ECE 544-MD: "Wavelets in Signal Processing"

Fall 2007

Instructor: Prof. Minh N. Do (115 Coordinated Science Lab, 244-4782, ).

Course description:
Wavelets have established themselves as an important tool in modern signal processing as well as in applied mathematics. The objective of this course is to establish the theory necessary to understand and use wavelets and related constructions. A particular emphasis will be put on constructions that are amenable to efficient algorithms, since ultimately these are the ones that are likely to have an impact. We thus study applications in signal processing, communications, and sensing where time-frequency transforms like wavelets play an important role. The course has computer and research projects involving independent study.

Lectures: Tuesdays and Thursdays, 10:00 - 11:20 am; 252 Mechanical Engineering Bldg.


Text books:

Lecture Topics:

1. Introduction and Background (6 hours)
    a. Why wavelets, filter banks, and multiresolution analysis?
    b. Signal spaces and operators
    c. Review of Fourier theory
    d. Multirate signal processing
    e. Time-frequency analysis

2. Discrete-Time Bases and Filter Banks (8 hours)
    a. Series expansions of discrete-time signals
    b. Analysis and design of filter banks
    c. Orthogonal and biorthogonal filter banks
    d. Tree-structured filter banks
    e. Discrete wavelet transform

3. Continuous-Time Bases and Wavelets (8 hours)
    a. Multiresolution analysis
    b. Iterated filter banks
    c. Wavelets and filter banks
    d. Wavelet series and its properties
    e. Regularity and approximation properties

4. Overcomplete Expansions and Continuous Transforms (5 hours)
    a. Frame theory
    b. Oversampled filter banks
    c. Continuous wavelet and short-time Fourier transforms

5. Advanced Topics (9 hours)
    a. Sparse representation
    b. Linear and non-linear approximation in various bases
    c. Non-linear signal estimation
    d. Multidimensional filter banks and wavelets
    e. Multiscale geometric representation and processing
    f. Compressed sensing

6. Applications (9 hours)
    a. Speech, audio, image, and video compression
    b. Signal denoising
    c. Feature extraction
    d. Inverse problems



Wavelet papers:

Wavelet links: