Rapidly Decaying Harmonic Wavelet Expansion

Tohru MORITA

doi:10.4036/iis.2008.89

Interdisciplinary Information Sciences

Online ISSN : 1347-6157
Print ISSN : 1340-9050
ISSN-L : 1340-9050

Regular Papers

Rapidly Decaying Harmonic Wavelet Expansion

Tohru MORITA

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Keywords: harmonic wavelet, rapidly decaying harmonic wavelet, orthogonal wavelet, Fourier analysis.

JOURNAL FREE ACCESS

2008 Volume 14 Issue 1 Pages 89-101

DOI https://doi.org/10.4036/iis.2008.89

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Abstract

Among orthogonal wavelets, Shannon’s wavelets are very simple but have the demerit that they are not well localized and decay slowly. Meyer’s wavelets, which are obtained by modifying Shannon’s wavelets, decay fast. For the general harmonic wavelets defined in a finite interval of time, an orthogonal system of rapidly decaying harmonic wavelets is constructed, and the wavelet expansion in terms of them is formulated.

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