Abstract
In this paper, we extend the Gabor transform to the quaternion valued functions on \({\mathbb{R}^{d}}\) in two different ways, where \({d\in \mathbb{N}}\) 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.
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Akila, L., Roopkumar, R. Multidimensional Quaternionic Gabor Transforms. Adv. Appl. Clifford Algebras 26, 985–1011 (2016). https://doi.org/10.1007/s00006-015-0634-x
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DOI: https://doi.org/10.1007/s00006-015-0634-x