Oversampled Wilson expansions

Author

Bolcskei, Helmut ; Grochenig, Karlheinz ; Hlawatsch, Franz ; Feichtinger, Hans G.

Author_Institution

Wien Univ., Austria

Volume

4

Issue

4

fYear

1997

fDate

4/1/1997 12:00:00 AM

Firstpage

106

Lastpage

108

Abstract

Orthonormal Wilson bases with good time-frequency localization have been constructed by Daubechies, Jaffard, and Journe (1991). We extend this construction to Wilson sets and frames with arbitrary oversampling (or redundancy). We state conditions under which dual Weyl-Heisenberg (WH) sets induce dual Wilson sets, and we formulate duality conditions in the time domain and frequency domain. We show that the dual frame of a Wilson frame has again a Wilson structure, and that it is generated by the dual frame of the underlying Weyl-Heisenberg frame. The Wilson frame construction preserves the numerical properties of the underlying Weyl-Heisenberg frame while halving its redundancy.

Keywords

duality (mathematics); signal sampling; time-frequency analysis; Weyl-Heisenberg frame; Wilson frames; Wilson sets; Wilson structure; dual Weyl-Heisenberg sets; dual Wilson sets; duality conditions; frequency domain; numerical properties; orthonormal Wilson bases; oversampled Wilson expansions; redundancy; time domain; time-frequency localization; Fourier transforms; Frequency domain analysis; Harmonic analysis; Mathematics; Prototypes; Signal analysis; Signal synthesis;

fLanguage

English

Journal_Title

Signal Processing Letters, IEEE

Publisher

ieee

ISSN

1070-9908

Type

jour

DOI

10.1109/97.566702

Filename

566702