Analysis of Phase Spectrum of Speech Signals Using Allpass Modeling

The phase spectrum of Fourier transform has received lesser prominence than its magnitude counterpart in speech processing. In this paper, we propose a method for parametric modeling of the phase spectrum, and discuss its applications in speech signal processing. The phase spectrum is modeled as the response of an allpass (AP) filter, whose coefficients are estimated from the knowledge of speech production process, especially the impulse-like nature of excitation source. A signal retaining only the phase spectral component of speech signal is derived by suppressing the magnitude spectral component, and is modeled as the output of an AP filter excited with a sequence of impulses. Entropy of energy of the input signal is minimized to estimate the coefficients of the AP filter. The resulting objective function, being nonconvex in nature, is minimized using particle swarm optimization. The group delay response of estimated AP filters can be used for accurate analysis of resonances of the vocal-tract system (VTS). The error signal associated with AP modeling provides unambiguous evidence about the instants of significant excitation of the VTS. The applications of the proposed AP modeling include, but not limited to, formant tracking, extraction of glottal closure instants, speaker verification and speech synthesis.