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Quantization of TF lattice-invariant operators on elementary LCA groups

  • Hans G. Feichtinger
  • Werner Kozek
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

Elementary locally compact abelian groups \( \mathcal{G} \) are a natural setup for an abstract view on time-frequency (TF) analysis. The function space Gelfand triple (S 0, L 2, S0)\( (\mathcal{G}) \) is adapted to the sampling and periodization procedures on the abstract TF-plane \( {\cal G} \times \widehat {\cal G} \) and it allows the definition of a generalized Kohn-Nirenberg correspondence for a “harmonic analysis and synthesis” of linear operators. We extend the concept of duality and biorthogonality of Gabor atoms to arbitrary discrete subgroups of \( {\cal G} \times \widehat {\cal G} \) with compact quotient. The setting of elementary LCA groups is not only an extension of standard Gabor analysis but admits a unified formulation for continuous-time, discrete-time, periodic, and multidimensional signals including the case of nonseparable lattices and/or nonseparable atoms.

Keywords

Operator Quantization Ambiguity Function Short Time Fourier Transform Spreading Representation Weyl Symbol 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Hans G. Feichtinger
  • Werner Kozek

There are no affiliations available

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