Courses | Dr. Balu Santhanam

ECE-539: Digital Signal Processing

Homework

Problem Set #xx.x

Exams

Midterm Exam

Term:Spring 2020
Location: ECE-237
Instructor: Balu Santhanam
Pre-requisites: ECE-314, ECE-340, ECE-439 recommended, linear algebra, MATLAB.
Course Abstract: Nyquist sampling theorem, Multirate operations and filterbanks, poylphase representations, perfect reconstruction filterbanks, paraunitary filterbanks, uniform and nonuniform quantization approaches, Minimum phase systems, linear prediction, Levinson--Durbin recursion, lattice structures, normalized lattice structures, DFT and Cooley-Tukey Algorithms, prime factor algorithms, Chirp Z Transform, spectral analysis, signal flow graphs, Quantization, Finite register length and digital filters, Short-time Fourier transform, Wigner distribution, Wavelet transform.

Class Notes

Sampling Theorem and Multirate Operations

[Expand]Mathematical Preliminaries

Notes on Vector Spaces and Hilbert Spaces
Notes on Fourier Series
Notes on Parseval's Theorem
Time-Frequency Uncertainty Theorem
Example: Nyquist-Shannon Wavelets
Haar Wavelets
Gram-Schmidt Algorithm

[Expand]Sampling Theorem Revisited

Notes on the Sampling Theorem
Example: Frequency Domain Sampling
Notes on Multirate Operations
Notes on the Spectral Zoom Operation
Note on the Decimation and Interpolation
Decimation and Interpolation Continued
Decimation and Interpolation as Matrix Operations
Example: Application of Noble Identities
Example: Fractional Sampling Rate Change
Cascade of Decimation Operations
Guide on MATLAB functions
Guide on MATLAB Multirate Operations

Filterbanks & Applications

[Expand]Polyphase Decomposition

Note on the Polyphase Decomposition
Examples of the Polyphase Decomposition
Efficiency of the Polyphase Structure

[Expand]Two-Channel Filterbanks

Quadrature Mirror Filterbanks
Example: IIR QMF Filterbank
Paraunitary Filterbanks
On PR Filterbanks
Design of PR Filterbanks
Example: PR-Filterbank Design: Polyphase Matrix Approach
Example: Filterbanks and Equalization
Example: PR Filterbanks

[Expand]TMUX Design

Tutorial on Filterbanks in Digital Communications
Filterbank Transceiver
Example: TMUX design

[Expand]Other Applications

Example: Multirate Frequency Transformation

QUANTIZATION

[Expand]Uniform Quantization

Notes on Uniform quantization
Uniform quantization function
Output of the Uniform Quantization Function
Output of fxquant.m function Continued
Example: Uniform Quantization
Example: Logarithmic Compression
Mu-law and A-law companding
White Noise Signal Model

[Expand]Noise Shaping

LTI processing of Random Signals
Random Signals and Multirate Systems
Noise Shaping Via Oversampling

[Expand]Non-Uniform Quantization

Nonuniform quantization Via the CDF Method
Notes on Non Uniform Quantization
Output of Non Uniform Quantization
Non Uniform Quantization MATLAB functions
Gain--Noise Model for Non Uniform Quantization
Differential Quantization

Systems

[Expand]System Functions, Properties, Factorization :

Minimum-phase System functions
Power Spectral Factorization
Example on Power Spectral Factorization
Frequency response of linear phase FIR systems
System functions Zeroes of linear phase FIR systems
Least-squares formulation : linear phase FIR system design
On Least Squares Inversion

[Expand]Structures for LTI Systems

On Sensitivity to Coefficient Quantzation
Example: Cascade Form
Example: Parallel Form
Example: Pole-Zero Combination
Notes on Lattice Structures
Example: Comparison of Approaches
FIR Lattice
Characteristics of FIR Lattice Structure
IIR Lattice
Example for Lattice Structure
Example: Schur-Cohn Stability
Example: Transposed Direct Form
Relation between Input Scaling Options
Example: Scaling and Overflow

Discrete Fourier Transform

[Expand]On the Discrete Fourier Transform

Discrete Fourier Series
Properties of the DFT
Radix 2 FFT algorithms
Radix 3 FFT algorithms
Cooley Tukey FFT Algorithms
Convolution Based DFT Algorithms
Linear Vs. Circular Convolution
Example: Linear Vs. Circular Convolution
DFT: Filterbank Viewpoint
Non Uniform DFT
Zero padding and Resolution

[Expand]Time-Frequency Analysis & Wavelets

Time Frequency Representations
Discrete Wavelet Transforms
Nonuniform DFT
Paraunitary Filterbanks and Biorthogonal Wavelets

References
Syllabus
Solutions to Problems
Z-transform Table
DTFT Table
fxquant.m
cdfquantn.m
[Expand]Preliminary

Problem Set 0.0
Notes on the Zee -transform

Copyright © 2013 Balu Santhanam. All rights reserved.