Single-channel Wavelet Threshold Denoising And Multi-channel Noisyica Blind Separation

In the traditional signal processing methods based on the Fourier transform, the frequency band between signal and noise must overlap as little as possible, thus they can be separated by the time-invariant filtering methods in the frequency domain. However, nonlinear filtering based on wavelet transform is completely different, in which the spectra of signal and noise can overlap, but their amplitudes of spectra must differ as much as possible instead of the position of spectra. The wavelet coefficients need to undergo the nonlinear processing such as cutting or shrinking for the sake of denoising. And due to the characteristic of time-frequency analysis based on the multi-resolution analysis, the local information in the signal can be effectively analyzed by the wavelet, which is superiority to process non-stationary signals. And in our daily life, many kinds of signals are non-stationary, so in this dissertation, we mainly do the denoising processing by using the wavelet analysis.In this dissertation, a detailed study is introduced to the denoising processing of one channel noised signal based on the wavelet threshold denoising algorithm, and the parameters of the algorithm are also analyzed. The parameters mainly include the wavelet function, the optimal decomposition order, the threshold value and the threshold function. Then a new method is proposed to select the optimal decomposition order. And in allusion to the pros and cons of the traditional soft and hard threshold functions, two typical new threshold functions are introduced, which make us propose a better new threshold function that has two variables. In the subsequent simulation application of the wavelet threshold denoising algorithm, an algorithm based on the 3σcriteria combining the mathematical statistical knowledge is introduced for the matlab artificial generated signals; and for speech signals, because of their particular characteristics, according to the different characteristics of the noise, the sonants and the surds in the noised speech, the noise-sonant-surd wavelet threshold denoising algorithm is proposed. The related simulation results show the effectiveness and the better performance.As for the case of instantaneous linear mixed signals of multi-channel signals, the independent component analysis (ICA) technique is introduced. Since ICA is a new method to process multi-channel data, its basic theory and the popular fixed-point ICA algorithm (FastICA) are introduced. Then simulations on artificially generated data and real speech data are done by using the FastICA algorithm. Because most of the conventional ICA algorithms are sensitive to noise in the transmission channels, at last we briefly introduce the noisyICA models, and propose an improved algorithm to solving the noisyICA problems based on the combination of the wavelet denoising and the ICA technique. Lastly simulations on noisy mixed speech data show the better performance of the improved algorithm.