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)
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 |
|||
|
Blackman |
Analysis of real speech signal (vowel "a")
|
window size=T0 |
window size=2T0 |
window size=3T0 |
|
|
Rectangular |
|||
|
Blackman |
Last update: 14th Dec, 2005