基于特征值问题的正交小波构造方法

The method of orthogonal wavelet construction based on eigenvalue problem

本文提出了一种基于具有高阶消失矩的IIR正交小波构造方法.从小波的正交性和正则性条件出发,可以得到一些约束IIR滤波器组的条件,并且探讨约束滤波器系数及其零极点的关系。依这些关系,可以直接将Remez算法应用于禁止带上,并制定了设计特征值问题形式的问题。其次,一组滤波器系数可以通过解它的特征值问题而容易地计算出来,并且通过施加迭代过程后将得到等波纹响应的最优滤波器系数,可以任意的指定消失矩的阶数。

This paper presents a method of IIR orthogonal wavelet construction method based on high order vanishing moments. Starting from the wavelet orthogonality and regularity conditions, we can get some constrained IIR filter group, and to explore the relationship between the filter coefficients and zero pole constraints. According to these relations, can be directly applied Remez algorithm to the forbidden to take on, and the design form of eigenvalue problem problem. Secondly, a set of filter coefficients by solving its eigenvalue problem and easily calculated, and by applying the iterative process will get the best response of corrugated filter coefficients, specify the number of vanishing moments can be arbitrary.