六进正交对称紧支小波的构造

发布时间：2018-03-23 03:33

本文选题：6进小波　切入点：尺度函数　出处：《北京交通大学》2015年硕士论文　论文类型：学位论文

【摘要】：小波理论因其独特的优势,一经出现便得到了广泛的应用。在实际应用中,人们总希望能够得到同时满足对称性、紧支性以及正交性的小波系统,而我们知道,除Haar小波以外的单小波无法同时满足对称性、紧支性以及正交性,这就限制了小波的应用。所以,多进小波成为人们解决这一矛盾的一个重要研究方向。本文正是在多进小波的理论基础上,深入研究了6进小波。首先,研究了尺度函数满足正交条件和两尺度符号因子模的代数多项式的等价关系,并给出了尺度符号因子Sm-1唯一性的条件；研究了正交尺度函数的最小支撑区间。给出了用尺度符号因子构造m正则阶的正交紧支尺度函数所满足的条件,在此基础上通过给两尺度符号因子添加约束,使尺度函数满足了对称性,并且6进小波函数满足正交性、紧支性以及对称性的构造性定理。本文最后给出了两个同时满足对称性、紧支性以及正交性6进小波的例子,每个小波系统是由一个尺度函数和5个正交小波函数构成的,其中正交小波函数包含2个对称和3个反对称的。
[Abstract]:Wavelet theory has been widely used because of its unique advantages. In practical applications, people always want to obtain wavelet systems which satisfy symmetry, compactness and orthogonality, and we know that, Simple wavelets other than Haar wavelets can not satisfy symmetry, compactness and orthogonality at the same time, which limits the application of wavelets. Therefore, multivariate wavelets have become an important research direction to solve this contradiction. In this paper, based on the theory of multivariate wavelets, we deeply study the 6-dyadic wavelets. Firstly, we study the equivalence of algebraic polynomials which the scaling functions satisfy the orthogonal conditions and the modulus of the two scale sign factors. The condition of the uniqueness of the scale symbol factor Sm-1, the minimum support interval of the orthogonal scale function are studied, and the conditions for constructing the orthogonal compact support scale function of m regular order by using the scale symbol factor are given. On this basis, by adding constraints to the two scale symbol factors, the scale function satisfies the symmetry, and the 6-ary wavelet function satisfies the orthogonality. In this paper, we give two examples of 6-dyadic wavelets satisfying symmetry, compactness and orthogonality at the same time. Each wavelet system is composed of a scale function and five orthogonal wavelet functions. The orthogonal wavelet function contains two symmetries and three antisymmetric ones.
【学位授予单位】：北京交通大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O174.2

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