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Modular functions and Ramanujan sums for the analysis of 1/f noise in electronic circuits

Michel Planat
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Abstract

A number theoretical model of $1/f$ noise found in phase locked loops is developed. The dynamics of phases and frequencies involved in the nonlinear mixing of oscillators and the low-pass filtering is formulated thanks to the rules of the hyperbolic geometry of the half plane. A cornerstone of the analysis is the Ramanujan sums expansion of arithmetical functions found in prime number theory, and their link to Riemann hypothesis.

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Michel Planat. 2003-02-24. Modular functions and Ramanujan sums for the analysis of 1/f noise in electronic circuits. https://arxiv.org/abs/hep-th/0209243

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