Multidimensional Quaternionic Gabor Transforms

In this paper, we extend the Gabor transform to the quaternion valued functions on R d in two different ways, where d ∈ N is arbitrary. We prove that the quaternionic Gabor transforms satisfy the properties including Parseval relation, inversion formula, linearity and uncertainity principle. We also...

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Veröffentlicht in:	Advances in applied Clifford algebras 2016-09, Vol.26 (3), p.985-1011
Hauptverfasser:	Akila, Lakshmanan, Roopkumar, Rajakumar
Format:	Artikel
Sprache:	eng
Schlagworte:	Applications of Mathematics Gabor transformation Mathematical and Computational Physics Mathematical Methods in Physics Physics Physics and Astronomy Quaternions Theoretical
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Zusammenfassung:	In this paper, we extend the Gabor transform to the quaternion valued functions on R d in two different ways, where d ∈ N is arbitrary. We prove that the quaternionic Gabor transforms satisfy the properties including Parseval relation, inversion formula, linearity and uncertainity principle. We also present an extension of a quaternionic Gabor transform to Boehmians.
ISSN:	0188-7009 1661-4909
DOI:	10.1007/s00006-015-0634-x