A Method Of Constructing Symmitric Wavelet And Its Application To Signal Denoising

Since the discovery of wavelets by Morlet in 1980s, various wavelet theories have been developed. Among them, Multiresolution Analysis is a very important concept to construct wavelet function. Wavelet construction methods based on Multiresolution Analysis have designed compactly supported orthogonal wavelets. However, these wavelets do not have linear phases except for Haar wavelet. Some researchers found methods to construct wavelets with linear phases using spline functions, filter banks, etc, but comparatively difficult. In addition, wavelet analysis has been shown to be a useful mathematical tool for many practical applications and become to a focus of attention recently. This paper talks about a new wavelet construction method and the research on signal denoising based on the new wavelets. It begins with the introduction of the basic concept of wavelet theory, and then the Multiresolution Analysis based on biorthogonal wavelet bases is concluded. Which will richen the wavelet theory. After that, a new method of designing symmetric wavelets with convolution-type condition is investigated. This method makes it possible to construct symmetric wavelets by solving linear equations. Some groups of new wavelets are shown in some restricted cases. Also, we studied the wavelet decomposing and reconstructing algorithm and do experiments on signal denoising to test the quality of the new constructed wavelets. And some new ideas are brought into the method of signal denoising. The simulation results show the good performance of the wavelets and the method. To make it easer to watch the performance of the experiments, the software based on MATLAB environment is developed at the last part of this paper.