Quaternion Fourier Transform on Quaternion Fields and Generalizations

By Eckhard M. S. Hitzer. arXiv.org, 2007

315 citations recorded by the source corpus.

Abstract.We treat the quaternionic Fourier transform (QFT) applied to quaternion fields and investigate QFT properties useful for applications. Different forms of the QFT lead us to different Plancherel theorems. We relate the QFT computation for quaternion fields to the QFT of real signals. We research the general linear (GL) transformation behavior of the QFT with matrices, Clifford geometric algebra and with examples. We finally arrive at wide-ranging non-commutative multivector FT generalizations of the QFT. Examples given are new volume-time and spacetime algebra Fourier transformations.

Subfields: Applied Mathematics, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/046060ffed2dc333e4bd15c70eff428af1646605

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In Applied Mathematics

1. Rémi Vaillancourt
2. Ryuichi Ashino
3. Mawardi Bahri

In Astronomy and Astrophysics

1. Ryuichi Ashino
2. Mawardi Bahri

Citations in the corpus

• Convolution Theorems for Quaternion Fourier Transform: Properties and Applications (2013, background): “(23) Some important properties of the QFT are stated in the following lemmas proved in [12, 17].”
• A Simplified Proof of Uncertainty Principle for Quaternion Linear Canonical Transform (2016, background): “For more details of the QFT, see [12–16].”
• Uncertainty principles associated with quaternionic linear canonical transforms (2016, unknown): “In the meantime, Hitzer et al. [44–47] investigated a directional uncertainty principle for the Clifford–Fourier transform, which describes how the variances (in arbitrary but fixed directions) of a multivector-valued function and its Clifford–Fourier transform are related.”