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Wavelets, Filter Banks and Applications >> Content Detail



Lecture Notes



Lecture Notes





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TOPICS #SLIDESHANDOUTS
Discrete-time Filters: Convolution; Fourier Transform; Lowpass and Highpass FiltersSlides 1 (PDF)Handout 1 (PDF)
Sampling Rate Change Operations: Upsampling and Downsampling; Fractional Sampling; InterpolationSlides 2 (PDF)Handout 2 (PDF)
Filter Banks: Time Domain (Haar example) and Frequency Domain; Conditions for Alias Cancellation and no DistortionSlides 3 (PDF)Handout 3 (PDF)
Filter Banks (contd.): Perfect Reconstruction; Halfband Filters and Possible FactorizationsSlides 4 (PDF)Handout 4 (PDF)
Modulation and Polyphase Representations: Noble Identities; Block Toeplitz Matrices and Block z-transforms; Polyphase ExamplesSlides 5 (PDF)Handout 5 (PDF)
MATLAB® Wavelet ToolboxSlides 6 (PDF)Handout 6 (PDF)
Orthogonal Filter Banks: Paraunitary Matrices; Orthogonality Condition (Condition O) in the Time Domain, Modulation Domain and Polyphase DomainSlides 7 (PDF)Handout 7 (PDF)
Maxflat Filters: Daubechies and Meyer Formulas. Spectral FactorizationSlides 8 (PDF)Handout 8 (PDF)
Multiresolution Analysis (MRA): Requirements for MRA; Nested Spaces and Complementary Spaces; Scaling Functions and WaveletsSlides 9 (PDF)Handout 9 (PDF)
Refinement Equation: Iterative and Recursive Solution Techniques; Infinite Product Formula; Filter Bank Approach for Computing Scaling Functions and WaveletsSlides 10 (PDF)Handout 10 (PDF)
Orthogonal Wavelet Bases: Connection to Orthogonal Filters; Orthogonality in the Frequency Domain. Biorthogonal Wavelet BasesSlides 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 BanksSlides 13 (PDF)Handout 13 (PDF)
Smoothness of Wavelet Bases: Convergence of the Cascade Algorithm (Condition E); Splines. Bases vs. FramesSlides 14 (PDF)Handout 14 (PDF)
Signal and Image Processing: Finite Length Signals; Boundary Filters and Boundary Wavelets; Wavelet Compression AlgorithmsSlides 15 (PDF)Handout 15 (PDF)
Lifting: Ladder Structure for Filter Banks; Factorization of Polyphase Matrix into Lifting Steps; Lifting Form of Refinement Equation SecSlides 16 (PDF)Handout 16 (PDF)
Wavelets and Subdivision: Nonuniform Grids; Multiresolution for Triangular Meshes; Representation and Compression of SurfacesSlides 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 EstimatesSlides 19 (PDF)Handout 19 (PDF)
M-band Wavelets: DFT Filter Banks and Cosine Modulated Filter Banks. MultiwaveletsSlides 20 (PDF)Handout 20 (PDF)




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