# [time-nuts] AVAR <-> S_Y conversion

Wolfgang Wallner wolfgang-wallner at gmx.at
Fri Mar 6 05:04:11 EST 2015

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On 03/05/2015 07:23 PM, Attila Kinali wrote:
> Servus!

Servus :)

> On Thu, 05 Mar 2015 14:35:51 +0100
> Wolfgang Wallner <wolfgang-wallner at gmx.at> wrote:
>
>> For the random walk noise the expected line is off by a factor of
>> exactly 2 from the calculated plot, and I don't know how to explain this
>> behavior.
>
> I'm probably the wrong one to answer, as I have never done any noise
> simulation or even read up the relevant papers, but...
> A factor of 2 sounds like the difference you would get between one sided
> and two sided noise PSD's.
>

I calculate the one-sided PSD of the FFD data as described in [1] (first
paragraph), so the code looks like this:

xdft = fft(x);
xdft = xdft(1:N/2+1);
psdx = (1/(Fs*N)) * abs(xdft).^2;
psdx(2:end-1) = 2*psdx(2:end-1);

Remark: Before calculating the PSD, I split the data into parts of equal
size, calculate the PSD for each one, and average over the set of PSDs.
This improves the graphical visualization a lot.

As the result matches my expectation exactly for 4 different kinds of
noise, I would have assumed that this PSD calculation approach is quite
reasonable.

As I see the unexpected behavior only with random walk noise, and the
main difference in the calculation is the term A, I would suspect that
it has something to do with it.

However, I'm a novice in this field, so any hint is very appreciated.

regards, Wolfgang

[1] http://de.mathworks.com/help/signal/ug/psd-estimate-using-fft.html
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