On Finite Group Presentations and Function Decomposition Based on Linearity of Discrete-Time Signal
S. G. Ngulde, B. A. Madu, D. Samaila
Asian Research Journal of Mathematics · pp. 1–17 · Published 10 Aug 2018
10.9734/ARJOM/2018/43157Abstract
Based on the concept of group representation theory, new representations can be generated by direct product (or tensor product) of any two representations of a group. In such case, their irreducible representations are also the direct product. But the conditions under which these representations can be chosen and how to decompose them is silent. In this work, a clear and efficient method for generating and decomposing representations is presented. The study is restricted to geometric group Dn of order 2n and its subgroups, where a new homomorphism called a transfer function based on the geometric group is constructed. Due to linearity of discrete-time signal, the generated transformations are used on signal space. Thus, a different approach to signal processing with the choice of a group of transformations is established.
Cited by 2
D. Samaila, G. N. Shu’aibu, B. Modu · Journal of Advances in Mathematics and Computer Science · 2021
D. Samaila, G. N. Shu’aibu, B. Modu · Journal of Advances in Mathematics and Computer Science · 2021
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