Design of IIR allpass fractional-delay fractional Hilbert transformer using complex cepstrum

Abstract

The IIR allpass fractional-delay fractional Hilbert transformer is designed in the complex-cepstrum domain. The maximal flatness criterion on the phase response is considered for the midband frequency. Two independent systems of linear equations are formulated, resulting in closed-form solutions of the even-index and odd-index parts of complex cepstrum of the denominator polynomial. Moreover, they are proportional to the two design parameters: fractional delay and phase shift. This is attractive in that a tunable scheme for variable parameters is realizable. Only two normalized complex-cepstrum sequences need to be designed, stored and tuned by scaling. Both nonrecursive and recursive algorithms are available for renewing the filter coefficients from the complex cepstrum.