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Complex and hypercomplex discrete Fourier transforms based on matrix exponential form of Euler’s formula

<13> This paper made a breakthrough in the study of discrete hypercomplex Fourier transforms by showing that regardless of the hypercomplex algebra being used, all such transforms can be represented (and computed – but inefficiently) using a matrix exponential form without a hypercomplex arithmetic library. This has important ramifications for verification of hypercomplex library implementations (which will be faster), and also for showing the theoretical links between transforms in different algebras. The result is being exploited by the authors and their collaborators particularly in recent work with Hendrik de Bie of the University of Gent, Belgium in 2013.