一种数字全通滤波器的等波纹逼近设计方法

The Equiripple Approximation Method for Designing All-pass Digital Filters

基于复倒谱系数,提出了一种等波纹逼近数字全通滤波器设计方案。由于平稳数字全通滤波器的分母多项式一定具有最小相位,因此,该方案首先基于最小相位滤波器的群延迟函数和其复倒谱系数之间的关系,采用切比雪夫最佳一致逼近准则求得分母多项式的倒谱系数,然后依据全通滤波器分母多项式与其复倒谱系数的关系求得分母多项式,由分母多项式系数确定全通滤波器的传递函数。仿真结果表明,采用该方案使所设计的滤波器的群延迟特性在整个频带上近似为理想群延迟,其误差在整个频带上呈均匀分布,误差的最大值也有所降低。

A method for designing digital all-pass filter using the equiripple approximation of Chebyshev is presented. The denominator polynomial of a stable all-pass filter is certain to have a minimum-phase. Based on the relationship between the delay function and the cepstral coefficients, the complex cepstral coefficients can be determined by the best uniform approximation criterion; by the complex cepstral coefficients, the all-pass filter denomination coefficients are obtained based on the relation between the complex cepstrum coefficient and the stable minimum phase sequence. The all-pass transfer function is completely determined from its denominator coefficients. The group delay of designed filter can approximate the desired group delay in all band, and the error distributes uniformly.