基于滤波器系数构造小波基方法的改进

Improving Method of Structuring Wavelet Base Based on Filter Coefficients

从两尺度方程的频域表达式出发,根据两尺度函数的递推关系,通过滤波器系数构造小波函数,并把这个过程由一维构造情况推广到多维构造情况.针对一维标量小波存在的问题,引入向量小波,对算法做了进一步改进,给出多小波的构造方法,构造出的尺度函数具有紧支撑性、正交性、对称性和较高的正则性.通过仿真对比实验,验证了改进算法的有效性.

Based on the frequency domain expression of two scaling function,according to recursion relation,filter coefficients were successfully applies to structure wavelet function, and this process was extended from one to many dimensions. Considering some shortcomings of scalar wavelet, anew idea that uses vector wavelets in order to improve the construction algorithm was put forward. Constructed vector wavelets were proved to own all characteristic of wavelet base such as compact support,orthonormat, symmetry and higher regularity. The simulation experiments proved the validity of this improved algorithm.