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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.


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.


o The permanent classroom for this class is ME-300. Please make a note of it. o PS 0.0 has been posted so that you can review the material from the undergraduate signal processing class. o 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. o Copies of the MATLAB assignment are outside my office. Please pick them up.


o Course Outline/Syllabus


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

Sampling Theorem and Multirate Operations:

o Notes on Vector Spaces and Hilbert Spaces o Notes on Fourier Series o Notes on Parseval's Theorem o Time-Frequency Uncertainty Theorem o Notes on the Sampling Theorem o Notes on Multirate Operations o Notes on the Spectral Zoom Operation o Note on the Decimation and Interpolation o Decimation and Interpolation Continued o Decimation and Interpolation as Matrix Operations o Cascade of Decimation Operations o Guide on MATLAB functions o Guide on MATLAB Multirate Operations

Filterbanks and Applications :

o Note on the Polyphase Decomposition o Examples of the Polyphase Decomposition o Efficiency of the Polyphase Structure o Quadrature Mirror Filterbanks o Example: IIR QMF Filterbank o Paraunitary Filterbanks o More on PR Filterbanks o Example: PR Filterbanks o Filterbank Transceiver o Example: TMUX design o Example: Multirate Frequency Transformation

Quantization and Noise Shaping:

o Notes on Uniform quantization o Uniform quantization function o Output of the Uniform Quantization Function o Output of fxquant.m function Continued o Example: Uniform Quantization o White Noise Signal Model o LTI processing of Random Signals o Random Signals and Multirate Systems o Noise Shaping Via Oversampling o Nonuniform quantization Via the CDF Method o Notes on Non Uniform Quantization o Output of Non Uniform Quantization o Gain--Noise Model for Non Uniform Quantization o Differential Quantization

System Functions, Properties, Factorization :

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

Structures for LTI Systems

o On Sensitivity to Coefficient Quantzation o Example: Cascade Form o Example: Parallel Form o Example: Pole-Zero Combination o Notes on Lattice Structures o Example: Comparison of Approaches o Example: Schur-Cohn Stability

On the Discrete Fourier Transform

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

Time-Frequency Analysis & Wavelets

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

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