1/f Noise



1/f
noise and flicker noises (i.e. the class of 1/f^alpha noises - with 0.5 < alpha < 1.5) 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 have shown 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 to the system. I have also shown that the eigenvalue densities of linear operators that reasonably describe diffusion and transport lead to 1/f or flicker noise. I have been able to derive the Hooge formula for the spectrum of conductance fluctuations.
 

Simulated white noise
 
 

Simulated 1/f noise
 
 

1/f noise appears to be ubiquitous indeed: the following figure shows the spectrum of the Wolf number for the period january 1953 - august 1995. The Wolf number is an indicator of the solar activity
 
 


 
 

To know more about 1/f noise you can read the paper (sorry ... italian text only) that I wrote for "Le Scienze" (italian edition of Scientific American) and which appeared in the june 1996 issue, or this review paper.


Last updated: 19 August 2002