[sdiy] Power spectra

[Aaron Lanterman]

On Sun, 10 Jul 2005, Ian Fritz wrote:

> So from what I have been reading, popcorn noise has a 1/f^2 power spectrum 
> above a cutoff fc.  So a first order lowpass operating on white noise might 
> be a good way to go.
>
> popcorn power ~ 1/(1 + (f/fc)^2)

One thing to remember is that if you have a deterministic signal with 
Fourier spectrum X(j w), and you filter with a filter with frequency 
response
H(j w), you get an output Fourier spectrum Y(j w) = H(j w) X(j w).

If instead you have a _random process_ with _power spectrum_ S_x(j w),
and you pass it through a filter with frequency response H(j_w), you get 
an output power spectrum of S_y(j w) = |H(j_w)|^2 S_x(j w).

So indeed, a first-order filter would probably give you the second order 
effect you want.

- Aaron

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