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http://hdl.handle.net/10773/14587
Title: | Some results on the lattice parameters of quaternionic Gabor frames |
Author: | Hartmann, Stefan |
Keywords: | Quaternionic Gabor system Quaternionic Gabor frames Windowed quaternionic Fourier transform Quaternionic Zak transform Critical density |
Issue Date: | 2015 |
Publisher: | Springer |
Abstract: | Gabor frames play a vital role not only modern harmonic analysis but also in several fields of applied mathematics, for instances, detection of chirps, or image processing. In this work we present a non-trivial generalization of Gabor frames to the quaternionic case and give new density results. The key tool is the two-sided windowed quaternionic Fourier transform (WQFT). As in the complex case, we want to write the WQFT as an inner product between a quaternion-valued signal and shifts and modulates of a real-valued window function. We demonstrate a Heisenberg uncertainty principle and for the results regarding the density, we employ the quaternionic Zak transform to obtain necessary and sufficient conditions to ensure that a quaternionic Gabor system is a quaternionic Gabor frame. We conclude with a proof that the Gabor conjecture do not hold true in the quaternionic case. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/14587 |
DOI: | 10.1007/s00006-015-0587-0 |
ISSN: | 0188-7009 |
Appears in Collections: | CIDMA - Artigos CHAG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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Hartmann_Quaternionic_Gabor.pdf | 356.72 kB | Adobe PDF | View/Open | |
Hartmann.pdf | 512.43 kB | Adobe PDF |
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