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OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
EE627 - Speech Signal ProcessingLecture 3/4 : Basic Signal Processing Techniques
for Speech Recognition
R. Hegde
Dept. of Electrical Engg.
IIT Kanpur
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
Outline
1 Overview
2 Discrete Time Sequences
3 Properties of Discrete Time Systems
4 The Discrete Time Fourier Transform and its Properties
5 The Z - Transform and ROC
6 Modeling Speech with the Transfer Function and Di�erence
Equations
7 Developing a Complete Digital Speech Model
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
Basic Problem
Overview of Digital Speech
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
Discrete Time Sequences
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
The Complex Exponential Sequence
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
Discrete Time Systems
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
Linear Discrete Time Invariant Systems
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
Convolution and Speech Processing
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
Stability and Causality
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
Stability and Causality : An Example
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
The DTFT Pair
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
Properties of DTFT relevant to Speech Recognition
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
Energy Density of a Signal
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
DTFT of Single and Multiple Exponential and Sinusoidalsequences
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
Important Generalizations
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
The Z - Transform
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
The IZT and ROC
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
The ROC for Four Typical Sequences
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
The ROC - Contd.
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
Transfer Function of LTI Systems
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
Convolution and Windowing Theoroem
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
Relating the Transfer Function and the Spectral Envelope
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
Relating the Transfer Function and the Spectral Envelope -Contd.
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
The Constant Co-e�cient Linear Di�erence Equation
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
Pole Zero concepts from the CCLDE
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
Speech Models as Linear Time Varying Systems
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
The Discrete Fourier Transform (DFT)
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
Sampling and Reconstruction of the Speech Signal
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
Sampling the Impulse Response
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
Pole Zero Modeling the Vocal Tract
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
Developing a Digital Model for Speech Production : VocalTract
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
Developing a Digital Model for Speech Production : All Polemodeling the Tract
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
Developing a Digital Model for Speech Production : VT +Lip radiation
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
Developing a Digital Model for Speech Production : TheComplete Model
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
OverviewDiscrete Time Sequences
Properties of Discrete Time SystemsThe Discrete Time Fourier Transform and its Properties
The Z - Transform and ROCModeling Speech with the Transfer Function and Di�erence Equations
Developing a Complete Digital Speech Model
References
Rabiner and Juang , Fundamentals of Speech Recognition,
Prentice Hall
T. Quatieri, Discrete Time Speech Signal Processing , Prentice
Hall
Rabiner and Schafer, Discrete Time Processing of Speech
Signals , Prentice Hall
rhegde@ iitk.ac.in EE627 - Speech Signal Processing, Lecture 3/4
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