Predicting the variance of a measurement with 1/f noise

TL;DR

This paper introduces a new method to compute the variance of measurements affected by 1/f noise, accounting for calibration and measurement durations to avoid infinite variance values.

Contribution

It proposes an alternative variance definition for 1/f noise processes that incorporates calibration and measurement timing, addressing the issue of infinite variance calculations.

Findings

The new variance depends on calibration and measurement durations.

It effectively avoids infinite variance values for 1/f noise.

Applicable to various phenomena with flicker noise.

Abstract

Measurement devices always add noise to the signal of interest and it is necessary to evaluate the variance of the results. This article focuses on stationary random processes whose Power Spectrum Density is a power law of frequency. For flicker noise, behaving as $1/f$ and which is present in many different phenomena, the usual way to compute the variance leads to infinite values. This article proposes an alternative definition of the variance which takes into account the fact that measurement devises need to be calibrated. This new variance, which depends on the calibration duration, the measurement duration and the duration between the calibration and the measurement, allows avoiding infinite values when computing the variance of a measurement.