order extracted or more
Amount (including residual componentu K (i))P 2 (i), …, P K (i), u K (i)It is overlapped processing, forms recombination signalP (i)。
The Product function outlier detection and the formula of rejecting are as follows:
In formulaM 0For signalP (i) = {P (i) j , j = 1, 2, …, nIntermediate value.E biWiths biRespectivelyP (i)Mean value and variance double kernel estimators values.In formulaM 1For absolute deviation intermediate value, i.e. data sample pointP (i) j Relative to letter
Number intermediate valueM 0Absolute deviation intermediate value.ParametercControl offset distance of each data point relative to data distribution center
From, usually take 6 <c< 9.For | u j | the case where > 1.0, then it is set to without exceptionu j = 0。E biWiths biTwo systems
Metering has stronger anti-outlier performance, obtainsE biWiths biEstimation after can applyInspection technology carries out outlier
Detection.Assuming thatP (i) k It is judged as outlier, then uses signalP (i)Intermediate value replace the outlier to realize unruly-value rejecting.
The miniature spike smooth based on waveform is eliminated and regular processing formula are as follows:
It is set in formulat j = j,t = {t j , j = 1, 2, …, n}.UsingmOrder polynomial carries out data fitting.It is logical
It crosses criterion of least squares and solves multinomial coefficienta 0, a 1, …, a m , and then realize band make an uproar Product function component waveform it is smooth,
Miniature spike is eliminated and regularization.
Detailed description of the invention
Fig. 1 is the implementation process diagram of the noise cancellation technology smooth based on recombination Product function waveform of the present invention；
Signal denoising algorithm process Fig. 2 smooth based on recombination Product function waveform；
The Product function waveform that Fig. 3 signal and its multistage local mean value are decomposed
Fig. 4 high-order band after superposition recombination is made an uproar the signal waveform of Product function；
Fig. 5 is by the signal waveform of wild point detection and the Product function after rejecting；
Fig. 6 by waveform smoothly with it is regular treated denoising after signal waveform；
De-noising Comparative result of a variety of noise cancellation technologies of Fig. 7 to " AM/FM amplitude modulation/frequency modulation signal "
Specific embodiment
The present invention is specifically described with reference to the accompanying drawing, if Fig. 1 is of the present invention based on recombination Product function waveform
The implementation process diagram of smooth noise cancellation technology, as shown, the multistage local mean value of use in conjunction is decomposed from by noise dirt
It extracts instantaneous envelope and pure frequency modulation component in the signal of dye, and is made an uproar the superposition of Product function component based on Product function reconstruct, high-order band
Recombination, wild point detection and waveform be smooth, regular processing technique, eliminates pulse repetition step by step and restores true source signal, finally
Achieve the purpose that noise remove.
The technical program using by the signal of white noise sound pollution as example illustrate signal noise silencing process, basic denoising principle
Are as follows: the high-order Product function component signal that band is made an uproar has significant Dual pulse characteristic, and this duality is made an uproar long-pending letter in the band of high-order
There is generality in number component signal.Most of Dual pulse ingredient therein is eliminated after superposition recombination；For remnants
Local pulse component, be considered as the outlier for deviating considerably from conceptual data distribution center, pass through Statistical Identifying Method carry out outlier inspection
It surveys and rejects；For micro-peeks remaining in signal, smoothly solved with regular processing by waveform.
Embodiment 1
By " heavy sine " signal noise silencing of white noise sound pollution
It is decomposed based on multistage local mean value, successively extracts instantaneous envelopea i (t) and pure frequency modulation components in (t), form product
Function component, such as Fig. 3.In figuresFor pure " heavy sine "
Signal,xFor by the virtual observation signal after white noise sound pollution, PF1-i, i=1,2,3,4 be respectively four Product functions
Component.Multipair Dual pulse is wherein marked, such as " 1.+with 1.-", " 2.+with 2.-" and " 3.+with 3.-".
The noise characteristic of four Product functions is identified, the first rank Product function component PF1-x is included as the result is shown
Noise energy exceeds the 85% of the energy of the first rank Product function component extracted from " pure " noise signal, is consequently belonging to make an uproar completely
Sound component can be rejected directly；Other three components belong to (part) band and make an uproar Product function component, need to retain and further progress
Denoising.
Resulting three bands high-order Product function component of making an uproar is decomposed to first order local mean value and is overlapped recombination, it is available
Recombinate Product function componentSuch as Fig. 4.It can be seen that apparent pulsecutting effect, and
And source signalsThe trend feature of waveform variation is also clear that.
