Time frequency representations of almost periodic functions

Yeon Hyang Kim, Amos Ron

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


In this paper, we characterize the space of almost periodic (AP) functions in one variable using either a Weyl-Heisenberg (WH) system or an affine system. Our observation is that the sought-for characterization of the AP space is valid if and only if the given WH (respectively, affine) system is an L 2(ℝ)-frame. Moreover, the frame bounds of the system are also the sharpest bounds in our characterization. This draws an intriguing and quite unexpected connection between L 2(ℝ) representations and AP-representations.

Original languageEnglish
Pages (from-to)303-323
Number of pages21
JournalConstructive Approximation
Issue number3
StatePublished - Jun 2009
Externally publishedYes


  • AP-frames
  • Affine systems
  • Almost-periodic functions
  • Dual Gramian
  • Fiberization of time frequency representations
  • Frames
  • Time frequency representations
  • Weyl-Heisenberg systems


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