Digital Signal Processing and Artificial Intelligence for Automatic Learning

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Digital Signal Processing and Artificial Intelligence for Automatic Learning

Group Theory and Fourier Analysis of Finite Abelian Groups

DuÃ…Â¡an B. Gajic and Radomir S. Stankovic
The University of NiÃ…Â¡, Faculty of Electronic Engineering Aleksandra Medvedeva 14 18000 NiÃ…Â¡ Serbia

Abstract: Group characters are an essential concept in group theory and Fourier analysis of finite Abelian groups. For example, in many applications, such as spectral processing of binary or p-valued logic functions, it is often necessary to construct a table of groups of characters for a given group. This is a computationally demanding task, both from a space and time point of view, especially when working with large groups. The group characters are represented in matrix notation as rows of p Ãƒâ€” pm matrices, with p as cardinality and m as the number of variables in the set. GPUs, a highly parallel computing platform, can help solve this complex problem. In this paper, we will discuss how GPU processing can be used to construct tables of group characters for finite abelian groups, represented as direct products of cyclic subgroups of order p, and how it can be used to redistribute related computing tasks across GPU resources. The results of the experiments show that the proposed solution provides a significant speed-up compared to the C / C++ C character construction method executed on the CPU.

Keywords: Abstract Harmonic Analysis, Finite Abelian Groups, Group Characters, Kronecker Product, GPU Computing, OpenCL Group Theory and Fourier Analysis of Finite Abelian Groups

DOI:https://doi.org/10.6025/dspaial/2023/2/4/109-117

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