Analyzing the Weyl–Heisenberg Frame Identity

  title={Analyzing the Weyl–Heisenberg Frame Identity},
  author={Peter G. Casazza and Mark Lammers},
  journal={Applied and Computational Harmonic Analysis},
  • P. Casazza, M. Lammers
  • Published 4 November 1999
  • Mathematics
  • Applied and Computational Harmonic Analysis
Abstract In 1990, Daubechies proved a fundamental identity for Weyl–Heisenberg systems which is now called the Weyl–Heisenberg (WH)-frame identity. WH-frame identity: If g ∈ W ( L ∞ , L 1 ), then for all continuous, compactly supported functions f we have ∑ m , n ∣〈f,E mb T na g〉∣ 2 = 1 b ∑ k ∫ R f ( t ) f(t−k/b) ∑ n g(t−na) g ( t − na − k / b ) dt. It has been folklore that the identity will not hold universally. We make a detailed study of the WH-frame identity and show (1) The identity does… 
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