Pseudo-periodicity and 1/f noise from the sum of similar intermittent signals

TL;DR

This paper demonstrates that summing similar two-level signals with the same relaxation time can produce 1/f noise and pseudo-periodic signals due to signal coincidences, supported by computer simulations.

Contribution

It introduces a novel model showing how superimposing similar signals creates 1/f noise and pseudo-periodicity, expanding understanding of noise origins.

Findings

Superposition of similar signals produces 1/f noise.

Coincidences induce pseudo-periodic pulse trains.

Computer simulations validate the model.

Abstract

The usual interpretation of noise is represented by a sum of many independent two-level elementary random signals with a distribution of relaxation times. In this paper it is demonstrated that also the superposition of many similar single-sided two-level signals, with the same relaxation time, produces noise. This is possible tanks to the coincidences among the signals which introduce cross-correlations and tune locally the resulting process in trains of pseudo-periodic pulses. Computer simulations demonstrate the reliability of this model, which permits to insert in an coherent framework other models solving problems still open.