Math @ Duke

Publications [#287082] of Hubert Bray
Papers Published
 Bray, H; McCormick, K; Wells, RO; Zhou, XD, Wavelet variations on the Shannon sampling theorem.,
Biosystems, vol. 34 no. 13
(January, 1995),
pp. 249257, Elsevier Science Ireland, ISSN 03032647 [science], [doi]
(last updated on 2021/05/12)
Author's Comments: This paper was a result of working as an undergraduate in the Computational Mathematics Laboratory run by Raymond O. Wells at Rice University.
Abstract: The Shannon sampling theorem asserts that a continuous squareintegrable function on the real line which has a compactly supported Fourier transform is uniquely determined by its restriction to a uniform lattice of points whose density is determined by the support of the Fourier transform. This result can be extended to the wavelet representation of functions in two ways. First, under the same type of conditions as for the Shannon theorem, the scaling coefficients of a wavelet expansion will determine uniquely the given squareintegrable function. Secondly, for a more general function, there is a unique extension from a given set of scaling coefficients to a full wavelet expansion which minimizes the local obstructions to translation invariance in a variational sense.


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