Current research has proposed a non-parametric speech waveform representation (rep) based on zeros of the z-transform (ZZT) [1] [2]. Empirically, the ZZT rep has successfully been applied in discriminating the glottal and vocal tract components in pitchsynchronously windowed speech by using the unit circle (UC) as discriminant [1,2]. Further, similarity between ZZT reps of windowed speech, glottal flow waveforms, and waveforms of glottal flow opening and closing phases has been demonstrated [1,3]. Therefore, the underlying cause of the separation on either side of the UC can be analyzed via the individual ZZT reps of the opening and closing phase waveforms; the waveforms are generated by the LF glottal flow model (GFM) [1]. The present paper demonstrates this cause and effect analytically and thereby supplement the previous empirical works. Moreover, this paper demonstrates that immiscibility is variant under changes in frame lengths; lengths that maximize or minimize immiscibility are presented.

s B. Bozkurt, Zeros of the z-transform (ZZT) representation and chirp group delay processing for the analysis of source and filter characteristics of speech signals, Ph.D. dissertation, Faculte Polytechnique de Mons, Belgium, October 2005. B. Bozkurt, B. Doval, C. D’Alessandro and Thierry Dutoit, Zeros of Z-Transform Representation With Application to Source-Filter Separation in Speech, IEEE Signal Processing Letters, vol. 12, No. 4, April 2005. C.F. Pedersen, P. Dalsgaard and O. Andersen, On Separability of the Opening and Closing Phases of the LF Glottal Flow Model by Zeros of the Z-transform, IEEE Transactions on Audio, Speech, and Language Processing, submitted for publication, 2009.