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

Abstract: A method for designing equiripple Fractional Hilbert Transformers（FHT） is presented. Fractional Hilbert transformers 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 nonlinear 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.

Key words: fractional hilbert transformers, equiripple approximation, allpass filters, minimum phase system, cepstral sequence