Abstract
We study quaternionic Gabor frames based on the two-sided quaternionic windowed Fourier transform. Since classical Hilbert space based methods do not work in this case we introduce appropriated versions of translation and modulation operators. We prove Janssen’s and Walnut’s representations, as well as modified versions of the Wexler–Raz biorthogonality and Ron–Shen duality based on the concept of correlation function. We end up with a characterization of tight quaternionic Gabor frames.
| Original language | English |
|---|---|
| Article number | 86 |
| Number of pages | 12 |
| Journal | Advances in Applied Clifford Algebras |
| Volume | 28 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 1 Nov 2018 |
| Publication type | A1 Journal article-refereed |
Keywords
- Frame bounds
- Janssen’s representation
- Quaternionic frame operator
- Quaternionic Gabor frames
- Two-sided QWFT
- Wexler–Raz biorthogonality
Publication forum classification
- Publication forum level 1
ASJC Scopus subject areas
- Applied Mathematics