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Summary: ALBERT-LUDWIGS-UNIVERSIT¨AT FREIBURG
INSTITUT F¨UR INFORMATIK
Lehrstuhl f¨ur Mustererkennung und Bildverarbeitung
Fourier Analysis in Polar and Spherical
Coordinates
Internal Report 1/08
Qing Wang, Olaf Ronneberger, Hans Burkhardt
Fourier Analysis in Polar and Spherical
Coordinates
Qing Wang, Olaf Ronneberger, Hans Burkhardt
Abstract
In this paper, polar and spherical Fourier Analysis are defined as the
decomposition of a function in terms of eigenfunctions of the Laplacian
with the eigenfunctions being separable in the corresponding coordinates.
Each eigenfunction represents a basic pattern with the wavenumber in-
dicating the scale. The proposed transforms provide an effective radial
decomposition in addition to the well-known angular decomposition. The
derivation of the basis functions is compactly presented with an emphasis
on the analogy to the normal Fourier transform. The relation between
the polar or spherical Fourier transform and normal Fourier transform is
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