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Open Access Green as soon as Postprint is submitted to ZB.
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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Publication type
Article: Journal article
Document type
Scientific Article
ISSN (print) / ISBN
1063-5203
e-ISSN
1096-603X
Quellenangaben
Volume: 6,
Issue: 3,
Pages: 382-399
Publisher
Academic Press
Publishing Place
San Diego, Calif. [u.a.]
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Institute of Biomathematics and Biometry (IBB)