Linear processes that produce 1/f or flicker noise.

Abstract

1/f noise and flicker noises---i.e., the class of 1/${\mathit{f}}^{\mathrm{\ensuremath{\alpha}}}$ noises with 0.51.5---are as ubiquitous as they are mysterious. Several physical mechanisms to generate 1/f noise have been devised, and most of them try to obtain a broad, nearly flat distribution of relaxation times, which would then yield a 1/f spectrum. However, they are all very specialized, and none of them addresses the question of the apparent universality of this noise, while they all fail in some respect. I show here that the power spectral density of a relaxing linear system driven by white noise is determined by the eigenvalue density of the linear operator associated with the system. I also show that the eigenvalue densities of linear operators that describe diffusion and transport lead to 1/f or flicker noise. Using the concepts developed in the paper and a rough approximation of transport in a resistor, I derive the Hooge formula for the spectrum of conductance fluctuations.