18.327/1.130 CLASS SCHEDULE

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.

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