NAJan 25, 2015
Reversible Digital Filters Total Parametric Sensitivity Optimization using Non-canonical Hypercomplex Number SystemsYakiv O. Kalinovsky, Yuliya E. Boyarinova, Iana V. Khitsko
Digital filter construction method, which is optimal by parametric sensitivity, based on using of non-canonical hypercomplex number systems is proposed and investigated. It is shown that the use of non-canonical hypercomplex number system with greater number of non-zero structure constants in multiplication table can significantly improve the sensitivity of the digital filter.
NADec 28, 2014
Generalized quaternions and their relations with Grassmann-Clifford procedure of doublingYakiv O. Kalinovsky, Yuliya E. Boyarinova, Alina S. Turenko et al.
The class of non-commutative hypercomplex number systems (HNS) of 4-dimension, constructed by using of non-commutative Grassmann-Clifford procedure of doubling of 2-dimensional systems is investigated in the article and established here are their relationships with the generalized quaternions. Algorithms of performance of operations and methods of algebraic characteristics calculation in them, such as conjugation, normalization, a type of zero divisors are investigated. The considered arithmetic and algebraic operations and procedures in this class HNS allow to use these HNS in mathematical modeling.