Volume 95, Number 6, September 2011
|Number of page(s)||5|
|Published online||08 September 2011|
“1/fα noise” is equivalent to an eigenstructure power relation
Gassco - Postbox 93, 5501 Haugesund, Norway
2 Department of Mathematics and the Peter Wall Institute for Advanced Studies, University of British Columbia 1984 Mathematics Road, Vancouver, BC, Canada
3 Department of Psychology, Brain Research Centre, and the Peter Wall Institute for Advanced Studies, University of British Columbia - 2136 West Mall, Vancouver, BC, Canada
Accepted: 5 August 2011
The discovery that the power spectrum of a time series of observations has a 1/fα character has been thought to imply that the generating process has some hidden, remarkable, nature, such as self-organized criticality or interaction across multiple scales. We show that 1/fα noise is equivalent to a Markovian eigenstructure power relation for natural systems. Fluctuations of a stationary reversible Markov process are characterized in terms of the eigenvalues, λ, and eigenfunctions, Pλ, of its generator. The power relation states that the product of the density of the eigenvalues and the squared first moment of the eigenfunctions is approximately a power function, λ−α, if and only if the power spectral density is approximately 1/fα. This characterization of 1/fα noise goes some distance toward explaining its ubiquity in natural systems.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 02.50.-r – Probability theory, stochastic processes, and statistics
© EPLA, 2011
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.