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Wavelets, Filter Banks and Applications >> Content Detail



Lecture Notes



Lecture Notes





SLIDES open as color slides in a pdf document. HANDOUTS open as black-and-white slides in a pdf document. To view the color 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 as-is.
    
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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