The Theory Of Multiwavelets

Wavelet analysis as a milestone in harmonic analysis history after the Fourier analysis already became a mathematical instrument that the scientific workers in every research area are all glad to use. It has obtained rapid development in theory and application in dozens of years after its birth. As an important kind of wavelet development direction - multiwavelets, it not only maintains the merits of scalar wavelet but also overcomes its shortcoming, which once again Cause the wavelet analysis to form the research upsurge and become international research focus.This article mainly takes multiwavelets as research object and takes the brief history and basic theory of scalar wavelet as a starting point. It presents development and theory knowledge of multiwavelets with emphasis. As a new kind of wavelet, designing multiwavelet systems with good nature is a goal which all the researchers pursue. This article mainly studies symmetry approximation and interpolation properties of multiwavelets. It mainly discusses symmetry and approximation questions in the third chapter and interpolation question in the fourth chapter.The article includes four chapters:The first chapter is an introduction which summarizes wavelet and multiwavelet history and points out the merits of multiwavelets compared with the scalar wavelet. But its shortcoming is the imbalance question caused by multi-input and multi-output.The second chapter introduces the theory of wavelet and multiwavelets. In the first part, it introduces continual wavelet transform and multiresolution analysis about scalar wavelet. In the second part, it emphatically introduces related knowledge of multiwavelets . In the same with scalar wavelet, multiwavelets also have multiresolution analysis. From here, we can see the similarity and difference between scalar wavelet and multiwavelets. Then, it introduces important decomposition and construction algorithms in signal processing. Finally, we introduce multiwavelets' properties. These properties are important performance indexes of multiwavelets in practical application. It is also important foundation of the following two chapter.In accordance with existed symmetry question about multiscaling functions with equal support of each component, the third chapter presents the time domain conditions of multifilter banks for symmetrical multiscaling functions with different support of...