2008•IEEE Signal Processing LettersRequires access

Relationships Among Various 2-D Quaternion Fourier Transforms

Min-Hung Yeh

Abstract

The recently developed quaternion Fourier transform (QFT) based on quaternion algebra has been found useful for color image processing and signal analysis. However, due to the noncommutative property of quaternion algebra, there exist various definitions for the QFT. The purpose of this letter is to establish and present an in-depth discussion on the relationships among the various QFTs.

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Key concepts: Quaternion, Noncommutative geometry, Algebra over a field, Quaternion algebra, Fourier transform, Mathematics, Signal processing, Property (philosophy)