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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。
In this paper, we propose a new construction method based on IIR orthogonal wavelet with high order vanishing moments. From the conditions of orthogonality and regularity of the wavelet, we can obtain the conditions of some constrained IIR filter banks, and discuss the constraint filter coefficients and their Pole-zero relationship. According to these relations, the Remez algorithm can be directly applied to the forbidden band and the problem of designing the eigenvalue problem form is formulated. Second, a set of filter coefficients can be easily calculated by solving its eigenvalue problem, and the order of the vanishing moments can be arbitrarily specified by applying the optimal filter coefficients for the equal-ripple response after the iterative process is applied.