Centre de documentation
scientifique

Transformation between surface spherical harmonic expansion of arbitrary high degree and order and double Fourier series on sphere / Toshio Fukushima in Journal of geodesy, vol 92 n° 2 (February 2018)  

Public [article]  inJournal of geodesy > vol 92 n° 2 (February 2018) . - pp 123 - 130 Titre : Transformation between surface spherical harmonic expansion of arbitrary high degree and order and double Fourier series on sphere Type de document : Article/Communication Auteurs : Toshio Fukushima, Auteur Année de publication : 2018 Article en page(s) : pp 123 - 130 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie [Termes IGN] harmonique sphérique [Termes IGN] série de Fourier [Termes IGN] transformation géométrique [Termes IGN] transformation inverse Résumé : (Auteur) In order to accelerate the spherical harmonic synthesis and/or analysis of arbitrary function on the unit sphere, we developed a pair of procedures to transform between a truncated spherical harmonic expansion and the corresponding two-dimensional Fourier series. First, we obtained an analytic expression of the sine/cosine series coefficient of the 4π fully normalized associated Legendre function in terms of the rectangle values of the Wigner d function. Then, we elaborated the existing method to transform the coefficients of the surface spherical harmonic expansion to those of the double Fourier series so as to be capable with arbitrary high degree and order. Next, we created a new method to transform inversely a given double Fourier series to the corresponding surface spherical harmonic expansion. The key of the new method is a couple of new recurrence formulas to compute the inverse transformation coefficients: a decreasing-order, fixed-degree, and fixed-wavenumber three-term formula for general terms, and an increasing-degree-and-order and fixed-wavenumber two-term formula for diagonal terms. Meanwhile, the two seed values are analytically prepared. Both of the forward and inverse transformation procedures are confirmed to be sufficiently accurate and applicable to an extremely high degree/order/wavenumber as 230≈109. The developed procedures will be useful not only in the synthesis and analysis of the spherical harmonic expansion of arbitrary high degree and order, but also in the evaluation of the derivatives and integrals of the spherical harmonic expansion. Numéro de notice : A2018-057 Affiliation des auteurs : non IGN Thématique : MATHEMATIQUE/POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-017-1049-3 Date de publication en ligne : 13/07/2017 En ligne : https://doi.org/10.1007/s00190-017-1049-3 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=89390 [article]