Ramanujan sums analysis of long-period sequences and 1/f noise

Details Ramanujan sums analysis of long-period sequences and 1/f noise Ramanujan sums analysis of long-period sequences and 1/f noise

2008-12-11

arxiv.org/abs/0812.2170v1

EPL 85 (2009) 40005

Physics

Mathematical Physics

10 pages

Scientific paper

10.1209/0295-5075/85/40005

Ramanujan sums are exponential sums with exponent defined over the irreducible fractions. Until now, they have been used to provide converging expansions to some arithmetical functions appearing in the context of number theory. In this paper, we provide an application of Ramanujan sum expansions to periodic, quasiperiodic and complex time series, as a vital alternative to the Fourier transform. The Ramanujan-Fourier spectrum of the Dow Jones index over 13 years and of the coronal index of solar activity over 69 years are taken as illustrative examples. Distinct long periods may be discriminated in place of the 1/f^{\alpha} spectra of the Fourier transform.

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