131 citations · 235 across the 6 of their papers we have counts for
6 papers
Connecting spatial and frequency domains for the quaternion Fourier transform
Hendrik De Bie, Nele De Schepper, Todd A. Ell +2
The quaternion Fourier transform (qFT) is an important tool in multi-dimensional data analysis, in particular for the study of color images. An important problem when applying the…
Instantaneous frequency and amplitude of complex signals based on quaternion Fourier transform
Nicolas Le Bihan, Stephen J. Sangwine, Todd A. Ell
The ideas of instantaneous amplitude and phase are well understood for signals with real-valued samples, based on the analytic signal which is a complex signal with one-sided Fouri…
Complex and Hypercomplex Discrete Fourier Transforms Based on Matrix Exponential Form of Euler's Formula
Stephen J. Sangwine, Todd A. Ell
We show that the discrete complex, and numerous hypercomplex, Fourier transforms defined and used so far by a number of researchers can be unified into a single framework based on…
Fundamental representations and algebraic properties of biquaternions or complexified quaternions
Stephen J. Sangwine, Todd A. Ell, Nicolas Le Bihan
The fundamental properties of biquaternions (complexified quaternions) are presented including several different representations, some of them new, and definitions of fundamental o…
On Systems of Linear Quaternion Functions
Todd A. Ell
A method of reducing general quaternion functions of first degree, i.e., linear quaternion functions, to quaternary canonical form is given. Linear quaternion functions, once reduc…
Quaternion Involutions
Todd A. Ell, Stephen J. Sangwine
An involution is usually defined as a mapping that is its own inverse. In this paper, we study quaternion involutions that have the additional properties of distribution over addit…