Digital Signal Processing I
Term: Spring 2009
filterbanks, paraunitary filterbanks, uniform and nonuniform quantization approaches,
Minimum phase systems, system function factorization, linear phase systems, linear prediction,
Levinson--Durbin recursion, lattice structures, normalized lattice structures,
DFT, 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.
Course Outline/Syllabus
Problem Set # 0
Notes on the Zee-transform
Z-transform tables
DTFT tables
Notes on Vector Spaces and Hilbert Spaces
Notes on Fourier Series
Notes on Parseval's Theorem
Time-Frequency Uncertainty Theorem
Notes on the Sampling Theorem
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
Cascade of Decimation Operations
Guide on MATLAB functions
Guide on MATLAB Multirate Operations
Note on the Polyphase Decomposition
Examples of the Polyphase Decomposition
Efficiency of the Polyphase Structure
Quadrature Mirror Filterbanks
Example: IIR QMF Filterbank
Paraunitary Filterbanks
More on PR Filterbanks
Example: PR Filterbanks
Filterbank Transceiver
Example: TMUX design
Example: Multirate Frequency Transformation
Notes on Uniform quantization
Uniform quantization function
Output of the Uniform Quantization Function
Output of fxquant.m function Continued
Example: Uniform Quantization
White Noise Signal Model
LTI processing of Random Signals
Random Signals and Multirate Systems
Noise Shaping Via Oversampling
Nonuniform quantization Via the CDF Method
Notes on Non Uniform Quantization
Output of Non Uniform Quantization
Gain--Noise Model for Non Uniform Quantization
Differential Quantization
Minimum-phase System functions
Power Spectral Factorization
Example on Power Spectral Factorization
Note on Frequency response of linear phase FIR systems
Note on System functions Zeroes of linear phase FIR systems
Least-squares formulation : linear phase FIR system design
On Least Squares Inversion
On Sensitivity to Coefficient Quantzation
Example: Cascade Form
Example: Parallel Form
Example: Pole-Zero Combination
Notes on Lattice Structures
Example: Comparison of Approaches
Example: Schur-Cohn Stability
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
Time Frequency Representations
Discrete Wavelet Transforms
Nonuniform DFT
Paraunitary Filterbanks and Biorthogonal Wavelets
ECE-539, Digital Signal Processing I
Term: Spring 2009Instructor: Balu Santhanam
Pre-requisites: EECE-314, EECE-340, ECE-439 recommended, linear algebra, MATLAB.
CATALOG COURSE DESCRIPTION :
Nyquist sampling theorem, Multirate operations and filterbanks, poylphase representations, perfect reconstructionfilterbanks, paraunitary filterbanks, uniform and nonuniform quantization approaches,
Minimum phase systems, system function factorization, linear phase systems, linear prediction,
Levinson--Durbin recursion, lattice structures, normalized lattice structures,
DFT, 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.
ANNOUNCEMENTS
COURSE MATERIALS
Course Outline/SyllabusPreliminaries:
Problem Set # 0 Notes on the Zee-transform Z-transform tables DTFT tablesSampling Theorem and Multirate Operations:
Notes on Vector Spaces and Hilbert Spaces Notes on Fourier Series Notes on Parseval's Theorem Time-Frequency Uncertainty Theorem Notes on the Sampling Theorem 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 Cascade of Decimation Operations Guide on MATLAB functions Guide on MATLAB Multirate Operations Filterbanks and Applications :
Note on the Polyphase Decomposition Examples of the Polyphase Decomposition Efficiency of the Polyphase Structure Quadrature Mirror Filterbanks Example: IIR QMF Filterbank Paraunitary Filterbanks More on PR Filterbanks Example: PR Filterbanks Filterbank Transceiver Example: TMUX design Example: Multirate Frequency Transformation Quantization and Noise Shaping:
Notes on Uniform quantization Uniform quantization function Output of the Uniform Quantization Function Output of fxquant.m function Continued Example: Uniform Quantization White Noise Signal Model LTI processing of Random Signals Random Signals and Multirate Systems Noise Shaping Via Oversampling Nonuniform quantization Via the CDF Method Notes on Non Uniform Quantization Output of Non Uniform Quantization Gain--Noise Model for Non Uniform Quantization Differential Quantization System Functions, Properties, Factorization :
Minimum-phase System functions Power Spectral Factorization Example on Power Spectral Factorization Note on Frequency response of linear phase FIR systems Note on System functions Zeroes of linear phase FIR systems Least-squares formulation : linear phase FIR system design On Least Squares Inversion 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 Example: Schur-Cohn Stability 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 Time-Frequency Analysis & Wavelets
Time Frequency Representations Discrete Wavelet Transforms Nonuniform DFT Paraunitary Filterbanks and Biorthogonal Wavelets 
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