Frames in two dimensions arising from wavelet transforms

L. Rebollo-Neira

doi:10.1098/rspa.2001.0730

Frames in two dimensions arising from wavelet transforms

L. Rebollo-Neira^*

^*Corresponding author for this work

Aston University

NCRG

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

A mathematical scheme for generating functions spanning the Hilbert space L²(R², (dτ ds/s²) is advanced. The completeness condition is guaranteed by the fact that the proposed functions constitute a frame for L²(R², (dτ ds/s²)). Such functions are built up out of the following ingredients: (i) the wavelet transform, and (ii) a frame for L²(R, dt).

Original language	English
Pages (from-to)	2079-2091
Number of pages	13
Journal	Proceedings of the Royal Society of London A
Volume	457
Issue number	2013
DOIs	https://doi.org/10.1098/rspa.2001.0730
Publication status	Published - 8 Sept 2001

Keywords

Frame representation
Time frequency time-scale representation
Two-dimensional frames
Wavelet transform
Wide-band Doppler imaging
Wide-band remote sensing

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10.1098/rspa.2001.0730

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KW - Time frequency time-scale representation

KW - Two-dimensional frames

KW - Wavelet transform

KW - Wide-band Doppler imaging

KW - Wide-band remote sensing

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Frames in two dimensions arising from wavelet transforms

Abstract

Keywords

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