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Fast Algorithms of Fourier and Hartley transform and their implementation in MATLAB

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VESELÝ Vítězslav

Year of publication 1998
Type Article in Proceedings
Conference Proceedings of Summer School DATASTAT'97, Folia Fac. Sci. Nat. Univ. Masaryk. Brunensis, Mathematica 7
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Faculty of Science

Field General mathematics
Keywords fast Fourier transform; fast Hartley transform; factorization of matrices; generalized Kronecker product of matrices; performance tests
Description Basics of wavelet expansions and wavelet de-noising (Donoho-Johnstone) are explained following the analogy with the classical Fourier analysis and using general concepts in the $L_2$ function space as the common background. Also the fundamental relations of the multiresolution analysis are derived. They yield a recurrent procedure allowing us to raise/lower the level of the wavelet approximation step by step. Figures of some commonly used wavelet shapes and examples of practical data analysis demonstrate the topics.
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