Root moments: a nonlinear signal transformation for minimum FIR filter design

In this work we propose to design a minimum phase FIR digital filter transfer function from a given linear phase FIR transfer function which has identical amplitude. We are concentrating on very high degree polynomials for which factorisation procedures for root extraction are unreliable. We also assume that the polynomials have roots on the unit circle. The approach taken involves the use of the Cauchy Residue Theorem applied to the logarithmic derivative of the transfer function. This leads into a set of parameters derivable directly from the polynomial coefficients that facilitate the factorisation problem. The concept is developed in a way that leads naturally to the celebrated Newton Identities. In addition to solving the above problem, the results of the proposed design scheme are very encouraging as far as robustness and computational complexity are concerned.