Software - Generate Power Law Noise 1/f^α

This page contains software for Matlab for generating noise time series whose power spectrum scales as a power law with frequency, i.e. |P(f)|² = 1/f^α. Special cases include 1/f noise (α = 1) and white noise (α = 0). The algorithm generates the appropriate Fourier domain sequence, with power-law spectral magnitudes and randomised phases. It then inverts this using the inverse FFT to generate the required time series. Note that, in order to cope with the degeneracy at f = 0, it sets the zero frequency component to an amplitude of 1. This guarantees power law scaling across the whole frequency range (right down to 0Hz), but the mean of the time series will not be exactly zero. For examples of techniques that can analyse this kind of power law time series, see FastDFA on this site.

Download the following code:

powernoise.m

Matlab code for generating power law noise. Requires signal processing toolbox.

Typing 'help powernoise' shows instructions for the routine. For further details, please contact the author, Max Little.