Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Spherical harmonic analysis, aliasing, and filtering
Abstract The currently practiced methods of harmonic analysis on the sphere are studied with respect to aliasing and filtering. It is assumed that a function is sampled on a regular grid of latitudes and longitudes. Then, transformations to and from the Cartesian plane yield formulations of the aliasing error in terms of spherical harmonic coefficients. The following results are obtained: 1) The simple quadratures method and related methods are biased even with band-limited functions. 2) A new method that eliminates this bias is superior to Colombo's method of least squares in terms of reducing aliasing. 3) But, a simple modification of the least-squares model makes it identical to the new method as one is the dual of the other. 4) The essential elimination of aliasing can only be effected with spherical cap averages, not with the often used constant angular block averages.
Spherical harmonic analysis, aliasing, and filtering
Abstract The currently practiced methods of harmonic analysis on the sphere are studied with respect to aliasing and filtering. It is assumed that a function is sampled on a regular grid of latitudes and longitudes. Then, transformations to and from the Cartesian plane yield formulations of the aliasing error in terms of spherical harmonic coefficients. The following results are obtained: 1) The simple quadratures method and related methods are biased even with band-limited functions. 2) A new method that eliminates this bias is superior to Colombo's method of least squares in terms of reducing aliasing. 3) But, a simple modification of the least-squares model makes it identical to the new method as one is the dual of the other. 4) The essential elimination of aliasing can only be effected with spherical cap averages, not with the often used constant angular block averages.
Spherical harmonic analysis, aliasing, and filtering
Jekeli, Christopher (Autor:in)
Journal of Geodesy ; 70
1996
Aufsatz (Zeitschrift)
Englisch
BKL:
38.73
Geodäsie
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