Re: algorithm to generate 1/f noise

• To: mathgroup at smc.vnet.net
• Subject: [mg22262] Re: algorithm to generate 1/f noise
• From: Artlandia Info <info at artlandia.com>
• Date: Sat, 19 Feb 2000 23:50:52 -0500 (EST)
• Organization: Artlandia Inc.
• References: <8889s2\$c5o@smc.vnet.net> <88ekch\$rf1\$5@dragonfly.wolfram.com> <88km5r\$mll\$8@dragonfly.wolfram.com>
• Sender: owner-wri-mathgroup at wolfram.com

```You might be referring to the article

Marvin S. Keshner, 1/f noise, Proc. IEEE, 1982, v. 70,
No. 3, p.212-218.

Yes, one can generate an *approximation* of 1/f noise by
superposition of Lorentzian spectra; the more sources,
the better approximation (the limit is given by
the corresponding integral).

On a practical note, the method I was referring to is
simpler, more direct, and in general faster.

Igor Bakshee

Joe Gwinn wrote:
>
> There was an article in The Proceedings of the IEEE titled "1/f Noise"
> twenty or thirty years ago, if memory serves.  The subject index will
> certainly have this article under "noise" and/or "1/f noise" or "noise,
> 1/f"This article gave simple ways to generate 1/f noise from a uniformly
> distributed noise.  The basic approach was a cascade of one-pole lowpass
> filters, each with one tenth the bandwidth of the previous filter, fed
> with uniform noise.
>
> Joe Gwinn
>
> In article <88ekch\$rf1\$5 at dragonfly.wolfram.com>, Artlandia Info
> <info at artlandia.com> wrote:
>
> > As a basic recipe for generating noises with arbitrary spectra,
> > one would: take a piece of white noise -> Fourier-transform it ->
> > multiply by a suitable kernel -> inverse-transform back to the
> > time domain.
> >
> > As to the implementation, you might have a look at Artlandia
> > (http://www.artlandia.com). Particularly, see examples at
> > http://www.artlandia.com/software/lab/
> >
> > 1/f noise (also called NaturalArray) is used quite extensively
> > in the package (albeit for the artistic purposes which might
> > not be want you want :-).
> >
> > Hope this helps.
> >
> > Igor Bakshee
> >
> >
> > David E. Burmaster wrote:
> > >
> > > Hi
> > >
> > > Can anyone point me towards a good algorithm or package to generate 1/f
> > > noise in a time series using Mathematica??
> > >
> > > Pointers to books and articles (using Mathematica) also appreciated!
> > >
> > > many thanks, and
> > > best wishes
> > > Dave
> > >
> > > ++++++++++++++++++++++++++++++
> > > David E. Burmaster, Ph.D.
> > > Alceon Corporation
> > > POBox 382669
> > > Harvard Square Station
> > > Cambridge, MA 02238-2669
> > >
> > > Voice   617-864-4300
> > > Fax     617-864-9954
> > >
> > > Web     http://www.Alceon.com
> > > Email   deb at Alceon.com
> > >
> > > +++++++++++++++++++++++++++++++

```

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