131 citations · 511 across the 14 of their papers we have counts for
14 papers
Octonion associators
Stephen J. Sangwine
The algebra of octonions is non-associative (as well as non-commutative). This makes it very difficult to derive algebraic results, and to perform computation with octonions. Given…
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…
The Orthogonal 2D Planes Split of Quaternions and Steerable Quaternion Fourier Transformations
Eckhard Hitzer, Stephen J. Sangwine
The two-sided quaternionic Fourier transformation (QFT) was introduced in \cite{Ell:1993} for the analysis of 2D linear time-invariant partial-differential systems. In further theo…
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…
The hyperanalytic signal
Nicolas Le Bihan, Stephen J. Sangwine
The concept of the analytic signal is extended from the case of a real signal with a complex analytic signal to a complex signal with a hypercomplex analytic signal (which we call…
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…