ECE 544-MD: "Fourier and Wavelet Representations"

Fall 2012

Prof. Minh N. Do (115 CSL, 244-4782, minhdo@).
Lectures: Tuesdays and Thursdays, 12:30 - 1:50 pm; 106B6 Engineering Hall.
Office hours: Wednesdays, 3:00-4:00 pm, 115 Coordinated Science Lab; plus appointments by email.

Course description:
Efficient or sparse signal representation provides the foundation for many signal processing tasks, including sensing, reconstruction, denoising, compression, and feature extraction. This course aims to establish the theory necessary to understand and to effectively use local Fourier and wavelet bases, and related constructions. A particular emphasis will be put on representations that are amenable to fast algorithms, since these are the ones that are likely to have an impact in applications. The course also includes machine problems and independent research projects.

Text books:

Lecture Topics:

1. Vector-Space Signal Processing (6 hours)
    a. Vector and Hilbert spaces
    b. Approximations, projections, and decompositions
    c. Bases and frames
    d. Computational aspects

2. Discrete-Domain Signal Processing (3 hours)
    a. Discrete-time signals and systems
    b. Discrete-time Fourier transform and z-transform
    c. Multirate signal processing

3. Wavelets and Filter Banks (9 hours)
    a. Orthogonal and biorthogonal two-channel filter banks
    b. Design of two-channel filter banks
    c. Tree-structured filter banks
    d. Discrete wavelet transform
    e. Non-linear approximation in the wavelet domain

4. Local Fourier Bases and Transforms (6 hours)
    a. N-channel filter banks
    b. Cosine-modulated local Fourier bases
    c. Lapped transforms
    d. Time-frequency analysis

5. Multidimensional Extensions (6 hours)
    a. Multidimensional filter banks
    b. Directional filter banks
    c. Multiscale geometric representations

6. Applications (6 hours)
    a. Sparse signal processing
    b. Speech, audio, image, and video compression
    c. Signal denoising
    d. Feature extraction
    e. Compressed sensing



Midterm Exams:
Research papers:

Other resources: