Interpolating multiwavelet bases and the sampling theorem

Research output: Contribution to journalArticle

Abstract

This paper considers the classical sampling theorem in multiresolution spaces with scaling functions as interpolants. As discussed by Xia and Zhang, for an orthogonal scaling function to support such a sampling theorem, the scaling function must be cardinal (interpolating). They also showed that the only orthogonal scaling function that is both cardinal and of compact support is the Haar function, which is not continuous. This paper addresses the same question, but in the multiwavelet context, where the situation is different. This paper presents the construction of compactly supported orthogonal multiscaling functions that are continuously differentiable and cardinal. The scaling functions thereby support a Shannon-like sampling theorem. Such wavelet bases are appealing because the initialization of the discrete wavelet transform (prefiltering) is the identity operator.

Original languageEnglish (US)
Pages (from-to)1615-1621
Number of pages7
JournalIEEE Transactions on Signal Processing
Volume47
Issue number6
DOIs
StatePublished - 1999

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Sampling
Orthogonal functions
Discrete wavelet transforms

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

Cite this

Interpolating multiwavelet bases and the sampling theorem. / Selesnick, Ivan.

In: IEEE Transactions on Signal Processing, Vol. 47, No. 6, 1999, p. 1615-1621.

Research output: Contribution to journalArticle

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