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Proceedings Paper

Invertible time-frequency representations
Author(s): Douglas J. Nelson; Owen Patrick Kenny
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Paper Abstract

In this paper, we present a new class of representations of signals in the time-frequency (TF) plane. These representations are complex valued, linear, and satisfy reconstruction conditions in which the signal and its complex spectrum may be uniquely reconstructed from their TF representation. These surfaces are generalizes of 1D linear transforms with which they share many properties. The primary advantage of these representations is that the phase of the surface may be used to recover signal information which is not contained in real TF surfaces. Linearity guarantees that cross-terms normally associated with TF distributions do not exist in these representations. Several examples of invertible surfaces are presented, and it is demonstrated that these surfaces agree with normal intuition. Finally, a method, based on the phase gradient, is proposed as a method of modifying Fourier surfaces to produce representations which are more focused or more concentrated in time and frequency.

Paper Details

Date Published: 2 October 1998
PDF: 12 pages
Proc. SPIE 3461, Advanced Signal Processing Algorithms, Architectures, and Implementations VIII, (2 October 1998); doi: 10.1117/12.325676
Show Author Affiliations
Douglas J. Nelson, Dept. of Defense (United States)
Owen Patrick Kenny, Defence Science and Technology Organization (United States)

Published in SPIE Proceedings Vol. 3461:
Advanced Signal Processing Algorithms, Architectures, and Implementations VIII
Franklin T. Luk, Editor(s)

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