TY  - INPR
A1  - Freeden, Willi
A1  - Michel, Volker
T1  - Least-squares Geopotential Approximation by Windowed Fourier and Wavelet Transform
N2  - Two possible substitutes of the Fourier transform in geopotential determination are windowed Fourier transform (WFT) and wavelet transform (WT). In this paper we introduce harmonic WFT and WT and show how it can be used to give information about the geopotential simultaneously in the space domain and the frequency (angular momentum) domain. The counterparts of the inverse Fourier transform are derived, which allow us to reconstruct the geopotential from its WFT and WT, respectively. Moreover, we derive a necessary and sufficient condition that an otherwise arbitrary function of space and frequency has to satisfy to be the WFT or WT of a potential. Finally, least - squares approximation and minimum norm (i.e. least - energy) representation, which will play a particular role in geodetic applications of both WFT and WT, are discussed in more detail.
T3  - Berichte der Arbeitsgruppe Technomathematik (AGTM Report) - 216 
KW  - windowed Fourier transform
KW  - harmonic WFT
KW  - geopotential determination
KW  - wavelet transform
KW  - inverse Fourier transform
KW  - arbitrary function
KW  - squares
Y1  - 1999
UR  - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/844
UR  - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-8075
ER  -