Oversampled Wilson expansions

Oversampled Wilson expansions

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 dua...

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Veröffentlicht in:IEEE signal processing letters 1997-04, Vol.4 (4), p.106-108
Hauptverfasser: Bolcskei, H., Grochenig, K., Hlawatsch, F., Feichtinger, H.G.
Format: Artikel
Sprache:eng
Schlagworte:
Fourier transforms
Frequency domain analysis
Harmonic analysis
Mathematics
Prototypes
Signal analysis
Signal synthesis
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Zusammenfassung: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.
ISSN:1070-9908
1558-2361
DOI:10.1109/97.566702