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26 October 1999 Biorthogonal Wilson bases
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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.
© (1999) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Kai Bittner "Biorthogonal Wilson bases", Proc. SPIE 3813, Wavelet Applications in Signal and Image Processing VII, (26 October 1999); https://doi.org/10.1117/12.366798
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