Modular functions and Ramanujan sums for the analysis of 1/f noise in electronic circuits
نویسنده
چکیده
A number theoretical model of 1/f noise found in phase locked loops is developed. Oscillators from the input of the non linear and low pass filtering stage are shown to lock their frequencies from continued fraction expansions of their frequency ratio, and to lock their phases from modular functions found in 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. Key-Words: Electronic circuits, number theory, signal processing, 1/f noise
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تاریخ انتشار 2002