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Open Access Green möglich sobald Postprint bei der ZB eingereicht worden ist.
From local cosine bases to global harmonics.
Appl. Comput. Harmon. Anal. 6, 382-399 (1999)
In this paper, the reproduction of trigonometric polynomials with two-overlapping local cosine bases is investigated. This study is motivated by the need to represent most effectively a Fourier series in the form of a localized cosine series for the purpose of local analysis, thus providing a vehicle for the transition from classical harmonic analysis to analysis by Wilson-type wavelets. It is shown that there is one and only one class, which is a one-parameter family, of window functions that allows pointwise reproduction of all global harmonics, where the parameter is the order of smoothness of the window functions. It turns out that this class of window functions is also optimal in the sense that all global harmonics are reproduced by using a minimal number of the local trigonometric basis functions.
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Publikationstyp
Artikel: Journalartikel
Dokumenttyp
Wissenschaftlicher Artikel
ISSN (print) / ISBN
1063-5203
e-ISSN
1096-603X
Zeitschrift
Applied and Computational Harmonic Analysis
Quellenangaben
Band: 6,
Heft: 3,
Seiten: 382-399
Verlag
Academic Press
Verlagsort
San Diego, Calif. [u.a.]
Nichtpatentliteratur
Publikationen
Begutachtungsstatus
Peer reviewed
Institut(e)
Institute of Biomathematics and Biometry (IBB)