Revision 1.00, 04 February 2004
Note: Course grade will be based primarily on the class project (presentation + final report).
Approximate breakdown:Project: 90%, Homework: 10%.
Location:Room 1-390.Hours:MW 1:30 PM - 3:00 PM.
All lecture notes, homeworks and solutions are in PDF format. To
view the lecture slides properly using Adobe Acrobat Reader, you might
need to install these fonts for
Windows (TTF) or these fonts for
Linux/Unix/OS X (AFM/PFB). The handouts have all the fonts embedded in
them and can be viewed or printed as-is.
| DATE | TOPICS | READING | LECTURE NOTES | ASSIGNMENTS | |
| February | 4 Wed | Discrete-time filters: convolution; Fourier transform;lowpass and highpass filters. | Sec 1.1-1.4, 2.1 |
Convolution Notes Slides Handouts |
|
| 9 Mon | Sampling rate change operations: upsampling and downsampling; fractional sampling; interpolation. | Sec 3.1-3.3 | Slides Handouts | ||
| 11 Wed | Filter Banks: time domain (Haar example) and frequency domain; conditions for alias cancellation and no distortion. | Sec 4.1 | Slides Handouts | HW1 out | |
| 16 Mon | Presidents Day. No Class. | ||||
| 17 Tues | Filter Banks (contd.): perfect reconstruction; halfband filters and possible factorizations. | Sec 4.1 | Slides Handouts | ||
| 18 Wed | Modulation and polyphase representations: Noble identities; block Toeplitz matrices and block z-transforms; polyphase examples. | Sec 3.4, 4.1-4.4 | Slides Handouts | ||
| 23 Mon | Matlab wavelet toolbox. | Slides Handouts | HW1 due, HW2 out | ||
| 25 Wed | |||||
| March | 1 Mon | Orthogonal filter banks: paraunitary matrices; orthogonality condition (Condition O) in the time domain, modulation domain and polyphase domain. | Sec 5.1-5.2 | Slides Handouts | |
| 3 Wed | Maxflat filters: Daubechies and Meyer formulas. Spectral factorization. | Sec 5.3-5.5 | Slides Handouts | ||
| 8 Mon | Multiresolution Analysis (MRA): requirements for MRA; nested spaces and complementary spaces; scaling functions and wavelets. | Sec 1.5, 6.1 | Slides Handouts | ||
| 10 Wed | Refinement equation: iterative and recursive solution techniques; infinite product formula; filter bank approach for computing scaling functions and wavelets. | Sec 6.2-6.4 | Slides Handouts | HW2 due, HW3 out | |
| 15 Mon | Project Brief. | ||||
| 17 Wed | Orthogonal wavelet bases: connection to orthogonal filters; orthogonality in the frequency domain. Biorthogonal wavelet bases. | Sec 6.2, 6.4, 6.5 | Slides Handouts | ||
| 22 Mon | Spring Break. No Class | ||||
| 24 Wed | Spring Break. No Class | ||||
| 29 Mon | Mallat pyramid algorithm | Sec 1.6, 6.2 | Slides Handouts | ||
| April | 5 Mon | Accuracy of wavelet approximations (Condition A); vanishing moments; polynomial cancellation in filter banks. | Sec 7.1 | Slides Handouts | |
| 7 Wed | Smoothness of wavelet bases: convergence of the cascade algorithm (Condition E); splines. Bases vs. frames. | Sec 7.2-7.4 | Slides Handouts | HW 3 Due | |
| 12 Mon | Signal and image processing: finite length signals; boundary filters and boundary wavelets; wavelet compression algorithms. | Sec 8.1-8.3, 8.5, 10.1, 11.1-11.5 | Slides Handouts | ||
| 14 Wed | Guest Lecture | ||||
| 19 Mon | Patriots Day. No Class | ||||
| 21 Wed | Lifting: ladder structure for filter banks; factorization of polyphase matrix into lifting steps; lifting form of refinement equation | Sec 6.5 | Slides Handouts | ||
| 26 Mon | Wavelets and subdivision: nonuniform grids; multiresolution for triangular meshes; representation and compression of surfaces. |
Slides-I
Handouts-I Slides-II Handouts-II |
|||
| 28 Wed | Numerical solution of PDEs: Galerkin approximation; wavelet integrals (projection coefficients, moments and connection coefficients); convergence. Subdivision wavelets for integral equations. Compression and convergence estimates | Sec 11.6 | Slides Handouts | ||
| May | 3 Mon | M-band wavelets: DFT filter banks and cosine modulated filter banks. Multiwavelets. | Sec 7.5, 9.1-9.4 | Slides Handouts | |
| 5 Wed | Project Presentations | ||||
| 10 Mon | Project Presentations | ||||
| 12 Wed | Project Presentations | ||||