Construction Of Compactly Supported Symmetric Orthonormal Wavelets With Dilation6

Wavelet theory is widely applied for its unique advantages. In practice, people always want to get the wavelets that simultaneously satisfy the habitude of compact support, symmetric and orthonormal. Yet we all know, there is not any2-band wavelets (except for Haar wavelets) that simultaneously satisfy the habitude of compact support, symmetric and orthonormal. This limits the application of wavelet. Thus, n-band wavelets become an important research direction to resolve this contradiction.This paper studied on the6-band wavelets. First, we got the equivalence relations between the scale function satisfying the orthogonal condition and the two-scale symbol factor mold algebraic polynomial, and we give the condition for the scale symbol factor Sm-1to be unique. Then we construct orthogonal compactly supported scaling function with regularity m by scaling function factor. Then we give the condition of symmetric. Finally we successfully construct compactly supported o.n. symmetric scaling functions with dilation6and regularity m. At the end, two examples are given. Each wavelet system consists of a scaling function and five orthogonal wavelet functions, two of the wavelet functions is symmetric and three are antisymmetric.