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A Quaternion Widely Linear Series Expansion and Its Applications

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3 Author(s)
Navarro-Moreno, J. ; Dept. of Stat. & Oper. Res., Univ. of Jaen, Jaen, Spain ; Fernandez-Alcala, R.M. ; Ruiz-Molina, J.C.

A series representation for continuous-time quaternion random signals is given. The series expansion is based on augmented statistics and provides uncorrelated scalar real-valued random variables. The proposed technique implies a dimension reduction of the four-dimensional original problem to a one-dimensional problem. As a particular case, the quaternion Karhunen-Loève expansion is obtained. Finally, two illustrative applications to the quaternion widely linear detection and estimation problems are presented.

Published in:

Signal Processing Letters, IEEE  (Volume:19 ,  Issue: 12 )