Functions and Analysis

    

Quadratic Phase Quaternion Domain Fourier Transform

Authors: Eckhard Hitzer

Based on the quaternion domain Fourier transform (QDFT)of 2016 and the quadratic-phase Fourier transform of 2018, we introduce the quadratic-phase quaternion domain Fourier transform (QPQDFT) and study some of its properties, like its representation in terms of the QDFT, linearity, Riemann-Lebesgue lemma, shift and modulation, scaling, inversion, Parseval type identity, Plancherel theorem, directional uncertainty principle, and the (direction-independent) uncertainty principle. The generalization thus achieved includes the special cases of QDFT, a quaternion domain (QD) fractional Fourier transform, and a QD linear canonical transform.

Comments: 12 Pages. Published in: Bin Sheng, Lei Bi, J inman Kim, Nadia Magnenat Thalmann, Daniel Thalmann (eds), Advances in Computer Graphics. CGI 2023. LNCS, vol 14498. Springer, Cham, First Online: 24 Dec. 2023. https://doi.org/10.1007/978-3-031-50078-7_21

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[v1] 2023-12-23 13:07:24

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