基于栅格结构的正交小波滤波器组逼近方法

Approximating Methods of Orthogonal Wavelet Filter Banks Based on Lattice Structure

提出一种基于栅格结构的小波滤波器逼近方法·应用栅格结构的特性,采用分步栅格优化和随机栅格优化两个过程来构造小波滤波器·在分步栅格优化中,提出两种优化策略:扔掉和保留;并证明这两个优化策略是等价的,这样可以采用扔掉策略也可以保证我们每步优化是最优的·同时,将这种构造算法推广到不同长度滤波器构造,也成功地将该算法应用到以下问题:构造二通道接近线性相位的正交小波滤波器和有限脉冲的信号自适应小波滤波器(主分量滤波器)·另外,分步栅格优化的部分结果已经出现在IEEEICIP2003上·

In this paper, we present a kind of wavelet filter approximating method based on lattice structure. By virtues of the properties of the lattice structure, two processes, step-by-step lattice optimization and random lattice optimization, are adopted to construct wavelet filters. During the step-by-step lattice optimization, we give two selections: throw-out principle and remained principle, and the two selections are proved to be equivalent to each other. Thus the throw-out principle can ensure that our optimization algorithm is optimal in each step. And we also extend the kind of method to construct wavelet filter banks with different length. In this paper, the algorithm is successfully applied in the following problem: constructing two channel orthogonal wavelet filter banks close to linear phase and constructing signal-adapted wavelet filter banks with finite impulse responses (Principal Component Filter Banks). Parts of results in the step-by-step optimization have been accepted by IEEE ICIP2003.