It makes an uproar Product function component to the high-order band of superposition recombination, applicationThe method of inspection carries out outlier detection and rejects.Such as
Fig. 5.It can be seen that pulse remaining in signal is greatly cut down, some small pulse residuals only are being locally present.In order to
Its adverse effect to signal denoising is eliminated, needs further to make smooth and regular processing to signal waveform.
Further to band make an uproar Product function component waveform smoothed, miniature spike eliminate and regularization.Such as
Fig. 6.It is clearly, there are the small pulse residual in the part in signal --- spike ingredient is further cut down, and is obtained more smooth
Signal waveform, the good results are evident for de-noising.
So far, first order denoising is completed.The denoising of x progress higher level is observed if necessary to make an uproar to band,
Repeat the above processing step.Certainly, the series of denoising cannot be too high, is usually no more than 3 grades, series is excessively high will be bad
Change the denoising performance of algorithm.Furthermore, it is necessary to which the ginseng such as distance controlling parameter, polynomial order and smooth cycle-index is arranged meticulously
Number, total principle is: should guarantee that the outlier after superposition recombinates in signal obtains more adequately rejecting and waveform reaches certain
Smoothness, guarantee that treated signal has enough extreme points again so that multistage local mean value decompose it is next
Grade is decomposed and can be gone on smoothly.
Embodiment 2
By " AM/FM amplitude modulation/frequency modulation " signal noise silencing of white noise sound pollution
Different technologies be compared respectively to the result for being carried out denoising by " AM/FM amplitude modulation/frequency modulation " signal of white noise sound pollution.
Other than based on the smooth noise cancellation technology (ML-LMD-OS) of recombination Product function waveform, also provides a comparison of primary local mean value and decompose base
Noise-removed technology (LMD-H and LMD-S), wavelet basis translation invariant threshold denoising technology (WT-H and WT-S) and improved warp
Test mode decomposition base Denoising Algorithm (EMD-H and EMD-S).Wherein, " H " and " S " is respectively indicated at rigidity and flexibility thresholding
Reason.SNR1 makes an uproar for band observes signal-to-noise ratio,SNR 2For denoised signal signal-to-noise ratio.Here primary local mean value is decomposed base denoising and is calculated
Method is exactly directly to carry out amplitude filtering and noise reduction to Product function component.Such as Fig. 7.
It can be seen that obtaining preferable stablize based on the smooth noise cancellation technology of recombination Product function waveform denoises effect.Always
For body, the effect of (S) generally is handled more than compliance threshold change using rigidity thresholdsization processing (H) for same Denoising Algorithm
It is good.Advantage based on the smooth noise cancellation technology of recombination Product function waveform be embodied in observation signal-to-noise ratio middle section (- 7 dB <SNR 1
< 2 dB), it is put up the best performance at this time, shows preferable comprehensive de-noising performance, is particularly suitable under middle and high state of signal-to-noise
The high-precision de-noising of signal.
Bibliography
[1] FLANDRIN P, RILLING G, and GONCALVES P. EMD equivalent filter
banks, from interpretation to applications. In Hilbert-Huang Transform and
Its Applications, HUANG N E and SHEN S, Eds., 1st ed. Singapore: World
Scientific, 2005.
[2] KOPSINIS Y and MCLAUGHLIN S. Development of EMD-Based Denoising
Methods Inspired by Wavelet Thresholding. IEEE Transactions on Signal
Processing, 2009, 57(4): 1351-1362.
[3] H. C. Huang and N. Cressie. Deterministic/stochastic wavelet
decomposition for recovery of signal from noisy data. Technometrics, 2000,
42: 262-276.
[4] VIJAYABASKAR V, RAJENDRAN V, and PHILIP M M. EMD Based Denoising
of Underwater Acoustic Signal. Journal of the Instrument Society of India,
2012, 42(2): 125-127.
Above-mentioned technical proposal only embodies the optimal technical scheme of technical solution of the present invention, those skilled in the art
The principle of the present invention is embodied to some variations that some of them part may be made, belongs to the scope of protection of the present invention it
It is interior.
Claims (7)
1. a kind of noise-eliminating method smooth based on recombination Product function waveform, which is characterized in that this method comprises the following steps:
1) extraction of instantaneous envelope and pure frequency modulation component；
2) building of Product function component；
3) identification of Product function noise characteristic；
4) band make an uproar Product function Energy distribution analysis；
5) band make an uproar high-order Product function component superposition recombination；
6) detection of Product function outlier and rejecting；
The Product function outlier detection and the formula of rejecting are as follows:
M in formula0For signal P(i)={ P(i) j, j=1,2 ..., n } intermediate value,
EbiWith sbiRespectively P(i)Mean value and variance double kernel estimators values,
M in formula1For absolute deviation intermediate value, i.e. data sample point P(i) jRelative to signal intermediate value M0Absolute deviation intermediate value,
Parameter c controls offset distance of each data point relative to data distribution center, usually takes 6 < c < 9,
For | uj| the case where > 1.0, then it is set to u without exceptionj=0,
EbiWith sbiTwo statistics have stronger anti-outlier performance, obtain EbiWith sbiEstimation after can using τ examine skill
Art carries out outlier detection,
Assuming that P(i) kIt is judged as outlier, then uses signal P(i)Intermediate value replace the outlier to realize unruly-value rejecting；
7) it is eliminated and regular processing based on the smooth miniature spike of waveform.
