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- W4385672020 abstract "This chapter first focusses on the theoretical foundations of quaternion Fourier transforms. Basically, in the complex Fourier transform the imaginary complex unit i is replaced by any constant unit pure quaternion squaring to −1. Since quaternion multiplication is generically non-commutative, a kernel factor can either be placed to the right or the left of the signal to be transformed, the signal itself may be scalar or quaternion valued as well. Furthermore, two kernel factors can be used, one on the left and one on the right, yielding a two-sided QFT. Due to quaternion non-commutativity it is not trivial to derive the properties of QFTs. A recent comprehensive treatment is given in E. Hitzer, Quaternion and Clifford Fourier Transforms, Chapman and Hall/CRC, London, 1st edition (September 22, 2021). The one-sided QFT had been implemented for quite a while in the Quaternion Toolbox for Matlab (QTFM) by S. Sangwine, and most recently he has expanded this in version 3.4 to include the two-sided QFT as well ( https://sourceforge.net/projects/qtfm/ )." @default.
- W4385672020 created "2023-08-09" @default.
- W4385672020 creator A5051974422 @default.
- W4385672020 date "2023-01-01" @default.
- W4385672020 modified "2023-10-16" @default.
- W4385672020 title "Quaternion Fourier Transform" @default.
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