Electrical and Computer Engineering 765
Multirate Filter Banks and Wavelets

Objective:
To provide a solid conceptual background in multi-rate filter banks, wavelets and multiresolution signal analysis so that you can understand the principles behind any device or algorithm based on such structures, regardless of the application. The background will also enable you to incorporate recent developments in the theory into your own application areas of interest.

Instructor:
Dr. Tim Davidson,
CRL 203, Ext. 27352.
davidson@mail.ece.mcmaster.ca

Recommended Text:
M. Vetterli and J. Kovacevic, Wavelets and Subband Coding, Prentice Hall, Englewood Cliffs, NJ, 1995.

Primer:
C. S. Burrus, R. A. Gopinath, and H. Guo, Introduction to Wavelets and Wavelet Transforms. A Primer, Prentice Hall, Upper Saddle River, NJ, 1998.

References:
G. Strang and T. Nguyen, Wavelets and Filter Banks, Wellesley-Cambridge Press, Wellesley, MA, 1996.

P. P. Vaidyanathan, Multirate Systems and Filter Banks, Prentice Hall, Englewood Cliffs, NJ, 1993.

Introductory Reading:

IEEE Magazine Articles

O. Rioul and M. Vetterli, ``Wavelets and Signal Processing,'' IEEE Signal Processing Magazine, 8(4):14-38, October 1991.

P. P. Vaidyanathan, ``Quadrature Mirror Filter Banks, M-Band Extensions and Perect Reconstruction Techniques,'' IEEE Antennas, Speech, and Signal Proceesing Magazine, 4(3):4-10, July 1987.

IEEE Proceedings Articles

K. Ramchandran, M. Vetterli and C. Herley, ``Wavelets, Subband Coding, and Best Bases,'' Proceedings of the IEEE (Special Issue on Wavelets), 84(4):541-560, April 1996. (Especially Sections I-III.)

A. Cohen and J. Kovacevic, ``Wavelets: The Mathematical Background,'' Proceedings of the IEEE (Special Issue on Wavelets), 84(4):514-522, April 1996.

P. P. Vaidyanathan, ``Multirate Digital Filters, Filter Banks, Polyphase Networks, and Applications: A Tutorial,'' Proceesings of the IEEE, 78(1):56-93, January 1990.

Prerequisite:
A basic undergraduate knowledge of signal processing, including Fourier and z transforms. (These will be reviewed, but only briefly.)

Course Outline:
Background
Fundamentals of signal decompositions, concepts and theory, including time-frequency decompositions; Review of Fourier and z transforms, Fourier series, etc;
Multirate Filtering
Basic input-output relationships; Two-channel filter banks; Perfect reconstruction; Interpretation as a series expansion of a discrete-time signal; Generalizations to M-channel filter banks, modulated filter banks, oversampled filter banks; Transmultiplexers, filter-bank precoders and multirate communication systems;
Multiresolution Analysis
Wavelets and wavelet packets; Interpretation as a series expansions of continuous-time signals; Connections with filter banks and fast transforms; Frames.
Applications
Student directed, but focussed on audio, image and video compression, communication systems, and reduction of computational cost of adaptive algorithms.

Assessment:
3 assignments (10% eaach); Application oriented seminar and report (30%); Implementation project (40%).

Term:
II.

Lectures:
There will be ten lectures, with the possibility of one extra, if required. For the winter term 2002, the lectures will be held on to be advised, in to be advised, and at other mutually agreeable times and places.

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Tim Davidson (davidson@mail.ece.mcmaster.ca).
Last change: 11 July 2001.