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Study of the Signal Denoising Method Based on the Lifting Wavelet Theory

Author: LuWei
Tutor: GuanShouPing
School: Northeastern University
Course: Control Theory and Control Engineering
Keywords: lifting wavelet threshold denoise GA adaptive filter varying step
CLC: TN911.4
Type: Master's thesis
Year: 2009
Downloads: 73
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Abstract


Signal and information processing is the fastest development subject in information science during the latest twenty years, and signal denoising is the most common in signal processing. The quality of the original signal will be severely interfered by the existence of noised signal which will bring us bad influence in ours research, work and our daily life. So it is necessary to do the signal denoising when we receive and detect the signal.The classical methods of signal denoising have their own limitations from Fourier transform to windowed Fourier transform. Wavelet is a new subject which has been developed quickly since 1980s. Because of its great characteristics of localization in time domain and frequency domain, wavelets have been widely used in signal processing fields.This paper has mainly adopted the method of wavelet threshold denoise(WTD) and also analyzed the mathematical model of WTD, as well as some key problems such as threshold, threshold function, layer number of decomposition. This paper has presented a new threshold function(TF) which is a fuzzy membership function and has been proved its derivation in the whole definition domain based on the soft and hard threshold function presented by Donoho. This TF has overcame the disadvantages of hard and soft TF in some extent, and improved the performance of signal denoising. Then I do the global optimization to the two variables of the fuzzy membership threshold function by using genetic algorithm(GA), obtaining numerical optimal solutions and this solution has improved the denoise performance a lot.Considering the requirement of real-time signal processing(RTSD) in many practical applications, and also because of the disadvantages of wavelet itself in RTSP, this paper has applied the wavelet transfer domain adaptive filter(AF) algorithm which was presented by Hour S into RSTP. Because of its good ability of removing signal relativity, wavelet transform can ameliorate the condition number of self-correlation matrix of input signal, improve the convergence velocity of AF. In the theory of AF, step factor plays an important role in AF performance. And this paper has presented a new varying step algorithm which can be proved convergence when the initial step dereferences a suitable value, and can improve the filter performance in tracking velocity and steady error in some extent, and the simulation examples has validate it.

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