Calculating noise power spectrum
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.