一种数字全通滤波器的最小二乘设计法  

On a Weighted Least-Squares Technique for Design All-pass Digital Filter

作　　者：刘渭清[1,2] 

机构地区：[1]西安文理学院物理与机械电子工程学院,西安710065 [2]西安电子科技大学电子工程学院,西安710065

出　　处：《西南师范大学学报（自然科学版）》2013年第12期90-94,共5页Journal of Southwest China Normal University(Natural Science Edition)

摘　　要：探讨了在复倒谱系数条件下,利用加权最小二乘法(WLS)实现等波纹逼近数字全通滤波器的设计方案.对于平稳的数字全通滤波器,其分母多项式一定具有最小相位;该方法是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,采用最小二乘等波纹逼近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.由全通滤波器的特性可知,分母多项式系数可完全确定全通滤波器的传递函数.这种方法能够使所设计的滤波器的群延迟特性在整个频带上近似理想群延迟,其误差在整个频带上呈均匀分布,同时降低了误差的最大值.A procedure for the design of equiripple digital all-pass filter with a weighted least-squares technique based on cepstral coefficients has been presented.The denominator polynomial of a stable allpass 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 a weighted least-squares technique; by means of 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 error is a uniform distribution.

关 键 词：加权最小二乘法(WLS) 全通滤波器 群延迟 等波纹逼近 复倒谱系数 最小相位 

分 类 号：TN713.7[电子电信—电路与系统]