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Title: Relaxed quaternionic Gabor expansions at critical density
Author: Hartmann, Stefan
Keywords: Gabor expansion
Critical density
Issue Date: 17-Jun-2015
Publisher: Wiley
Abstract: Shifted and modulated Gaussian functions play a vital role in the representation of signals. We extend the theory into a quaternionic setting, using two exponential kernels with two complex numbers. As a final result, we show that every continuous and quaternion-valued signal f in the Wiener space can be expanded into a unique l2 series on a lattice at critical density 1, provided one more point is added in the middle of a cell. We call that a relaxed Gabor expansion.
Peer review: yes
ISSN: 1099-1476
Appears in Collections:CIDMA - Artigos
CHAG - Artigos

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