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- W4299355431 abstract "The two-sided quaternionic Fourier transformation (QFT) was introduced in cite{Ell:1993} for the analysis of 2D linear time-invariant partial-differential systems. In further theoretical investigations cite{10.1007/s00006-007-0037-8, EH:DirUP_QFT} a special split of quaternions was introduced, then called $pm$split. In the current change{chapter} we analyze this split further, interpret it geometrically as change{an} emph{orthogonal 2D planes split} (OPS), and generalize it to a freely steerable split of $H$ into two orthogonal 2D analysis planes. The new general form of the OPS split allows us to find new geometric interpretations for the action of the QFT on the signal. The second major result of this work is a variety of emph{new steerable forms} of the QFT, their geometric interpretation, and for each formchange{,} OPS split theorems, which allow fast and efficient numerical implementation with standard FFT software." @default.
- W4299355431 created "2022-10-02" @default.
- W4299355431 creator A5011005704 @default.
- W4299355431 creator A5051974422 @default.
- W4299355431 date "2013-06-10" @default.
- W4299355431 modified "2023-10-16" @default.
- W4299355431 title "The Orthogonal 2D Planes Split of Quaternions and Steerable Quaternion Fourier Transformations" @default.
- W4299355431 doi "https://doi.org/10.48550/arxiv.1306.2157" @default.
- W4299355431 hasPublicationYear "2013" @default.
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