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| TOPICS # | SLIDES | HANDOUTS |
|---|---|---|
| Discrete-time Filters: Convolution; Fourier Transform; Lowpass and Highpass Filters | Slides 1 (PDF) | Handout 1 (PDF) |
| Sampling Rate Change Operations: Upsampling and Downsampling; Fractional Sampling; Interpolation | Slides 2 (PDF) | Handout 2 (PDF) |
| Filter Banks: Time Domain (Haar example) and Frequency Domain; Conditions for Alias Cancellation and no Distortion | Slides 3 (PDF) | Handout 3 (PDF) |
| Filter Banks (contd.): Perfect Reconstruction; Halfband Filters and Possible Factorizations | Slides 4 (PDF) | Handout 4 (PDF) |
| Modulation and Polyphase Representations: Noble Identities; Block Toeplitz Matrices and Block z-transforms; Polyphase Examples | Slides 5 (PDF) | Handout 5 (PDF) |
| MATLAB® Wavelet Toolbox | Slides 6 (PDF) | Handout 6 (PDF) |
| Orthogonal Filter Banks: Paraunitary Matrices; Orthogonality Condition (Condition O) in the Time Domain, Modulation Domain and Polyphase Domain | Slides 7 (PDF) | Handout 7 (PDF) |
| Maxflat Filters: Daubechies and Meyer Formulas. Spectral Factorization | Slides 8 (PDF) | Handout 8 (PDF) |
| Multiresolution Analysis (MRA): Requirements for MRA; Nested Spaces and Complementary Spaces; Scaling Functions and Wavelets | Slides 9 (PDF) | Handout 9 (PDF) |
| Refinement Equation: Iterative and Recursive Solution Techniques; Infinite Product Formula; Filter Bank Approach for Computing Scaling Functions and Wavelets | Slides 10 (PDF) | Handout 10 (PDF) |
| Orthogonal Wavelet Bases: Connection to Orthogonal Filters; Orthogonality in the Frequency Domain. Biorthogonal Wavelet Bases | Slides 11 (PDF) | Handout 11 (PDF) |
| Mallat Pyramid Algorithm Sec | Slides 12 (PDF) | Handout 12 (PDF) |
| Accuracy of Wavelet Approximations (Condition A); Vanishing Moments; Polynomial Cancellation in Filter Banks | Slides 13 (PDF) | Handout 13 (PDF) |
| Smoothness of Wavelet Bases: Convergence of the Cascade Algorithm (Condition E); Splines. Bases vs. Frames | Slides 14 (PDF) | Handout 14 (PDF) |
| Signal and Image Processing: Finite Length Signals; Boundary Filters and Boundary Wavelets; Wavelet Compression Algorithms | Slides 15 (PDF) | Handout 15 (PDF) |
| Lifting: Ladder Structure for Filter Banks; Factorization of Polyphase Matrix into Lifting Steps; Lifting Form of Refinement Equation Sec | Slides 16 (PDF) | Handout 16 (PDF) |
| Wavelets and Subdivision: Nonuniform Grids; Multiresolution for Triangular Meshes; Representation and Compression of Surfaces | Slides 17 (PDF) | Handout 17 (PDF) |
| Wavelets and Subdivision (contd.): Nonuniform Grids; Multiresolution for Triangular Meshes; Representation and Compression of Surfaces | Slides 18 (PDF) | Handout 18 (PDF) |
| Numerical Solution of PDEs: Galerkin Approximation; Wavelet Integrals (Projection Coefficients, Moments and Connection Coefficients); Convergence. Subdivision Wavelets for Integral Equations. Compression and Convergence Estimates | Slides 19 (PDF) | Handout 19 (PDF) |
| M-band Wavelets: DFT Filter Banks and Cosine Modulated Filter Banks. Multiwavelets | Slides 20 (PDF) | Handout 20 (PDF) |