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From: Dirk on 12 May 2010 08:04
Hello,
I need to create a surface of which shape I only know the autocorrelation function; namely:
R(z)=sigma1^2*exp(-|z|/D1) + sigma2^2*cos(2pi*z/D2)
I know that the autocorrelation function is related to the power spectral density and therefore to the amplitude spectrum. But I lack the phase information.

So my question is it possible to create a noise function in Matlab with that autocorrelation function?

If not, what paramters will be needed to fully describe that process?
If, yes, how do I do it?

Thanks alot, Dirk
From: TideMan on 12 May 2010 16:14
On May 13, 12:04 am, "Dirk " <dja...(a)web.de> wrote:
> Hello,
> I need to create a surface of which shape I only know the autocorrelation function; namely:
> R(z)=sigma1^2*exp(-|z|/D1) + sigma2^2*cos(2pi*z/D2)
> I know that the autocorrelation function is related to the power spectral density and therefore to the amplitude spectrum. But I lack the phase information.
>
> So my question is it possible to create a noise function in Matlab with that autocorrelation function?
>
> If not, what paramters will be needed to fully describe that process?
> If, yes, how do I do it?
>
> Thanks alot, Dirk

Phase is irrelevant for PSD, so you can make it anything you like.
One option is random phase:
phase=2*pi*rand(n,1);
but phase=0; would be just as valid.
Once you get the amplitude spectrum, you can combine with whatever
phase you choose and ifft to get a time series.
If the combined amplitude and phase is X(f), where f=0,df,2*df,
3*df,.... and df is the interval in frequency, you get the time
series like this:
x=ifft([X;0;flipud(X(2:end)')]); % for length(X) even
x=ifft([X;flipud(X(2:end)')]; % for length(X) odd

You may need to scale, depending on the units of X, but it is easily
figured out by matching the variance of x with the area under the PSD.
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