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pro vyhledávání: '"Sangwine, Stephen J."'
Autor:
Sangwine, Stephen J.
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 a product of more than two octonions, in general, the order of evalua
Externí odkaz:
http://arxiv.org/abs/1509.07718
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 qFT is the mismatch between the spatial and frequency domains: the con
Externí odkaz:
http://arxiv.org/abs/1506.07033
Autor:
Sangwine, Stephen J.
Publikováno v:
Mathematical Methods in the Applied Sciences, 40(1), 15 January 2017, 22-30
A vector-valued signal in N dimensions is a signal whose value at any time instant is an N-dimensional vector, that is, an element of $\mathbb{R}^N$. The sum of an arbitrary number of such signals of the same frequency is shown to trace an ellipse in
Externí odkaz:
http://arxiv.org/abs/1404.2492
Autor:
Hitzer, Eckhard, Sangwine, Stephen J.
Publikováno v:
In E. Hitzer, S. Sangwine (eds.), "Quaternion and Clifford Fourier transforms and wavelets", Trends in Mathematics 27, Birkhauser, Basel, 2013
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 theoretical investigations \cite{10.1007/s00006-007-0037-8, EH:DirUP_QFT}
Externí odkaz:
http://arxiv.org/abs/1306.2157
Publikováno v:
Signal Processing, Volume 94, January 2014, pages 308-318
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 Fourier transform. We extend these ideas to signals with complex-valued sam
Externí odkaz:
http://arxiv.org/abs/1208.1363
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 a hyperanalytic signal) The hyperanalytic signal may be interpreted as
Externí odkaz:
http://arxiv.org/abs/1006.4751
Autor:
Sangwine, Stephen J., Ell, Todd A.
Publikováno v:
Applied Mathematics and Computation, 219(2), October 2012, 644-655
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 a matrix exponential version of Euler's formula $e^{j\theta}=\cos\thet
Externí odkaz:
http://arxiv.org/abs/1001.4379
Publikováno v:
Advances in Applied Clifford Algebras, 21 (3), September 2011, 607-636
The fundamental properties of biquaternions (complexified quaternions) are presented including several different representations, some of them new, and definitions of fundamental operations such as the scalar and vector parts, conjugates, semi-norms,
Externí odkaz:
http://arxiv.org/abs/1001.0240
Autor:
Sangwine, Stephen J., Alfsmann, Daniel
Publikováno v:
Advances in Applied Clifford Algebras, 20 (2), May 2010, 401-410
The biquaternion (complexified quaternion) algebra contains idempotents (elements whose square remains unchanged) and nilpotents (elements whose square vanishes). It also contains divisors of zero (elements with vanishing norm). The idempotents and n
Externí odkaz:
http://arxiv.org/abs/0812.1102
Publikováno v:
Advances in Applied Clifford Algebras, 20, (1), March 2010, 111-120
We present a new polar representation of quaternions inspired by the Cayley-Dickson representation. In this new polar representation, a quaternion is represented by a pair of complex numbers as in the Cayley-Dickson form, but here these two complex n
Externí odkaz:
http://arxiv.org/abs/0802.0852