ECE 251CN: Wavelets and Filter Banks – Fall 2009

Department of Electrical and Computer Engineering

University of California, San Diego

Textbook:

G. Strang and T. Nguyen, Wavelets and Filter Banks, Wellesley-Cambridge Press, 1997

References:

P. P. Vaidyanathan, Multirate Systems and Filter Banks, Prentice Hall, 1992.

M. Vetterli and J. Kovacevic, Wavelets and Subband Coding, Prentice Hall, 1995.

Instructor:

Philip Dang – pdang@ece.ucsd.edu

Lecture: Time: 12:30 – 1:50 pm, T-Th

Location: Solis Hall 110

Office Hour: Time: 2:00 – 3:00 pm, T-Th

Location: EBUI - 4604

No lecture and office hours on Thanksgiving November 26, 2009

Course Information:

This course covers fundamentals of multirate systems (noble identities, polyphase representations), maximally decimated filter banks (QMF filters for 2-channels, M-channel perfect reconstruction systems), paraunitary perfect reconstruction filter banks, the wavelet transform (multiresolution, discrete wavelet transform, filter banks and wavelet).

Lecture:

Date	Topic	Lecture Summary	Reading	Handout
09/24/09	Introduction: - Brief history of wavelets and filter banks - Course topics	LS 1	Chapter 1	Syllabus
09/29/09	Review: - Z-Transform and its properties	LS 2	Chapter 2
10/01/09	Basic Filter Bank Building Blocks - Upsampler - Downsampler	LS 3	Section 3.1, 3.2
10/06/09	Multirate System - Decimation Filter - Interpolation Filter - Fractional Decimation Filter	LS 4	Section 3.3
10/08/09	- Noble Identity - Polyphase	LS 5	Section 3.4	HW#1
10/13/09	Maximally Decimated Filter Banks -Two-Channel Filter Bank	LS 6	Section 4.1
10/15/09	- Perfect Reconstruction	LS 7	Section 4.1, 5.4
10/20/09	- Halfband Filter - Quadrature Mirror Filter Bank	LS 8	Section 4.1, 5.3, 5.5	HW#2
10/22/09	- M-Channel Filter bank - Modulation Matrix	LS 9	Section 4.4, 9.2	Solution HW#1
10/27/09	- Polyphase Matrix for Two-Channel Filter Bank	LS 10	Section 4.2, 4.3
10/29/09	- Polyphase Matrix for M-Channel Filter Bank	LS 11	Section 4.4, 9.2	Sol HW#2 HW#3
11/03/09	- Lattice Structure Orthogonal Filter Banks - Paraunitary Matrix	LS 12	Section 4.5, 5.1	Sol HW#3
11/05/09	Midterm		Chapter 1 to Section 4.4
11/10/09	- Orthonormal Filter Banks	LS 13	Section 5.2	Midterm Solultion
11/12/09	- Spectral Factorization	LS 14	Section 5.3, 5.4	HW#4 CA#1
11/17/09	- Daubechies’ Maxflat Filters	LS 15	Section 5.5
11/19/09	Multiresolution Analysis	LS 16	Section 6.1, 6.2	Sol HW#4

Homework:

Homework #1: Due October 22, 2009

Problem set 3.3: #1-4

Problem set 3.4: #1-4

Homework #2: Due November 3, 2009

Problem set 4.1: #3, 5, 8-10

Problem set 4.2: #1-2, 5, 7

Homework #3: Due November 5, 2009

Problem set 4.3: #17-18

Problem set 4.4: #8

Homework #4: Due November 24, 2009

Problem set 4.5: #1, 7, 12, 18

Problem set 5.1: #2, 3, 5

Problem set 5.2: #2, 5, 10

Computer Assignment:

CA #1: Due November 24, 2009

Problem #4-5 (Page 460-461)

Suggested Reading:

Filter Banks:

- A. Croisier, D. Esteban, and C. Galand, “Perfect Channel Splitting by Using Interpolation, Decimation, Tree Decomposition Techniques” Proceeding of Int. Conf. Inform. Sci. /Syst. (Patras, Greece), August 1976, pp. 443-446.

- M. T. J. Smith, and T. P. Barnwell, “Exact Reconstruction for Tree Structure Subband Coder” IEEE Transactions on Acoustics, Speech, Signal Processing, vol. 34, June 1986, pp. 434-441.

- P. P. Vaidyanathan, “Quarature Mirror Filter Banks, M-band Extension with Perfect Reconstruction Techniques” IEEE Acoustics, Speech, Signal Processing Magazine, vol. 4, July 1987, pp. 4-20.

- T. Q. Nguyen and P. P. Vaidyanathan, “Two-Channel Perfect Reconstruction FIR QMF Structure Which Yield Linear Phase Analysis and Synthesis Filters” IEEE Transaction on Acoustics, Speech, Signal Processing, vol. 37, May 1989, pp. 976-980.

- Y. M. Lu and M. N. Do, Multidimensional Directional Filter Banks and Surfacelets, IEEE Transactions on Image Processing, vol. 16, no. 4, pp. 918-931, Apr. 2007.

- H. T. Nguyen and M. N. Do, Hybrid Filter Banks with Fractional Delays: Minimax Design and Application to Multichannel Sampling, IEEE Transactions on Signal Processing, vol. 56, no. 7, pp. 3180-3190, July 2008.

Wavelets:

- S. Mallat, “A Theory for Multiresolution Signal Decomposition: The Wavelet Representation,” IEEE Transaction on Pattern Analysis and Machine Intelligence, vol. 11, p. 674-693, July 1989

- I. Daubechies. Ten Lectures on Wavelets. CBMS-NSF Regional Conf. Series in Appl. Math., Vol. 61. Society for Industrial and Applied Mathematics, Philadelphia, PA, 1992.

- A. Cohen, I. Daubechies, and J. Feauveau. “Bi-orthogonal Bases of Compactly Supported Wavelets.” Comm. Pure Appl. Math., 45:485.560, 1992.

- M. Vetterli and C. Herley, “Wavelets and Filter Banks: Theory and Design,” IEEE Transactions on Signal Processing, vol. 40, Sep. 1992, pp. 2207-2232.

- G. Strang, “Wavelets,” American Scientist 8 (April 1994) 250-255.

- W. Sweldens. The Lifting Scheme: A Custom-design Construction of Biorthogonal Wavelets. Appl. Comput. Harmon. Anal., 3(2):186.200, 1996.

- I. Daubechies, W. Sweldens, B-L. Yeo, “Wavelet Transforms that Map Integers to Integers”, Applied and Computational Harmonic Analysis Journal, 5(3):332.369, 1998.

- I. Daubechies, W. Sweldens, “Factoring Wavelet Transforms into Lifting Steps” J. Fourier Anal. Appl., Vol. 4, Nr. 3, pp. 247-269, 1998.

- M. N. Do and M. Vetterli, Framing Pyramids, IEEE Transactions on Signal Processing, vol. 51, pp. 2329-2342, Sep. 2003.

- A. L. Cunha, J. Zhou, and M. N. Do, The Nonsubsampled Contourlet Transform: Theory, Design, and Applications, IEEE Transactions on Image Processing, vol. 15, no. 10, pp. 3089-3101, Oct. 2006.