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

Abstract

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.