Re: 1/f noise

*To*: mathgroup at christensen.cybernetics.net*Subject*: [mg1500] Re: [mg1432] 1/f noise*From*: el at qua.crl.melco.co.jp (E. Lange)*Date*: Tue, 20 Jun 1995 01:17:41 -0400

> Can anyone suggest a way to have Mma generate a sequence of random numbers > that have are distributed as 1/f noise? If you want to generate just a few short sequences (with random phase and 1/f amplitude in the frequency space), then you could start in the frequency space, n = 2^13; fnoise = Table[E^(2Pi I Random[]) 1/f, {f, n/2}] // N; and use InverseFourier[] for constructing a sequence of numbers with the desired property (the first two lines impose two constraints on `fnoise': `noise' should be real, and the average of `noise' should be zero): fnoise[[-1]] = Re[ fnoise[[-1]] ]; fnoise = Join[{0}, fnoise, Conjugate @ Reverse @ Drop[fnoise, -1] ]; noise = InverseFourier[fnoise] // Chop; ListPlot[noise] ListPlay[noise] Eberhard Lange