1
$\begingroup$

I have some sampled data that has $1/f$ noise in it, with departures from the mean. These are long term departures. I could use something like a median filter but the window length would be longer than I would like.

  • Is there any way to measure its departure from a Gaussian distribution?
  • Or measure how 'Gaussian-like' a time series statstical sample is?
$\endgroup$
  • $\begingroup$ The Gaussian distribution has some properties that are useful. You can start here. $\endgroup$ – Envidia Apr 3 '17 at 21:44
  • $\begingroup$ I have troubles understanding was you really are looking for: a measure of gaussianity? Characterization of $1/f$ noise? Why is your original data Gaussian? Why does a median filter come into play? $\endgroup$ – Laurent Duval Apr 3 '17 at 21:54
  • 1
    $\begingroup$ I have taken a few statistical courses and I'm aware of the math. I want to know what other people use $\endgroup$ – Voltage Spike Apr 4 '17 at 4:57
3
$\begingroup$

One way to measure the similarity between two distributions is the Kullbeck-Leibler divergence. Granted, it is not a norm because it is not symmetric, but it is a way of quantifying the distance between two pdfs.

EDIT: There is a topic called "Normality testing" or "Gaussianity testing" that is devoted to that very task. Perhaps some tools from that field will help.

$\endgroup$
2
$\begingroup$

A classical measure of "gaussianity" is the kurtosis of your random variable (RV). Kurtosis is the forth order cumulant of a RV. Say $y$ is your RV with zero mean, the kurtosis can be defined as: $$kurt(y)=E[y^4] - 3(E[y^2])^2$$ If $y$ is gaussian, $E[y^4]=3(E[y^2])^2$ and therefore $$kurt(y)=0$$

$\endgroup$
1
$\begingroup$

Have a look at https://doi.org/10.1063/1.3504369

In this reference the authors check for gaussian behavior of the 1/f noise of a resistor using a fourth order frequency spectrum.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.