Convolution Theorems for Quaternion Fourier Transform: Properties and Applications

By Mawardi Bahri, Ryuichi Ashino, Rémi Vaillancourt. 2013

55 citations recorded by the source corpus.

General convolution theorems for two-dimensional quaternion Fourier transforms (QFTs) are presented. It is shown that these theorems are valid not only for real-valued functions but also for quaternion-valued functions. We describe some useful properties of generalized convolutions and compare them with the convolution theorems of the classical Fourier transform. We finally apply the obtained results to study hypoellipticity and to solve the heat equation in quaternion algebra framework.

Subfields: Applied Mathematics, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/be6a261199f9337a3d99bf7fe2d4b8fd50fa347c

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In Applied Mathematics

1. Ryuichi Ashino
2. Mawardi Bahri

In Astronomy and Astrophysics

1. Ryuichi Ashino
2. Mawardi Bahri

Citations in the corpus

• A Simplified Proof of Uncertainty Principle for Quaternion Linear Canonical Transform (2016, background): “For more details of the QFT, see [12–16].”