Separation of mixed phase signals by zeros of the z-transform - A reformulation of complex cepstrum based separation by causality

In recent studies, a non-parametric speech waveform representation (rep.) based on zeros of the z-transform (ZZT) has been proposed. The ZZT rep. has successfully been applied in separating mixed phase signals, e.g. pitch-synchronously windowed speech, into min/max phase by using the unit circle as discriminant. As the ZZT rep. is obtained by factorization of the z-transform, relations to the complex cepstrum (CC) exist. The present paper interrelates the ZZT rep. with the CC via factorization of the z-transform, and demonstrates that unit circle discrimination of a ZZT rep. can be formulated as a CC based separation by causality. A numerical experiment supplements theory by separating a range of LF glottal flow waveforms into their opening and closing phase constituents. Further, randomized mixed phase sequences are separated. As the CC based separation also can be obtained via FFT it has a lower time and space complexity than the ZZT based counterpart.