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

Magnus Danielson magnus at rubidium.dyndns.org
Fri Mar 6 16:29:27 EST 2015

```Wolfgang,

I have checked several sources, and they match up with the IEEE 1139 in
this regard.

I have also evaluated the equation for Allan variance for the random
walk noise, and it matches up with the references and what I put here:
https://en.wikipedia.org/wiki/Allan_variance#Power-law_noise

So, the A formula you have matches up.

You will need to find another source of the mismatch.

Cheers,
Magnus

On 03/06/2015 11:04 AM, Wolfgang Wallner wrote:
>
>
> 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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