Selective digital filters with quadratic phase

Abstract

A method for design of a new class of digital infinite impulse response filters realized as parallel connection of two all-pass filters is presented in this paper. A new approach to approximation of quadratic phase of all-pass filter at all frequencies is given. Chosen parallel structure offers opportunity for realization of filters with arbitrary shape phase. The presented algorithm is based on all-pass filter phase approximation. Phases of both all-pass filters approximate ideal quadratic phase in minimax sense at all frequencies. Such filters can be applied for chirp signal compression or expansion. Magnitude characteristic of described filters is very selective and elliptic-like. Obtained filters are compared with elliptic filter and group delay corrector in cascade. For the same specifications, much better results are achieved by the proposed filters. Parallel connection of all-pass filters introduces lower signal delay, and for a given maximal phase, approximation error demands less complex network. Examples to illustrate the proposed method are given.