一种非90°移相器的等波纹逼近设计方法

摘要

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.%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。