Minimum phase FIR filter design from linear phase systems using root moments

In this contribution we propose a method for a minimum phase finite impulse response (FIR) filter design from a given linear phase FIR function with the same amplitude response. We concentrate on very high degree polynomials for which factorisation procedures for root extraction are unreliable. The approach taken involves using the Cauchy residue theorem applied to the logarithmic derivative of the transfer function. This leads to a set of parameters derivable directly from the polynomial coefficients which 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.