Some results on the lattice parameters of quaternionic Gabor frames (Q284522)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Some results on the lattice parameters of quaternionic Gabor frames |
scientific article; zbMATH DE number 6581611
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some results on the lattice parameters of quaternionic Gabor frames |
scientific article; zbMATH DE number 6581611 |
Statements
Some results on the lattice parameters of quaternionic Gabor frames (English)
0 references
18 May 2016
0 references
The author establishes a windowed quaternionic Fourier transform using the two-sided quaternionic Fourier transform and initiates the investigation of quaternionic Gabor systems. The interplay between the translation and modulation operators is more intricate because of non-commutativity. Conditions are derived which ensure that the quaternionic Gabor system constitutes a (quaternionic) Gabor frame. This is done by an application of the quaternionic Zak transform. Furthermore, it is shown that the Gabor conjecture does not hold in the quaternionic case.
0 references
quaternionic Gabor frame
0 references
windowed quaternionic Fourier transform
0 references
Fourier transform
0 references
quaternionic Zak transform
0 references
critical density
0 references
