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

```

• Prev by Date: Re: Question about interpolation and ListPlot3D
• Next by Date: Re: Complex variables
• Previous by thread: Re: Complex variables