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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Bibliographic Details
Published in:Advances in applied Clifford algebras 2016-09, Vol.26 (3), p.985-1011
Main Authors: Akila, Lakshmanan, Roopkumar, Rajakumar
Format: Article
Language:English
Subjects:
Applications of Mathematics
Gabor transformation
Mathematical and Computational Physics
Mathematical Methods in Physics
Physics
Physics and Astronomy
Quaternions
Theoretical
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Summary: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