Courses:

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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)

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