520.646 - Wavelets and Filter Banks

520.646 Wavelets and Filter Banks

Department of Electrical and Computer Engineering
The Johns Hopkins University
Fall 2018

Instructor
- Prof. Trac D. Tran
  Address: 215 Barton Hall
  Phone: (410) 516-7416
  Email: trac@jhu.edu
  Office Hours : Mon 2-4 or by appointment

TA
- Shuwen Wei
  Address: Barton 223C
  Email: swei14@jhu.edu Office Hours : Thurs 2-4 in Barton 223C or by appointment

Homework Assignments
- Problem Set I, due Sep 14 in class.
- Problem Set II, due Sep 21 in class.
- Problem Set III, due Sep 28 in class.
- Problem Set IV, due Oct 5 in class.
- Problem Set V, due Oct 22 in class.
- Problem Set VI, due Nov 2 in class.
- Problem Set VII, due Nov 16 in class.
- Problem Set VIII, due Nov 26 in class.

Texts
- G. Strang and T. Q. Nguyen, Wavelets and Filter Banks, Wellesley-Cambridge Press, Wellesley, MA, Revised Edition, 1998. (Required).
- M. Vetterli, J. Kovacevic, and V. Goyal, Foundations of Signal Processing and Fourier and Wavelet Signal Processing, Cambridge University Press, to be published.

Additional References
- P. P. Vaidyanathan, Multirate Systems and Filter Banks, Prentice Hall, Englewood Cliffs, NJ, 1993.
- C. S. Burrus, Ramesh A. Gopinath, and Haitao Guo, Introduction to Wavelets and Wavelet Transforms : A Primer, Prentice Hall, 1997.
- A. N. Akansu and M. J. T. Smith (Editors), Subband and Wavelet Transforms : Design and Applications, Kluwer Academic, 1996.
- L. Cohen, Time-Frequency Analysis, Prentice-Hall, 1995.
- C. K. Chui, An Introduction to Wavelets, Academic Press, 1992.
- R. E. Crochiere and L. R. Rabiner, Multirate Digital Signal Processing, Prentice Hall, 1983.
- I. Daubechies, Ten Lectures on Wavelets, CBMS-NSF, SIAM, 1992.
- G. Kaiser, A Friendly Guide to Wavelets, Birkhauser, 1994.
- S. Mallat, A Wavelet Tour of Signal Processing, Academic Press, Second Edition, 1999.
- H. S. Malvar, Signal Processing with Lapped Transforms, Artech House, 1992.
- K. R. Rao and P. Yip, Discrete Cosine Transform: Algorithms, Advantages, Applications, Academic Press, 1990.
- R. M. Rao and A. S. Bopardikar, Wavelet Transforms: Introduction to Theory and Applications, Addison-Wesley, 1998.
- B. W. Suter, Multirate and Wavelet Signal Processing, Academic Press, 1998.
- P. N. Topiwala (Editor), Wavelet Image and Video Compression, Kluwer Academic, 1998.

Topics
- Multirate Signal Processing: filter banks, multirate systems, filtering, decimation, upsampling, polyphase, perfect reconstruction, aliasing cancellation, signal representation and signal decomposition using vectors and matrices.
- Wavelets: wavelets from filter banks, bases, frames, orthogonality and biorthogonality, multiresolution, smoothness, vanishing moments, time-frequency and time-scale analysis, continuous-time and discrete-time wavelet transform, famous wavelet pairs, wavelet packet, symmetric extensions, complexity issues.
- Design methods: spectral factorization, polyphase matrix factorization, lattice structure, ladder structure (lifting scheme), integer wavelets, cosine modulation, time-domain optimization.
- Applications: Audio/Image/Video compression -- lossy and lossless, subband coding, quantization effect, signal denoising, wavelet shrinkage, inverse halftoning, database retrieval and indexing, multicarrier modulation, transmultiplexers, edge detection.
- Connections to compressed sensing, sparse recovery, convolutional neural networks, deep learning!

Final Project
- Students are expected to work on a related topic of choice.
- The topic can be chosen from a list of suggestions provided by the instructor.
- A final project report and an oral demonstration/presentation are required from each project.

Grading
- Midterm Exams: 50%
- Homework / Class Participation: 25%
- Final Project: 25%

Important Dates
- First lecture: Thurs - Fri, 08/30 - 08/31/2018, 11:00AM, Shaffer 304
- No class on Monday, 09/03/2018

Ethics Issues
- Please read the information provided by the Ethics Board.
- Midterm Exam will be closed book and closed notes. One 8.5 x 11 handwritten formula sheet will be permitted.
- On homework and projects, you are permitted to discuss the problems for clarification purposes, and to help each other with specific points. However, the overall solution and write-up should be your own work.