Modular functions and Ramanujan sums for the analysis of 1/f noise in electronic circuits
Abstract
Description
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.
weakly expanded version of an invited paper at ICNF 2003
weakly expanded version of an invited paper at ICNF 2003