Relaxed quaternionic Gabor expansions at critical density | Zendy

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Relaxed quaternionic Gabor expansions at critical density

Author(s) -

Hartmann Stefan

Publication year - 2016

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.4087

Subject(s) - mathematics , quaternion , exponential function , gaussian , lattice (music) , space (punctuation) , pure mathematics , point (geometry) , representation (politics) , critical point (mathematics) , series (stratigraphy) , mathematical analysis , geometry , paleontology , linguistics , philosophy , physics , quantum mechanics , politics , political science , acoustics , law , biology

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 ℓ 2 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 . Copyright © 2016 John Wiley & Sons, Ltd.

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