EMD―basedSpeechSignalNoiseReductionWithSoftThresholding-2019年文档

1、EMbased Speech Sig nal Noise Reduction With Soft Thresholdi ng：In our project , a speech signal with white Gaussian no ise has bee n deno ised by a brand-new method called Empirical Mode Decomposition(EMD . The signal isdecomposed into many comp onents called Intrin sic Mode Function (IMF) firstly ,

2、 and then with Soft ThresholdingMethod， most part of the noise has been removed efficiently. Fin ally , for n oise with -5dB , 0dB and 5dB SNR , our denoising result turns out to be 4dB, 7dB and 10dB ,respectively. The denoising system based on EMD in our project turn out to have the ability to deal

3、 with the signal which are non-stationary and non-linear signal ， which have the self-adaptability at the same time.1 Introduction1.1 BackgroundFourier transform is a typical linear transformation and is a steady-state transformation ， therefore ， Fourier an alysis is only suitable for an alysis of

4、lin ear,stationary signal whose frequency does not change with time , and do a global analysis of the signal ； not suitable, and local an alysis offor time- Non-statio nary sig nalsthe sig nal.Speech sig nal is a typicalnon-stati on arysig nal , sowe need to apply a new method, Empirical ModeComposi

5、tion Method in Hilbert-Huang transform. Hilbert-Huang transform is a new two-step signal processing method for time-freque ncy an alysis of nonlin ear non-stati on ary signals.First , a finite number of IMFs (Intrinsic modefunction ) are obtained by EMD(Empirical ModeComposition Method) . Then the t

6、ime - spectrum - Hilbert spectrum of the signal is obtained by Hilbert transform and instantaneous frequency method.1.2 ObjectiveThe aim of the project is to deal with the audio file added with white Gaussia n no ise of differe nt inten sity,a system is proposed to reduce the noise in the audio sign

7、al and remai n the orig inal sig nal at the same time. In the project , the empiricalmodedecomposition method and softthreshold ing method are used and the snr of no isy sig nal and denoised signal will be illustrated in the result.2 EMD-Based Sig nal Noise Reductio n2.1 Theory2.1.1 Empirical Mode D

8、ecomposition ( EMDSince the in sta ntan eous freque ncy method cannot be applied to any sig nal , it can only be meanin gful for the Mono-comp onent sig nal. For n atural and engin eeri ng applications , the signal obtained cannot meet the requirement of single-component signal. The signal must be p

9、roperly processed. Empirical mode decomposition( EMD)is the decompositi on of the sig nal, so that it can beexpressed as the sum of many sin gle-comp onent sig nal.Intrin sic Mode Fu nction(IMF)： In carryi ng out the EMDmethod, the obtained Intrinsicmodefunction(IMF) mustsatisfy the following two co

10、nditions1：(1)The entire signal length , an IMFs extreme points and the nu mber of zero-cross ing must be equal or at most only a differenee. (2) At any time , the upper envelope defined by the maximum point and the average value of the lower envelope defined by the minimumpoint are zero , which mean

11、s that the upper and lower en velopes of the IMF are symmetrical to the time axis.Sifting process : Given a signal x (t) , the effective algorithm of EMD can be summarized as follows1(1) Identifyall extrema of x (t) ;( 2) Interpolatebetween minima(resp. maxima), ending up with someenvelope emin (t)(

12、resp.emax (t) );( 3) Compute the mean m (t)=(emin (t) +emax(t) ) /2 ；(4) Extract the detail d (t)=x (t) -m (t) ;( 5) Iterate on the residual m(t).Once this is achieved , the detail is referred to asIntrinsic Mode Function(IMF) . By construction, thenumber of extrema is decreased when going from one

13、residual to the next , and the whole decomposition is guaranteed to be completely with a fin ite nu mber of modes.2.1.2 Soft thresholdi ng2.3 ResultThe original audio signal with white Gaussian noise of snr二 0dB is decomposed into 19 in tri nsic modefu ncti ons and residual signalWeadd white Gaussia

14、n noise with different intensities into the signal and implement the denoising process respectively.For noise -5dB, 0dB and 5dB, EMDdenoising result is 4dB, 7dB and 10dB , respectively.The result has shown that the denoising system have the self-adaptability for different intensity noise.3 Analysis

15、and DiscussionAs is illustrated in the graph that the first four IMF contains high freque ncy sig nals and most no ises areincluded in these components. If we directly apply low pass filters , because the frequency spectrum of speech signal and noise are overlapped , the useful speech signal will be

16、 bound to be filtered at the same time. A floati ng threshold is used to ide ntify data that carries lessenergy , i.e. , data less than or equal to the thresholdis con sidered to carry less en ergy, these values aretreated as zero in the actual process , and only data above the threshold value is re

17、tained.Besides , the choice of threshold value play animporta nt role to determ ine the performa nee of thedenoising system. If the threshold value is too big , then some orig inal sig nal will be removed and if the threshold value is too small some noise can not be removed clearly.In the system , s

18、ince the amplitude of the no ise in eachIMF is differe nt , and as the order of IMF in creases the amplitude of the noise decreases , thus the threshold value for each IMF should decreases as the order of the IMF increases.What s more, to get the best denoising performanee ,the value of a also chang

19、e for differentintensityof whiteGaussian noise and a is usually between 0 and 1, to choose the appropriate value of a, the plot of SNRfor the denoised signal and the value of a is showed below, where the snrof no isy sig nal is 0dB. The best performa nee could be obta ined if a is set to be about 0.

20、4.4 Con clusi ons and further work4.1 Con clusio nIn the project , we have made it to remove the whiteGaussia n no ise with differe nt inten sityon speech sig nal ,which is non-stati onary and non-li near. For no ise with-5dB, 0dB and 5dB SNR our denoising result turns out to be 4dB, 7dB and 10dB ,

21、respectively. It has been turned out that the larger the noise is， the more noise we canremove from the signal ， which have showed the self-adaptability of the EMD method. So we can get the conclusion that the Fast Fourier method can be replaced by the EMD method when to deal with non-stationary sig

22、nals.4.2 Further workHowever, the denoising signal could be improved since the noise is not completely removed and some part of original signal is not saved in the denoising process ， so we can make the improveme nt in two aspectsFirstly , the stopping criteria for sifting can be more precise. In th

23、e EMD method we used in the project, whenthe root of mean square deviati on of residue is smaller tha n the 6 , which is set to be 0.2 based on experienee. However, to get the best performanee, the value of 6 should becha nged due to differe nt sig nals. Thus cha nging the value of 6 may lead to a better result.Secondly , the choice of thresholding value i