%0 Report %1 wang2008fourier %A Wang, Qing %A Ronneberger, Olaf %A Burkhardt, Hans %D 2008 %K Fourier_transform basis_functions linear_algebra numerics polar_coordinates radial_basis_function %T Fourier analysis in polar and spherical coordinates %U http://lmb.informatik.uni-freiburg.de/papers/download/wa_report01_08.pdf %X 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 explored. Possible applications of the proposed transforms are discussed.

@techreport{wang2008fourier, 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 explored. Possible applications of the proposed transforms are discussed.}, added-at = {2014-09-01T20:41:45.000+0200}, author = {Wang, Qing and Ronneberger, Olaf and Burkhardt, Hans}, biburl = {https://www.bibsonomy.org/bibtex/2e3ede022c042c956308ca4055b7af1ef/peter.ralph}, institution = {Technical Report Internal Report 1/08, IIF-LMB, Computer Science Department, University of Freiburg}, interhash = {2ccd18ab861a745939281f9f520bc296}, intrahash = {e3ede022c042c956308ca4055b7af1ef}, keywords = {Fourier_transform basis_functions linear_algebra numerics polar_coordinates radial_basis_function}, timestamp = {2014-09-01T20:41:45.000+0200}, title = {Fourier analysis in polar and spherical coordinates}, url = {http://lmb.informatik.uni-freiburg.de/papers/download/wa_report01_08.pdf}, year = 2008 }