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.
|Number of pages||12|
|Journal||Proceedings of SPIE - The International Society for Optical Engineering|
|Publication status||Published - 1999|
|Event||Proceedings of the 1999 Wavelet Applications in Signal and Image Processing VII - Denver, CO, USA|
Duration: 19 Jul 1999 → 23 Jul 1999