On 15 Okt., 18:16, Sampo Niskanen <spnis...@[EMAIL PROTECTED]
> wrote:
> Andor <andor.bari...@[EMAIL PROTECTED]
> wrote:
> > This sounds a bit contradicting. Either you are intersted in 1/f^{5/3}
> > noise, or you are worried about values in the series deviating from
> > zero for long periods.
> > You can't have both.
>
> The application in my case was simulating wind turbulence. =A0Wind
> turbulence freqency has a power spectrum density pro****tional to
> 1/(1+K*f)^(5/3), which for large f is equal to 1/f^(5/3). =A0The
> simulation time scale, however, is quite short, so I don't want a gust
> of wind to last the whole simulation duration (that would effectively
> change the average wind speed).
>
> By choosing the number of poles suitably one can choose how much low
> frequency components to include. =A0The original (empirical) formula
> doesn't go to infinity at f=3D0 either, so one could estimate it with a
> suitable number of poles. =A0In my case I wanted even less low-frequency
> components, and using 2 poles with a 20Hz sampling rate yields maximum
> wind gust lengths of approximately 3-5 seconds (the spectrum turns flat
> below 0.3Hz). =A0So in my application, it is desireable that the noise
is
> pink at the high end of the spectrum, but flat at the low end.
Ok, I see. I think I had a similar discussion with somebody here some
time ago who wanted to use "pink noise" for audio testing purposes. He
was also interested in generating series with PSD pro****tional to
1/(1+ K f),
with a finite cutoff, going flat towards DC, and having the 1/f
property for audible frequencies. Perhaps it would be a suitable
nomenclature to call that kind (with finite cutoff frequency towards
DC) of series "pink noise", as compared to 1/f^alpha noise. By
definition, 1/f^alpha noise has a PSD satisfying
lim_{f->0} ( P(f) / [c |f|^{-alpha}] ) =3D 1
for some constant c, so only the behaviour towards DC is im****tant (as
opposed to "pink noise", where only the behaviour towards infinity is
im****tant).
Regards,
Andor
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