Equiripple minimum phase FIR filter design from linear phase systems using root moments

In this brief we propose to design a minimum phase finite-impulse response (FIR) digital filter transfer function from a given equiripple linear phase FIR transfer function which has identical amplitude. The brief deals with two important issues. The first issue is that we are concentrating on very high degree polynomials for which factorization procedures for root extraction are unreliable. A novel approach is taken, that involves the use of a set of parameters called root moments of a polynomial, derivable directly from the polynomial coefficients that immensely facilitate the factorization of polynomials of very large order. The second issue is that the polynomials we deal with have roots on the unit circle. In the paper we propose a method to overcome this problem. The results of the proposed design scheme are very encouraging as far as robustness and computational complexity are concerned.