A Programmable Approach to Evaluate Ramanujan Sums

DOI

10.2991/iccsee.2013.9How to use a DOI?

Keywords

Ramanujan sum, programmable, primitive roots of unity

Abstract

Ramanujan sums, which have been widely researched in mathematics, recently began to attract more attentions in signal processing and communications. The traditional methods to get the values of Ramanujan sums follow the definition and formulas in number theory, both of which need factorization information. As it is complex and the amount of time needed is unpredictable in hardware programming, a programmable approach base on the primitive roots of unity is proposed in this paper. Only simple arithmetic computing and cosine function is involved. Considering that each value of Ramanujan sums is an integer, the number of sample points required is no more than the period of Ramanujan sums, and quantification bits required are no more than 16 bits, as the simulation results demonstrated.

Copyright

© 2013, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Lina Zhou
AU  - Zulin Wang
AU  - Jiadong Shang
AU  - Lei Zhao
AU  - Song Pan
PY  - 2013/03
DA  - 2013/03
TI  - A Programmable Approach to Evaluate Ramanujan Sums
BT  - Proceedings of the 2nd International Conference on Computer Science and Electronics Engineering (ICCSEE 2013)
PB  - Atlantis Press
SP  - 33
EP  - 37
SN  - 1951-6851
UR  - https://doi.org/10.2991/iccsee.2013.9
DO  - 10.2991/iccsee.2013.9
ID  - Zhou2013/03
ER  -