The fast Fourier Transform and fast Wavelet Transform for Patterns on the Torus

Details The fast Fourier Transform and fast Wavelet Transform for Patterns on the Torus The fast Fourier Transform and fast Wavelet Transform for Patterns on the Torus

2011-07-27

arxiv.org/abs/1107.5415v1

Mathematics

Numerical Analysis

23 pages, 8 figures

Scientific paper

We introduce a fast Fourier Transform on regular d-dimensional lattices. We investigate properties of congruence class representants, i.e. their ordering, to classify directions and derive a Cooley-Tuckey-Algorithm. Despite the fast Fourier techniques itself, there is also the advantage of this transform to be parallelized efficiently, yielding even faster versions than the one-dimensional Fourier transform. These properties of the lattice can also be used to perform a fast multivariate wavelet decomposition, where the wavelets are given as trigonometric polynomials. Furthermore the preferred directions of the decomposition itself can be characterised.

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