Rational orthogonal bases satisfying the Bedrosian identity

Lihui Tan, Lixin Shen, Lihua Yang

Research output: Contribution to journalArticle

23 Scopus citations

Abstract

We develop a necessary and sufficient condition for the Bedrosian identity in terms of the boundary values of functions in the Hardy spaces. This condition allows us to construct a family of functions such that each of which has non-negative instantaneous frequency and is the product of two functions satisfying the Bedrosian identity. We then provide an efficient way to construct orthogonal bases of L2(ℝ) directly from this family. Moreover, the linear span of the constructed basis is norm dense in Lp(ℝ), 1 < p < ∞. Finally, a concrete example of the constructed basis is presented.

Original languageEnglish (US)
Pages (from-to)285-303
Number of pages19
JournalAdvances in Computational Mathematics
Volume33
Issue number3
DOIs
StatePublished - Jan 1 2010

Keywords

  • Analytic signal
  • Bedrosian identity
  • Hardy space
  • Hilbert transform
  • Positive instantaneous frequency

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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