ECE 544 MD
Wavelets in Signal Processing

Displaying course information from Fall 2012.

Section Type Times Days Location Instructor
MD LEC 1230 - 1350 T R   106B6 Engineering Hall  Minh Do
Web Page http://courses.engr.illinois.edu/ece544md/
Official Description Lectures and discussions related to advanced topics and new areas of interest in signal processing: speech, image, and multidimensional processing. Course Information: May be repeated 8 hours in a term to a total of 20 hours. Credit towards a degree from multiple offerings of this course is not given if those offerings have significant overlap, as determined by the ECE department. Prerequisite: As specified each term. It is expected that each offering will have a 500-level course as prerequisite or co-requisite.
Subject Area Signal Processing
Course Prerequisites Credit in ECE 551
Course Directors Minh N Do
Detailed Description and Outline

Topics:

  1. Introduction and background: why wavelets, filter banks, and multiresolution analysis? signal spaces and operators; review of Fourier theory; multirate signal processing; time-frequency analysis.
  2. Discrete-time bases and filter banks: series expansions of discrete-time signals; analysis and design of filter banks; orthogonal and biorthogonal filter banks; tree-structured filter banks; discrete wavelet transform.
  3. Continuous-time bases and wavelets: multiresolution analysis; iterated filter banks; wavelets and filter banks; wavelet series and its properties; regularity and approximation properties.
  4. Overcomplete expansions and continuous transforms: frame theory; oversampled filter banks; continuous wavelet and short-time Fourier transforms.
  5. Advanced topics: sparse representation; linear and nonlinear approximation in various bases; nonlinear signal estimation; multidimensional filter banks and wavelets; multiscale geometric image processing; compressed sensing.
  6. Applications: speech, audio, image and video compression; denoising; feature extraction; inverse problems.
Texts
M. Vetterli, J. Kovacevic, and V. K. Goyal, The World of Fourier and Wavelets: Theory, Algorithms and Applications; and research papers.
Last updated: 2/13/2013