Some Of The Research About Omra Wavelet

Wavelet analysis is current a new area which develops rapidly in applied mathema-tics and engineering mathematics. It is a great creation after Fourier analysis and can solve many problems which can not be settled in Fourier analysis. Moreover, it provides us with a powerful tool for theory science and applied science, and has promoting effect in studying non-linear problems, numerical calculation, network and information security and so on.It is about of studying of A-expansive dilation wavelets. The wavelets have beco-me a hot spot which is studied by many wavelets experts recently at home and abroad, and the concept of which were firstly given by Qing Gu and Deguang Han. It is evolved from the original MRA definition and the idea of the wavelet set. This kind of wavelets have some of the advantages of the wavelet set and MRA wavelets at the same time. For examples, it can easily construct wavelet examples or counter-examples and can also be used in OMRA wavelet construction along with the orthogonality, compact support and symmetry of the good nature of the wavelet.It is known that the two-scale equations play a very important role in wavelet anal-ysis, signal processing and computer Graphics. A founction is a scale function if it sati-fies the two-scale equations. Therefore, by constructing a scaling function and then get the wavelet is a very importat way to construct wavelet.This paper focuses on the construction of A-expansive dilation OMRA wavelets, and orthogonal multiwavelets with compact support in two-dimensional space, and we get the corresponding results. Therefore, it promote the development of wavelet theory. This paper is composed of four chapers.The first chapter. Introduction. Briefly describes the generation and development process of the wavelet analysis theory and the development status of A-expansive dilati-on OMRA wavelet theory.The second chapter. It firstly gives the basic definitions and basic properties of wavelet sets in the one-dimensional space; And then, it introducts the definitions of A-expansive dilation OMRA wavelet sets and gets some relevant conclusions.The third chapter, A-expansive dilation OMRA wavelet and its existence. Firstly, it gives the knowledge of A-expansive dilation OMRA wavelet and thus establishes A- expansive dilation orthogonal multiresolution analysis. By defining the course of its construction, we get A-expansive dilation OMRA existence of relevant conclusions.The fourth chapter, From the multiresolution analysis of the definition of two-dimensionnal space, it gets the definition of the scaling function and wavelet function according to the definition of A-expansive dilation OMRA, and studies the their’nature. Finally, it gives a construction method of with compact support OMRA wavelet.