Minimum phase signal derived from root cepstrum

Abstract

A root cepstrum based approach is presented to derive a minimum phase signal from a given magnitude spectrum. The approach is based on computing the root homomorphic cepstrum. It is found that the causal portion of the signal obtained by taking the inverse Fourier transform of the squared magnitude spectrum is a minimum phase signal. Two separate root cepstra for a signal are defined, one which is derived from the squared magnitude spectrum referred to as xrp(n) and the other from the inverted squared magnitude spectrum referred to as xrz(n). It is observed that, for any non-minimum phase test signal, the causal portion of xrp(n) and xrz(n) contain information about the exact locations of poles and zeros respectively, which correspond to the minimum phase equivalent poles and zeros of the original signal.