1/|f| Noise in Physical Measurements

Abstract

The purpose of this paper is to provide an insight into low frequency divergent noises with spectral density |f|α, where α` ≤ -1, and into their effect on physical measurements, with special reference to 1/|f| noise. This class of noise is widespread in nature, and it presents unique limitations to the measurement accuracy. In an attempt to present a picture of this class of noise with regard to the measurements of observable physical quantities, the questions about generation of noise, its divergence, correlation properties and measurements of variance are discussed. A statistical model for generation of low frequency divergent noises is used to consider the divergence problem in both the frequency and time domain. It is shown that 1/|f| noise is "weakly divergent," and that power limitation presents no reason to impose a low frequency limit within time intervals observable in nature. Correlation properties are discussed in terms of the time-dependent correlation function, using an ideal impulse response which generates low frequency noise from white noise. Two general models for generation of 1/|f| noise are summarized and discussed. Generation of 1/|f| noise from white noise over a limited frequency range by distributed and lumped-parameter filters is described. It is shown that the variance (i.e. mean square noise) is determined by the frequency limits of the observation method.