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Proceedings Paper

Biorthogonal Wilson bases
Author(s): Kai Bittner
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Paper Abstract

Wilson bases consist of products of trigonometric functions with window functions which have good time-frequency localization, so that the basis functions themselves are well localized in time and frequency. Therefore, Wilson bases are well suited for time-frequency analysis. Daubechies, Jaffard and Journe have given conditions on the window function for which the resulting Wilson basis is orthonormal. In particular, they constructed an example where the basis functions have exponential decay in the time and the frequency domain. Here, we investigate biorthogonal Wilson bases with arbitrary shape. Necessary and sufficient conditions for the Riesz stability of these bases are given. Furthermore, we determine exact Riesz bounds and the dual bases.

Paper Details

Date Published: 26 October 1999
PDF: 12 pages
Proc. SPIE 3813, Wavelet Applications in Signal and Image Processing VII, (26 October 1999); doi: 10.1117/12.366798
Show Author Affiliations
Kai Bittner, GSF-National Research Ctr. for Environment and Health (Germany)


Published in SPIE Proceedings Vol. 3813:
Wavelet Applications in Signal and Image Processing VII
Michael A. Unser; Akram Aldroubi; Andrew F. Laine, Editor(s)

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