Wavelet-Galerkin approximation of linear translation invariant operators
- 1 January 1991
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- p. 2021-2023 vol.3
- https://doi.org/10.1109/icassp.1991.150800
Abstract
It is shown that the wavelet-Galerkin discretization of linear translation invariant (LTI) operators has good numerical properties, arising from the vanishing moments property of wavelets. If a wavelet has M vanishing moments, then it can have at most M-1 continuous derivatives, and hence operators of the form d/sup p//dx/sup p/, where p>M, have to be considered as generalized derivatives. Even in this case the approximation results derived hold. Also, the virtual expansion theorem is useful in the sense that there is no need to compute the expansion coefficients of the function at some level V/sub triangle x/.Keywords
This publication has 1 reference indexed in Scilit:
- Orthonormal bases of compactly supported waveletsCommunications on Pure and Applied Mathematics, 1988