The course grade is based primarily on the class project (presentation + final report). Approximate breakdown: Project: 90%, Homework: 10%.
READINGS refer to the Text: Strang and Nguyen. Wavelets and Filter Banks. WellesleyCambridge Press, 1997.
LECTURE NOTES: Slides open as color slides in a pdf document. Handouts open as blackandwhite slides in a pdf document. To view the lecture slides properly, you might need special fonts. If this happens, please refer to the handouts instead, which have all the fonts embedded in them and can be viewed or printed asis.
SES #  TOPICS  READINGS  LECTURE NOTES  ASSIGNMENTS 

1  Discretetime Filters: Convolution; Fourier Transform; Lowpass and Highpass Filters  Sec 1.11.4, 2.1  
2  Sampling Rate Change Operations: Upsampling and Downsampling; Fractional Sampling; Interpolation  Sec 3.13.3  
3  Filter Banks: Time Domain (Haar example) and Frequency Domain; Conditions for Alias Cancellation and no Distortion  Sec 4.1  HW 1 out (PDF)  
4  Filter Banks (contd.): Perfect Reconstruction; Halfband Filters and Possible Factorizations  Sec 4.1  
5  Modulation and Polyphase Representations: Noble Identities; Block Toeplitz Matrices and Block ztransforms; Polyphase Examples  Sec 3.4, 4.14.4  
6  MATLAB^{®} Wavelet Toolbox 
HW 1 due HW 2 out (PDF) 

7  Orthogonal Filter Banks: Paraunitary Matrices; Orthogonality Condition (Condition O) in the Time Domain, Modulation Domain and Polyphase Domain  Sec 5.15.2  
8  Maxflat Filters: Daubechies and Meyer Formulas. Spectral Factorization  Sec 5.35.5  
9  Multiresolution Analysis (MRA): Requirements for MRA; Nested Spaces and Complementary Spaces; Scaling Functions and Wavelets  Sec 1.5, 6.1  
10  Refinement Equation: Interative and Recursive Solution Techniques; Infinite Product Formula; Filter Bank Approach for Computing Scaling Functions and Wavelets  Sec 6.26.4 
HW 2 due HW 3 out (PDF) 

11  Project Brief  
12  Orthogonal Wavelet Bases: Connection to Orthogonal Filters; Orthogonality in the Frequency Domain. Biorthogonal Wavelet Bases  Sec 6.2, 6.4, 6.5  
13  Mallat Pyramid Algorithm  Sec 1.6, 6.2  
14  Accuracy of Wavelet Approximations (Condition A); Vanishing Moments; Polynomial Cancellation in Filter Banks  Sec 7.1  
15  Smoothness of Wavelet Bases: Convergence of the Cascade Algorithm (Condition E); Splines. Bases vs. Frames  Sec 7.27.4  HW 3 due  
16  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  
17  Guest Lecture. Physical Wavelets and their Sources: Real Physics in Complex Spacetime  
18  Lifting: Ladder Structure for Filter Banks; Factorization of Polyphase Matrix into Lifting Steps; Lifting Form of Refinement Equation  Sec 6.5  
19  Wavelets and Subdivision: Nonuniform Grids; Multiresolution for Triangular Meshes; Representation and Compression of Surfaces  
20  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  
21  Mband Wavelets: DFT Filter Banks and Cosine Modulated Filter Banks. Multiwavelets  Sec 7.5, 9.19.4  
22  Project Presentations  
23  Project Presentations  
24  Project Presentations  
25  Project Presentations 