ECE 544-MD: "Fourier and Wavelet Representations"
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.
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.
- M. Vetterli, J. Kovacevic, and V. K. Goyal, "Signal
Processing" (Vol. 1: Foundations; Vol. 2: Fourier and Wavelet
Representations). Available online at http://www.fourierandwavelets.org
- Research papers.
- S. Mallat, "A Wavelet Tour of Signal Processing," Academic Press,
Second Edition, 3rd ed., 2008.
- G. Strang and T. Q. Nguyen, "Wavelets and Filter Banks," Wellesley-Cambridge
Press, Revised Edition, 1998.
- I. Daubechies, "Ten Lectures on Wavelets," SIAM, 1992.
- P. P. Vaidyanathan, "Multirate Systems and Filter Banks," Prentice
- M. Vetterli and J. Kovacevic, "Wavelets and Subband Coding," Prentice Hall, 1995; downloadable from http://www.waveletsandsubbandcoding.org
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
- Homework: 25%
- First midterm: 25%
- Second midterm: 25%
- Final project: 25%
by G. Strang, American Scientist 8 (April 1994)
- Wavelets and signal processing, by O.
Rioul and M. Vetterli, IEEE Signal Processing Magazine, vol. 8, no.
4, Oct. 1991, pp. 14-38.
theory for multiresolution signal decomposition: the wavelet
representation, by S. Mallat, IEEE Transaction on Pattern Analysis
and Machine Intelligence, vol. 11, p. 674-693, July 1989.
- Wavelets and filter banks: theory and design,
by M. Vetterli and C. Herley, IEEE Transactions on Signal
Processing, vol. 40, Sep. 1992, pp. 2207-2232.
approximation and compression, by M. Vetterli, IEEE Signal
Processing Magazine, vol. 18, no. 5, Sep. 2001, pp. 59-73.
foundations of transform coding, by V. K. Goyal,
IEEE Signal Processing Mag., vol. 18, no. 5, pp. 9-21, Sept.