Global spherical harmonic computation by two-dimensional Fourier methods |
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| Authors: | Nico Sneeuw Richard Bun |
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| Institution: | (1) Institut für Astronomische und Physikalische Geodäsie, Technische Universität München, Arcisstraße 21, D-80290 München, Germany;(2) Faculteit der Geodesie, Technische Universiteit Delft, Thijsseweg 11, NL-2629 JA Delft, The Netherlands |
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| Abstract: | A method is presented for performing global spherical harmonic computation by two-dimensional Fourier transformations. The method goes back to old literature (Schuster 1902) and tackles the problem of non-orthogonality of Legendre-functions, when discretized on an equi-angular grid. Both analysis and synthesis relations are presented, which link the spherical harmonic spectrum to a two-dimensional Fourier spectrum. As an alternative, certain functions of co-latitude are introduced, which are orthogonal to discretized Legendre functions. Several independent Fourier approaches for spherical harmonic computation fit into our general scheme. |
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