ZZT-domain immiscibility of the opening and closing phases of the LF GFM under frame length variations

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 pitch-synchronously 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.