Octonion Spectrum of 3D Octonion- Valued Signals - Properties and Possible Applications

The aim of this paper is to investigate the properties of octonion Fourier transform (OFT) of octonion-valued functions of three variables and its potential applications in signal processing. This work has been inspired by the original papers by Hahn and Snopek concerning octonion Fourier transform definition and its applications in the analysis of the hypercomplex analytic signals. First, the generalization of the OFT definition to the octonion-valued functions is provided, and then the octonion analogues of classical Fourier transform properties are derived, e.g. argument scaling, modulation and shift theorem. Finally, the results are illustrated with some examples that indicate possible applications.