2. the noise-eliminating method smooth based on recombination Product function waveform according to claim 1, which is characterized in that described instantaneous
The extraction-type of envelope and pure frequency modulation component are as follows:
hij(t)=x (t)-mij(t),sij(t)=hij(t)/aij(t),
sin(t)=hin(t)/ain(t) .i=1 ..., m, j=1 ..., n
H in formulaijIt (t) is the signal after the removal local mean value from original noise polluted signal x (t), ai(t) it is taken out for the i-th step
The instantaneous envelope component taken, also referred to as instantaneous amplitude, sin(t) the pure frequency modulation component extracted for the i-th step.
3. the noise-eliminating method smooth based on recombination Product function waveform according to claim 1, which is characterized in that the long-pending letter
The building formula of number component are as follows:
Pi(t)=ai(t)sin(t), i=1 ..., m
P in formulai(t) the Product function component extracted for the i-th step.
4. the noise-eliminating method smooth based on recombination Product function waveform according to claim 1, which is characterized in that the long-pending letter
The recognition principle of number noise characteristic are as follows:
If Et≥E1n, then PiFor complete noise component(s)；
Otherwise PiIt makes an uproar component for (part) band；
Wherein
E in formula1nThe first Product function component P extracted from " pure " noise signal is decomposed for local mean value1nEnergy,
EiSignal x (t), which is polluted, for raw noise decomposes i-th of the Product function component P extracted by local mean valueiNoise energy
Estimation,
Median () is mediant estimation.
5. the noise-eliminating method smooth based on recombination Product function waveform according to claim 1, which is characterized in that the band is made an uproar
Product function Energy distribution analysis mode are as follows:
I=2,3....
C is constant in formula,
For the i-th rank Product function component PiEstimation of noise energy,
E1nFor the first rank " pure " noise Product function component P1nEnergy,
For some specific local mean value decomposable process, parameter ρ and β depend primarily on the iteration time that local mean value is decomposed
Number.
6. the noise-eliminating method smooth based on recombination Product function waveform according to claim 1, which is characterized in that the band is made an uproar
The superposition of high-order Product function component recombinates calculating formula are as follows:
I is the series that multistage local mean value is decomposed in formula,
To the high-order Product function component of the second-order extracted or more (including residual component uK(i))P2 (i),…,PK (i),uK (i)
It is overlapped processing, forms recombination signal P(i)。
7. the noise-eliminating method smooth based on recombination Product function waveform according to claim 1, which is characterized in that described to be based on
The smooth miniature spike of waveform is eliminated and regular processing formula are as follows:
P(1) OD=a0+a1t+a2t2+...+amtm,
T is set in formulaj=j, t={ tj, j=1,2 ..., n },
Data fitting is carried out using m order polynomial,
Multinomial coefficient a is solved by criterion of least squares0, a1..., am, and then realize the waveform smoothing processing of signal.
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| CN101822548A (en) * | 2010-03-19 | 2010-09-08 | 哈尔滨工业大学（威海） | Ultrasound signal de-noising method based on correlation analysis and empirical mode decomposition |
| US20120207325A1 (en) * | 2011-02-10 | 2012-08-16 | Dolby Laboratories Licensing Corporation | Multi-Channel Wind Noise Suppression System and Method |
| CN104182625A (en) * | 2014-08-15 | 2014-12-03 | 重庆邮电大学 | Electrocardiosignal denoising method based on morphology and EMD (empirical mode decomposition) wavelet threshold value |
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| CN101822548A (en) * | 2010-03-19 | 2010-09-08 | 哈尔滨工业大学（威海） | Ultrasound signal de-noising method based on correlation analysis and empirical mode decomposition |
| US20120207325A1 (en) * | 2011-02-10 | 2012-08-16 | Dolby Laboratories Licensing Corporation | Multi-Channel Wind Noise Suppression System and Method |
| CN104182625A (en) * | 2014-08-15 | 2014-12-03 | 重庆邮电大学 | Electrocardiosignal denoising method based on morphology and EMD (empirical mode decomposition) wavelet threshold value |
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