王雨亭

Abstract：In our project， a speech signal with white Gaussian noise has been denoised by a brand-new method called Empirical Mode Decomposition （EMD）. The signal is decomposed into many components called Intrinsic Mode Function （IMF） firstly， and then with Soft Thresholding Method， most part of the noise has been removed efficiently. Finally， for noise 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 with the signal which are non-stationary and non-linear signal， which have the self-adaptability at the same time.

Key words：speech signal；white Gaussian noise；EMD；soft-threshold

中圖分類號(hào)：TN912 文獻(xiàn)標(biāo)識(shí)碼：A 文章編號(hào)：1671-2064（2017）23-0012-02

1 Introduction

1.1 Background

Fourier transform is a typical linear transformation and is a steady-state transformation， therefore， Fourier analysis is only suitable for analysis of linear， stationary signal whose frequency does not change with time， and do a global analysis of the signal； not suitable for time- Non-stationary signals， and local analysis of the signal.

Speech signal is a typical non-stationary signal， so we need to apply a new method， Empirical Mode Composition Method in Hilbert-Huang transform. Hilbert-Huang transform is a new two-step signal processing method for time-frequency analysis of nonlinear non-stationary signals. First， a finite number of IMFs （Intrinsic mode function） are obtained by EMD （Empirical Mode Composition Method）. Then the time - spectrum - Hilbert spectrum of the signal is obtained by Hilbert transform and instantaneous frequency method.

1.2 Objective

The aim of the project is to deal with the audio file added with white Gaussian noise of different intensity， a system is proposed to reduce the noise in the audio signal and remain the original signal at the same time. In the project， the empirical mode decomposition method and soft thresholding method are used and the snr of noisy signal and denoised signal will be illustrated in the result.

2 EMD-Based Signal Noise Reduction

2.1 Theory

2.1.1 Empirical Mode Decomposition（EMD）

Since the instantaneous frequency method cannot be applied to any signal， it can only be meaningful for the Mono-component signal. For natural and engineering applications， the signal obtained cannot meet the requirement of single-component signal. The signal must be properly processed. Empirical mode decomposition （EMD） is the decomposition of the signal， so that it can be expressed as the sum of many single-component signal.endprint

Intrinsic Mode Function（IMF）： In carrying out the EMD method， the obtained Intrinsic mode function （IMF） must satisfy the following two conditions[1]：

（1）The entire signal length， an IMF's extreme points and the number of zero-crossing must be equal or at most only a difference.（2）At any time， the upper envelope defined by the maximum point and the average value of the lower envelope defined by the minimum point are zero， which means that the upper and lower envelopes 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 follows[1]：

（1）Identify all extrema of x（t）；（2）Interpolate between minima（resp. maxima）， ending up with some envelope emin（t）（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 as Intrinsic Mode Function （IMF）. By construction， the number of extrema is decreased when going from one residual to the next， and the whole decomposition is guaranteed to be completely with a finite number of modes.

2.1.2 Soft thresholding

2.3 Result

The original audio signal with white Gaussian noise of snr=0dB is decomposed into 19 intrinsic mode functions and residual signal

We add white Gaussian noise with different intensities into the signal and implement the denoising process respectively.

For noise -5dB， 0dB and 5dB， EMD denoising 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 and Discussion

As is illustrated in the graph that the first four IMF contains high frequency signals and most noises are included 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 bound to be filtered at the same time. A floating threshold is used to identify data that carries less energy， i.e.， data less than or equal to the threshold is considered to carry less energy， these values are treated as zero in the actual process， and only data above the threshold value is retained.

Besides， the choice of threshold value play an important role to determine the performance of the denoising system. If the threshold value is too big， then some original signal will be removed and if the threshold value is too small some noise can not be removed clearly.endprint

In the system， since the amplitude of the noise in each IMF is different， and as the order of IMF increases the amplitude of the noise decreases， thus the threshold value for each IMF should decreases as the order of the IMF increases.

Whats more， to get the best denoising performance， the value of a also change for different intensity of white Gaussian noise and a is usually between 0 and 1， to choose the appropriate value of a， the plot of SNR for the denoised signal and the value of a is showed below， where the snr of noisy signal is 0dB. The best performance could be obtained if a is set to be about 0.4.

4 Conclusions and further work

4.1 Conclusion

In the project， we have made it to remove the white Gaussian noise with different intensity on speech signal， which is non-stationary and non-linear. For noise with -5dB， 0dB and 5dB SNR， our denoising result turns out to be 4dB， 7dB and 10dB， respectively. It has been turned out that the larger the noise is， the more noise we can remove 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 signals.

4.2 Further work

However， 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 improvement in two aspects：

Firstly， the stopping criteria for sifting can be more precise. In the EMD method we used in the project， when the root of mean square deviation of residue is smaller than the θ， which is set to be 0.2 based on experience. However， to get the best performance， the value ofθshould be changed due to different signals. Thus changing the value of θmay lead to a better result.

Secondly， the choice of thresholding value is floating for different IMF， the denoising result may be optimized if we fit the thresholding value into different situations.

Thirdly， the result could be improved if the IMFs is decomposed into several components using wavelet transform， which is also a traditional method to remove the noise. This means we combine the wavelet transform and the EMD method together to get a better performance.

References

[1]G. Rilling，P.Flandrin，P.Goncalves，“On empirical mode decomposition and its algorithms”，F(xiàn)rance.

[2]A.O. Boudraa，J.C.Cexus，and Z.Saidi，EMD-Based Signal Noise Reduction，World Academy of Science，Engineering and Technology，2007.

[3]LiuLiwei，LiJinbao，Zhao Kongxin，Ding Tiefu，The application of Hilbert-Huang Transform in speech Enhancement，2007.endprint