Wavelet variations on the Shannon sampling theorem.

Journal Article (Journal Article)

The Shannon sampling theorem asserts that a continuous square-integrable 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 square-integrable 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.

Full Text

Duke Authors

Cited Authors

  • Bray, H; McCormick, K; Wells, RO; Zhou, XD

Published Date

  • January 1995

Published In

Volume / Issue

  • 34 / 1-3

Start / End Page

  • 249 - 257

PubMed ID

  • 7727702

Electronic International Standard Serial Number (EISSN)

  • 1872-8324

International Standard Serial Number (ISSN)

  • 0303-2647

Digital Object Identifier (DOI)

  • 10.1016/0303-2647(94)01457-i


  • eng