On the Uniquity of 1/f Noise

Bruce J. West and Michael F. Shlesinger

International Journal of Modern Physics, B , vol. 3, no.6, 795-819 (1989)

Abstract

A generic mechanism for the ubiquitous phenomenon of 1/f noise is reviewed. This mechanism arises in random processes expressible as a product of several random variables. Under mild conditions this product form leads to the log-normal distribution which we show straightforwardly generates 1/f noise. Thus, 1/f noise is tied directly to a probability limit distribution. A second mechanism involving scaling is introduced to provide a natural crossover from log-normal to inverse power-law behavior and generates 1/fa noise instead of pure 1/f noise. Examples of these distributions and the transitions between them are drawn from such diverse areas as economics, scientific productivity, bronchial structure and cardiac activity.

math model of 1/f section