کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4977599 | 1451929 | 2017 | 11 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The geometry of proper quaternion random variables
ترجمه فارسی عنوان
هندسه متغیرهای تصادفی کواترنیک مناسب
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موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
پردازش سیگنال
چکیده انگلیسی
Second order circularity, also called properness, for complex random variables is a well known and studied concept. In the case of quaternion random variables, some extensions have been proposed, leading to applications in quaternion signal processing (detection, filtering, estimation). Just like in the complex case, circularity for a quaternion-valued random variable is related to the symmetries of its probability density function. As a consequence, properness of quaternion random variables should be defined with respect to the most general isometries in 4D, i.e. rotations from SO(4). Based on this idea, we propose a new definition of properness, namely the (μ1, μ2)-properness, for quaternion random variables using invariance property under the action of the rotation group SO(4). This new definition generalizes previously introduced properness concepts for quaternion random variables. A second order study is conducted and symmetry properties of the covariance matrix of (μ1, μ2)-proper quaternion random variables are presented. Comparisons with previous definitions are given and simulations illustrate in a geometric manner the newly introduced concept.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Signal Processing - Volume 138, September 2017, Pages 106-116
Journal: Signal Processing - Volume 138, September 2017, Pages 106-116
نویسندگان
Nicolas Le Bihan,