A Polynomial Factorisation Method for Low Group Delay Fir Equiripple Filter Design from Linear Phase Systems

In this contribution we propose a method for reduced-groupdelay Finite Impulse Response (FIR) equiripple filter design from a given linear phase FIR filter. Our restriction is to keep the amplitude response identical. We are concentrating on very high degree polynomials (transfer functions) for which factorisation procedures for root extraction are unreliable. The initial linear phase transfer functions are obtained by standard design algorithms and particularly in this study by the Remez algorithm. The approach taken involves the use of the Cauchy Residue Theorem applied to the contour integral of the logarithmic derivative of the transfer function around appropriate curves. This leads into a set of parameters related directly to the polynomial coefficients, which facilitate the factorisation problem. The results of the proposed design scheme are very encouraging as far as robustness and computational complexity are concerned.