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18.327 Wavelets, Filter Banks and Applications | Mathematics

Wavelets are localized basis functions, good for representing short-time events. The coefficients at each scale are filtered and subsampled to give coefficients at the next scale. This is Mallat's pyramid algorithm for multiresolution, connecting wavelets to filter banks. Wavelets and multiscale algorithms for compression and signal/image processing are developed. Subject is project-based for engineering and scientific applications.... Show More

Keywords:: Smoothness of wavelet bases, ractional sampling, conditions for alias cancellation and no distortion, perfect reconstruction, Filter Banks, Refinement equation, Spectral factorization, interpolation, Accuracy of wavelet approximations (Condition A), ladder stru, connection to orthogonal filters, orthogonality condition (Condition O) in the time domain, Discrete-time filters, modulation domain and polyphase domain, infinite product formula, Lifting, Daubechies and Meyer formulas, upsampling and downsampling, wavelet compression algorithms, polyphase examples, block Toeplitz matrices and block z-transforms, time domain (Haar example) and frequency domain, owpass and highpass filters, nested spaces and complementary spaces, Bases vs. frames, scaling functions and wavelets, Multiresolution Analysis (MRA), boundary filters and boundary wavelets, splines, Mallat pyramid algorithm, requirements for MRA, Orthogonal filter banks, iterative and recursive solution techniques, Orthogonal wavelet bases, orthogonality in the frequency domain, finite length signals, convergence of the cascade algorithm (Condition E), filter bank approach for computing scaling functions and wavelets, Modulation and polyphase representations, Signal and image processing, Biorthogonal wavelet bases, Fourier transform, Sampling rate change operations, Maxflat filters, convolution, Matlab wavelet toolbox, halfband filters and possible factorizations, vanishing moments, polynomial cancellation in filter banks, paraunitary matrices, Noble identities

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Mathematics and Statistics / Mathematics

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Material Type:: Online Course
Date Added to MERLOT:: May 12, 2016
Date Modified in MERLOT:: May 12, 2016
Author:: Unknown (Know the author?)
Submitter:: Barbra Bied Sperling

Primary Audience:: Graduate School
Technical Format:: Website
Mobile Compatibility:: Not specified at this time
Language:: English
Cost Involved:: No
Source Code Available:: No
Creative Commons:: This work is licensed under a Attribution-NonCommercial-ShareAlike 3.0 United States