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pro vyhledávání: '"Ell, Todd"'
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
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
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:
Ell, Todd A.
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 reduced to canonical form, can be maintained in this form under functional
Externí odkaz:
http://arxiv.org/abs/math/0702084
Autor:
Ell, Todd A., Sangwine, Stephen J.
Publikováno v:
Computers and Mathematics with Applications, 53, (1), January 2007, 137-143
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 addition and multiplication. We review formal axioms for such involutions,
Externí odkaz:
http://arxiv.org/abs/math/0506034
Publikováno v:
In Signal Processing January 2014 94:308-318
Autor:
Sangwine, Stephen J., Ell, Todd A.
Publikováno v:
In Applied Mathematics and Computation 1 October 2012 219(2):644-655
Publikováno v:
Wiley-ISTE, pp.160, 2014, 978-1-84821-478-1
International audience
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::02c6335becc5f08555a5b1d2b162401f
https://hal.archives-ouvertes.fr/hal-00987367
https://hal.archives-ouvertes.fr/hal-00987367