Digital Signal Processing I

ECE-539, Digital Signal Processing I

Term: Spring 2009

Instructor: 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 reconstruction 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.

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ANNOUNCEMENTS

The permanent classroom for this class is ME-300. Please make a note of it. PS 0.0 has been posted so that you can review the material from the undergraduate signal processing class. Midterm exam will be posted to this page on March 24, Tue, 4:00 PM and will be due back in class March 25, 4:00 PM. Copies of the MATLAB assignment are outside my office. Please pick them up.

COURSE MATERIALS

Course Outline/Syllabus

Preliminaries:

Problem Set # 0 Notes on the Zee-transform Z-transform tables DTFT tables

Sampling 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