# Calculating noise power spectrum

I have some signal which I have measured N different times and I want to calculate the noise power spectrum of it. Intuitively to me the way I would do this is simply calculating the power spectrum of the noise. To do this I would take the magnitude square of the fourier transform of the auto covariance of the standard deviation over my N different trials. That is a bit of a mouthful so I'll try to clarify what I mean. First I want to get the noise from my N repeated measurements, so I take the standard deviation over the N measurements and estimate this as my "noise waveform". Then to calculate the power spectrum I do the usual routine which is by taking the fourier transform of the autocovariance, and squaring the result.

This seems intuitive to me, however I can't find any text books or journal articles that confirm my intuition, so I'm left being a bit confused about whether this is really the right technique or not. Could anyone shed any light on the matter if they have experience with this?

• I think that's right. (I find it hard to believe you can't find anything on the web.. how about this en.wikipedia.org/wiki/Spectral_density) And then there are the usual caveat's, You have to sample at a rate that is above the Nyquist limit. (and make sure there are no frequencies above that in your noise signal.) Oh and also that there aren't any "real" signals in your noise signal. – George Herold Nov 10 '14 at 20:41
• Hello, thanks for the reply the closest thing I have found is for xray imaging, and they use a procedure quite a bit different than what I put down. Also that link provides good information about computing the spectral density, but little on the noise spectral density. And the matlab link on that page is very unhelpful. – user2551700 Nov 10 '14 at 21:07

So I've never done this digitally.
But there's no reason you can't copy.
So first this is just a spot measurement technique.
You can set some filter bandwidth (BW) with known properties*.
And then gain up the signal. With the BW limit somewhere in the gain chain.
(amp BW much bigger than the filter...)
At the end you multiply the signal by itself.
(analog/ digital.. your choice.) Then put a low pass filter on the output.
The longer the filter time constant the better the number.
The DC voltage is a measure of the noise. (in that BW, units of V^2/Hz.)

*of course knowing the properties of your analog filter is the hard part.
A nice digital technique could certainly be better.