Equiripple minimum phase FIR filter design from linear phase systems using a novel technique for polynomial factorisation

We propose a method for a minimum phase finite impulse response (FIR) equiripple filter design from a given linear phase FIR filter with the same amplitude response. 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 logarithmic derivative of the 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