New spectral methods for analysis of source/filter characteristics of speech signals

This study proposes a new spectral representation called the Zeros of _Z-_
Transform (ZZT), which is an all-zero representation of the _z-_ transform of
the signal. In addition, new chirp group delay processing techniques are
developed for analysis of resonances of a signal. The combination of the ZZT
representation with the chirp group delay processing algorithms provides a
useful domain to study resonance characteristics of source and filter
components of speech. Using the two representations, effective algorithms are
developed for: source-tract decomposition of speech, glottal flow parameter
estimation, formant tracking and feature extraction for speech recognition.
The ZZT representation is mainly important for theoretical studies. Studying
the ZZT of a signal is essential to be able to develop effective chirp group
delay processing methods. Therefore, first the ZZT representation of the
source-filter model of speech is studied for providing a theoretical
background. We confirm through ZZT representation that anti-causality of the
glottal flow signal introduces mixed-phase characteristics in speech signals.
The ZZT of windowed speech signals is also studied since windowing cannot be
avoided in practical signal processing algorithms and the effect of windowing
on ZZT representation is drastic. We show that separate patterns exist in ZZT
representations of windowed speech signals for the glottal flow and the vocal
tract contributions. A decomposition method for source-tract separation is
developed based on these patterns in ZZT. We define chirp group delay as group
delay calculated on a circle other than the unit circle in _z-_ plane. The
need to compute group delay on a circle other than the unit circle comes from
the fact that group delay spectra are often very noisy and cannot be easily
processed for formant tracking purposes (the reasons are explained through ZZT
representation). In this thesis, we propose methods to avoid such problems by
modifying the ZZT of a signal and further computing the chirp group delay
spectrum. New algorithms based on processing of the chirp group delay spectrum
are developed for formant tracking and feature estimation for speech
recognition. The proposed algorithms are compared to state-of-the-art
techniques. Equivalent or higher efficiency is obtained for all proposed
algorithms. The theoretical parts of the thesis further discuss a mixed-phase
model for speech and phase processing problems in detail. Index Terms—spectral
representation, source-filter separation, glottal flow estimation, formant
tracking, zeros of z-transform, group delay processing, phase processing.