Syllabus
The Discrete Fourier Transform: Basic Properties of the Discrete Fourier Transform, Translation-Invariant Linear Transformations, The Fast Fourier Transform. Wavelets on Z_n: Construction of Wavelets on Z_n – The First Stage, Construction of Wavelets on Z_n – The Iteration Step, Examples and Applications.Wavelets on Z: l^2 (Z), complete Orthonormal Sets in Hilbert Spaces, L^2 ([-?,?)) and Fourier Series, The Fourier Transform and Convolution on l^2 (Z), First-Stage Wavelets on Z, The Iteration Step for Wavelets on Z, Implementation and Examples. Wavelets on R:L^2 (R)and Approximate Identities, The Fourier Transform on R, Multiresolution Analysis and Wavelets, Construction of Multiresolution Analyses, Wavelets with Compact Support and their Computation.