Spherical harmonic analysis and synthesis for global multiresolution applications |
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| Authors: | J A R Blais D A Provins |
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| Institution: | (1) Department of Geomatics Engineering, Pacific Institute for the Mathematical Sciences, University of Calgary, Calgary, Alberta, T2N 1N4, Canada e-mail: blais@ucalgary.ca/dprovins@ucalgary.ca; Tel.: +1-403-220-7379/6995; Fax: +1-403-284-1980, CA |
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| Abstract: | On the Earth and in its neighborhood, spherical harmonic analysis and synthesis are standard mathematical procedures for
scalar, vector and tensor fields. However, with the advent of multiresolution applications, additional considerations about
convolution filtering with decimation and dilation are required. As global applications often imply discrete observations
on regular grids, computational challenges arise and conflicting claims about spherical harmonic transforms have recently
appeared in the literature. Following an overview of general multiresolution analysis and synthesis, spherical harmonic transforms
are discussed for discrete global computations. For the necessary multi-rate filtering operations, spherical convolutions
along with decimations and dilations are discussed, with practical examples of applications. Concluding remarks are then included
for general applications, with some discussion of the computational complexity involved and the ongoing investigations in
research centers.
Received: 13 November 2000 / Accepted: 12 June 2001 |
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| Keywords: | : Harmonic Analysis – Spherical Harmonics – Multiresolution Analysis |
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