一种非90°移相器的等波纹逼近设计方法  

Equiripple approximation method for designing fractional hilbert transformers

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：《计算机工程与应用》2014年第12期202-206,共5页Computer Engineering and Applications

基　　金：西安市科技计划项目--西安文理学院科技创新基金专项项目资助(No.CXY1352WL34)

摘　　要：提出了一种非90°移相希尔伯特变换器的等波纹逼近设计方法。非90°移相器本质上是一种指定相位特性的全通滤波器。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。通过构造一个纯虚奇对称相位函数的方法推导出了分母多项式的相位函数与其复倒谱序列之间的关系;利用加权最小二乘法求得分母相位的等波纹逼近函数,进而利用上述关系求出其倒谱序列;依据复倒谱的基本理论,通过求解一个非线性递归差分方程得到分母多项式系数。设计实例表明,这种方法能够使设计的非90°移相器的相位函数在指定频带上实现等波纹逼近的要求,从而提高了非90°移相器的频率选择性。A method for designing equiripple Fractional Hilbert Transformers（FHT）is presented. Fractional Hilbert trans-formers are essentially allpass digital filters with the specified phase. It is well known that the denominator polynomial of a stable allpass filter must be a minimum phase system. By constructing a pure imaginary odd symmetry phase function , the relation between phase function and cepstral sequence has been derived;equiripple approximation function of denominator phase can be obtained by using a weighted least-squares technique, and its cepstral sequence can be got by above-mentioned relation;based on the theory of basic cepstral, the denominator polynomial coefficients can be determined through a non-linear recursive difference equation. Design examples indicate that the proposed filters exhibit good approximation to the desired phase response , and improve the frequency of selectivity of FHT.

关 键 词：非90°移相器 等波纹逼近 全通滤波器 最小相位系统 复倒谱序列 

分 类 号：TN713.7[电子电信—电路与系统]