Electrical and Computer Engineering 765
Multirate Filter Banks and Wavelets
Objective:
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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.
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Instructor:
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Dr. Tim Davidson,
CRL 203, Ext. 27352.
davidson@mail.ece.mcmaster.ca
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Recommended Text:
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M. Vetterli and J. Kovacevic, Wavelets and Subband Coding,
Prentice Hall, Englewood Cliffs, NJ, 1995.
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Primer:
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C. S. Burrus, R. A. Gopinath, and H. Guo,
Introduction to Wavelets and Wavelet Transforms. A Primer,
Prentice Hall, Upper Saddle River, NJ, 1998.
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References:
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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.
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Introductory Reading:
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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.
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Prerequisite:
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A basic undergraduate knowledge of signal processing, including Fourier
and z transforms. (These will be reviewed, but only briefly.)
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Course Outline:
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Background
-
Fundamentals of signal decompositions, concepts and
theory, including time-frequency decompositions;
Review of Fourier and z transforms, Fourier series, etc;
- Multirate Filtering
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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
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Wavelets and wavelet packets;
Interpretation as a series expansions of continuous-time signals;
Connections with filter banks and fast transforms; Frames.
- Applications
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Student directed, but focussed on
audio, image and video compression,
communication systems, and
reduction of computational cost of
adaptive algorithms.
- Assessment:
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3 assignments (10% eaach); Application oriented seminar and report (30%);
Implementation project (40%).
- Term:
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II.
- Lectures:
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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.
Back to
Tim Davidson's technical home page.
Back to the
Department of Electrical
and Computer Engineering home page.
Tim Davidson
(davidson@mail.ece.mcmaster.ca).
Last change: 11 July 2001.