Zeros of the z-transform (ZZT) representation and chirp group delay processing for the analysis of source and filter characteristics of speech signals

Dissertation submitted to the Faculté Polytechnique de Mons for the degree of Doctor of Philosophy in applied sciences (October 2005)

by Baris Bozkurt

Supervisor: Prof. Thierry Dutoit

(In collaboration with LIMSI/CNRS Orsay-France . Summary of the ZZT is available on LIMSI Pages)

Thesis Manuscript:doc version , pdf version

The presentation: ppt presentation

 

MOVIES:

Movie 1: ZZT of a sinusoid: sinusZeros.avi

Movie 2: ZZT of a causal all-pole filter response: causalResponseZeros1.avi (with three pole-pairs at : 500Hz,1000Hz and 2000Hz)

Movie 3: The effect of exponential decay coefficient on ZZT of a damped sinusoid: expCoeffInDampedSinusoid.avi

 

Movies for studying window size-location effects on :

-ZZT representation

-Amplitude spectrum

-Group delay function

(Points to concentrate while watching the movie: For the windowing with Blackman function, both the amplitude spectrum and group delay function is very smooth when the center of window coincides the center of gravity pointer(in green) close to the GCI of the speech signal. At that instant, the number of zeros close to the unit circle is least and there exist zero lines outside and inside the unit circle with gaps at formant frequencies)

Analysis of synthetic speech signal (with F1=600Hz, F2=1200Hz,F3=2200Hz and F4=3200Hz)

window size=T0

window size=2T0

window size=3T0

Rectangular

synthT0Rect.avi

synth2T0Rect.avi

synth3T0Rect.avi

Blackman

synthT0Blackman.avi

synth2T0Blackman.avi

synth3T0Blackman.avi

Analysis of real speech signal (vowel "a")

window size=T0

window size=2T0

window size=3T0

Rectangular

realT0Rect.avi

real2T0Rect.avi

real3T0Rect.avi

Blackman

realT0Blackman.avi

real2T0Blackman.avi

real3T0Blackman.avi

Last update: 14th Dec, 2005