Eigenstructure and fractionalization of the quaternion discrete Fourier transform

Ribeiro, Guilherme B.; Lima, Juliano B.

doi:10.1016/j.ijleo.2019.163957

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Cited by 3 publications

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“…As for the one-dimensional QDFT, this issue has not been studied in detail, since many computer scientists simply did not see the use of such a transform. That is why there are relatively few research studies on this topic [16,[19][20][21][22][23][24]. In this article, we would like to fill this gap and give a detailed definition of 1-D QDFT, as well as propose a fast method for its implementation.…”

Section: Introductionmentioning

confidence: 99%

One-Dimensional Quaternion Discrete Fourier Transform and an Approach to Its Fast Computation

Majorkowska-Mech,

Cariow

2023

Electronics

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This paper proposes a new method for calculating the quaternion discrete Fourier transform for one-dimensional data. Although the computational complexity of the proposed method still belongs to the O(Nlog2N) class, it allows us to reduce the total number of arithmetic operations required to perform it compared to other known methods for computing this transform. Moreover, compared to the method using symplectic decomposition, the presented method does not require changing the basis in the subspace of pure quaternions and, consequently, calculating the new basis vectors and change-of-basis matrix.

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