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Simulators >> Circuit Simulators >> PSD from transient noise
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Message started by Geoffrey_Coram on Mar 12^th, 2008, 10:54am

Title: PSD from transient noise
Post by Geoffrey_Coram on Mar 12^th, 2008, 10:54am

What's the right way to compute the power spectral density from a transient noise analysis? Eg, suppose I put a resistor in a netlist and ran transient noise, how do I get the 4kTR white PSD?

It seems like I need to compute the autocorrelation of the voltage waveform and then Fourier-transform it, but I'm not sure how best to compute the autocorrelation.

Title: Re: PSD from transient noise
Post by thechopper on Mar 13^th, 2008, 4:45am

Hi Geoffrey,

Among the special functions you could use in ADE, there is one that directly calculates the psd of a transient signal. It is called just "psd" and it takes care of the autocorrelation calculation you are looking for.
As in the case of a dft, you have to choose the number of points and the type of window.

Hope this helps.

Tosei

Title: Re: PSD from transient noise
Post by Geoffrey_Coram on Mar 13^th, 2008, 9:24am

Tosei -
Thanks for the pointer; I'll go check the documentation.

It seems what I'm looking for fits in the general category of "spectral estimation," on which much research has been done.

Title: Re: PSD from transient noise
Post by didac on Mar 13^th, 2008, 10:56am

Hi Geoffrey,
If you end up needing to do the processing outside ADE, some useful formulas are:
1.Unbiased estimator of correlation(high variance):
R=XX^H, were X it's the vector of samples,H denotes hermitic.
Making the Fourier transform of this will give you the "Periodogram" as estimator.
2.The same estimator but with a reduction in variance(reduces resolution):
R=(1/M)Σ_m=1..MX_mX_m^H, in this expression you divide the samples into M vectors and made an average to reduce variance after transformation.

There exists other estimators but this two are the basic ones that I remember.

If you are doing a wider search you can look for keywords like:Blackman-Tuckey,Welch,Capon,Normalized Capon(Lagunas method),MUSIC or PISARENKO(the two first are Periodograms with modified windowing, the last two ones are called "superesolution estimators" that are good for estimate the frequency of an unknown signal).
Also is worth the effort to look at Matlab since it contains at least the periodogram and welch estimators.
Hope it helps,

Title: Re: PSD from transient noise
Post by thechopper on Mar 13^th, 2008, 6:26pm

What Didac suggested is another absolutely valid method. Sometimes I use Matlab's PSD estimators for getting actual measured noise PSDs, based on captured data from scope.

Tosei