Action of Finite Group Presentations on Signal Space
D. Samaila, G. N. Shu’aibu, B. A. Modu
Journal of Advances in Mathematics and Computer Science · pp. 17–29 · Published 25 Oct 2021
10.9734/jamcs/2021/v36i930398Abstract
The use of finite group presentations in signal processing has not been exploit in the current literature. Based on the existing signal processing algorithms (not necessarily group theoretic approach), various signal processing transforms have unique decomposition capabilities, that is, different types of signal has different transformation combination. This paper aimed at studying representation of finite groups via their actions on Signal space and to use more than one transformation to process a signal within the context of group theory. The objective is achieved by using group generators as actions on Signal space which produced output signal for every corresponding input signal. It is proved that the subgroup presentations act on signal space by conjugation. Hence, a different approach to signal processing using group of transformations and presentations is established.
References (11)
- 1 Handbook of Computational Group Theory [DOI]
- 2 Mathematical Methods for Physics and Engineering [DOI]
- 3 Geometrical grouplets [DOI]
- 4 Turkish Journal of Analysis and Number Theory
- 5 Transformation Groups for Beginners [DOI]
- 6 G-Lets: A New Signal Processing Algorithm [DOI]
- 7 On Finite Group Presentations and Function Decomposition Based on Linearity of Discrete-Time Signal [DOI]
- 8 Asian Research Journal of Mathematics [DOI]
- 9 Arbitrary Functions in Group Theory [DOI]
- 10 Representation Theory of Finite Groups [DOI]
- 11 The Standard Representation of the Symmetric Group $S_n$ over the Ring\n of Integers [DOI]
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