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)


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.


Operator Quantization Ambiguity Function Short Time Fourier Transform Spreading Representation Weyl Symbol 
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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Hans G. Feichtinger
  • Werner Kozek

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