EE 596, Wavelets, Fall 1996
Instructor
Antonio Ortega
Signal and Image Processing Institute
Integrated Media Systems Center
University of Southern California
3740 McClintock Ave., EEB 436
Los Angeles, CA 90089-2564
Tel: (213) 740-2320
Fax: (213) 740-4651
Email: ortega@sipi.usc.edu
Schedule
Classes
Monday and Wednesday, 10:30-11:45am, OHE 100
-
Office hours
Monday and Wednesday, 1:30-3:30pm, EEB 436
Abstract
Wavelets have emerged in the past few years as a powerful tool for
many applications in signal processing and communications, including
for example image compression, indexing and noise removal. This
course will present the theory and application of wavelet decomposition
of signals. It will include coverage of subband coding with applications
to image compression, multiresolution signal processing, analysis and
design of multirate filterbanks and time-frequency tilings. The course
will cover the basis of wavelet theory but will also emphasize the
applications side.
Course organization
Grading will be based on a midterm, a final as well as several
homeworks. The homeworks will include both computer assignments
and solution of textbook problems. The computer assignments will
be based on Matlab.
Prerequisites
EE 483, Introduction to Digital Signal Processing,
or equivalent course.
Recommended preparation
MATH 599, Introduction to Wavelets, and EE 569, Introduction to
Digital Image Processing
Texbook and tools
Required
Recommended
Recent research
- Proceedings of the IEEE, Special Issue on Wavelets, April 1996.
This special issue contains an excellent overview of how wavelets have
been used in many fields, including Compression, Digital Communications,
Computer Graphics and Biomedical engineering. I will be ordering several
copies of the special issue from IEEE, please let me know if you are
interested by sending me email at
ortega@sipi.usc.edu
Tentative outline of the course
- Week 1. Introduction. Why wavelets, subband coding and
multiresolution signal processing.
Application examples.
- Week 2. Review: Hilbert spaces, orthonormal bases, Fourier theory,
sampling, signal processing, time-frequency representations.
- Week 3. Multirate signal processing. Discrete-time bases.
Analysis of filter banks.
- Week 4. Orthonormal filter banks. Biorthogonal and
IIR filter banks.
- Week 5. Tree-structured filter banks, discrete
wavelet transforms, M channel filter banks.
- Week 6. Multidimensional filter banks,
transmultiplexers and various applications.
Series expansion of continuous-time signals.
- Week 7. Haar and Sinc wavelets. Multiresolution analysis.
- Week 8. Fourier construction of wavelets. Meyer and
spline wavelets.
- Week 9. Filter bank based generation of compactly
supported wavelets. Properties.
Multidimensional wavelets.
- Week 10. The short-time Fourier transform and the
continuous-time wavelet transform. Frames.
- Week 11. Compression. Review of R(d), KLT, bit
allocation.
- Week 12. Speech and audio compression.
- Week 13 Image and video compression.
- Week 14. Special topics. Time-frequency tilings, wavelet
maximas, etc.
Additional Information and Links
There are numerous sites storing wavelet-related information in the
web. Here are a few, including some with interesting demos.
Check them out!
©1996 Antonio Ortega.
Last modified: Wed Mar 10 20:22:14 PST 2010