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 1390.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 asis.
DATE  TOPICS  READING  LECTURE NOTES  ASSIGNMENTS  
February  4 Wed  Discretetime filters: convolution; Fourier transform;lowpass and highpass filters.  Sec 1.11.4, 2.1 
Convolution Notes Slides Handouts 

9 Mon  Sampling rate change operations: upsampling and downsampling; fractional sampling; interpolation.  Sec 3.13.3  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 ztransforms; polyphase examples.  Sec 3.4, 4.14.4  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 5.15.2  Slides Handouts  
3 Wed  Maxflat filters: Daubechies and Meyer formulas. Spectral factorization.  Sec 5.35.5  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 6.26.4  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 7.27.4  Slides Handouts  HW 3 Due  
12 Mon  Signal and image processing: finite length signals; boundary filters and boundary wavelets; wavelet compression algorithms.  Sec 8.18.3, 8.5, 10.1, 11.111.5  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. 
SlidesI
HandoutsI SlidesII HandoutsII 

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  Mband wavelets: DFT filter banks and cosine modulated filter banks. Multiwavelets.  Sec 7.5, 9.19.4  Slides Handouts  
5 Wed  Project Presentations  
10 Mon  Project Presentations  
12 Wed  Project Presentations 