Discrete sets of coherent states and their use in signal analysis

  • Ingrid Daubechies
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1285)

Abstract

We discuss expansions of L2-functions into {φmn; m,nZ}, where the φmn are generated from one function φ, either by translations in phase space, i.e. \(\phi _{mn} (x) = e^{imp_0 x} \phi (x - nq_0 )\), (p0, q0 fixed), or by translations and dilations, i.e. φmn(x)=a0m/2φ(a0mxnb0). These expansions can be used for phase space localization.

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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Ingrid Daubechies
    • 1
  1. 1.Courant Institute of Mathematical SciencesNew York UniversityNew York

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