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Fourier and Wavelet Analysis

Number of credits: 6 hp

Examiner: Mats Aigner

Course literature: C. Gasquet, P. Witomski: Fourier Analysis and Application. Filtering, Numerical Computation, Wavelets, Springer-Verlag, 1998. Material handed out.

Course contents: Introduction to the Lebesgue integral. Hilbert spaces: Inner products, orthogonal projection, convergence, completeness, orthonormal systems, orthonormal bases. Fourier series: Convergence theorems, Parseval's identity. The Fourier transform: Basic properties, inversion, Plancherel's identity, the Schwa1tz class. Distributions: Operations on distributions, tempered distributions, the Fourier transform, convolutions, periodic distributions, the Poisson summation formula, the sampling theorem. Wavelets: The Haar system, MRA
(multiresolutional analysis), the Shannon wavelet, Meyer's wavelets, and wavelets with compact suppo1t, e.g., Daubechies' wavelets. Applications to differential equations and filter theory.

Organisation: Lectures

Examination: Written assignments

Prerequisites: Linear Algebra, Caculus in one and severel variables, Fourier Analysis or Transform Theory

Course webpage (same as for the course TATA66 Fourier and Wavelet Analysis)

Page manager: karin.johansson@liu.se
Last updated: 2018-06-15