131 citations · 511 across the 14 of their papers we have counts for
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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…
Fast complexified quaternion Fourier transform
Salem Said, Nicolas Le Bihan, Stephen J. Sangwine
A discrete complexified quaternion Fourier transform is introduced. This is a generalization of the discrete quaternion Fourier transform to the case where either or both of the si…
Quaternion Singular Value Decomposition based on Bidiagonalization to a Real Matrix using Quaternion Householder Transformations
Stephen J. Sangwine, Nicolas Le Bihan
We present a practical and efficient means to compute the singular value decomposition (svd) of a quaternion matrix A based on bidiagonalization of A to a real bidiagonal matrix B…