On the frequency and amplitude spectrum and the fluctuations at theoutput of a communication receiver

摘要

A mixer cascaded with a low-pass filter is the basic piece of anyncommunication receiver. The frequency and amplitude fluctuations of beatnsignals recorded at the output of the mixer plus filter set-up areninvestigated experimentally and explained on the basis of number theorynin relation to the Riemann problem concerning the distribution of primennumbers. The frequency of the beat signal is obtained from a diophantinenapproximation of the frequency ratio of the input oscillators. Thenamplitude is defined globally from the position of resolved fractionsnwith respect to an equally spaced graduation. Time series analysisnmethods show that frequency fluctuations present a transition from whitenfrequency noise to 1/f frequency noise close to resonance; the latter isncompatible with an underlying fractal attractor. The same transition isnobserved in the case of time series computed from continued fractionnexpansions