[time-nuts] Convert ADEV specs to MDEV?

[Magnus Danielson]

Hi again,

On 04/23/2016 06:58 AM, Magnus Danielson wrote:
> Hi,
>
> On 04/23/2016 02:54 AM, Stewart Cobb wrote:
>> TimeLab can show "mask" overlays on various plots. It comes with a set of
>> ADEV masks for cesium clocks, derived from the manufacturer's
>> specifications for those clocks.
>>
>> Those masks don't show up on MDEV plots, because the manufacturers don't
>> provide MDEV specs.
>>
>> For the mathematicians out there: is there a way to convert ADEV specs
>> into
>> equivalent MDEV specs?
>>
>> If not, does anyone have good measured MDEV data on any of the popular
>> cesium clocks?
>
> The slopes of ADEV for the different noises can be converted to slopes
> in MDEV. It is the separation of white phase modulation and flicker
> phase modulation that doesn't go very well with ADEV, but works in MDEV,
> but if you ignore the flicker then you should be able to translate
> without too much difficulty.

I realized that this was a little short description of what I was 
actually thinking.

For each noise-form, there exists a formula for the amplitude of ADEV 
and MDEV given a certain amount of noise-level. By estimating the 
noise-level from the ADEV, the particular MDEV slope level can be 
concluded. Doing so for the noise-forms identified allows conversion 
from ADEV to MDEV, giving the assumption that white phase modulation 
noise and flicker phase modulation noise isn't separated but is 
dominated by white phase modulation noise. Not perfect, but good enough.

The more scientifically correct matching of ADEV slopes would be to 
actually match AVAR, as these sum together as non-coherent noise power 
rather than coherent sine power. Matching on ADEV causes biases. 
Typically is a least-square matching used. Similarly is MVAR used rather 
than MDEV.

It should be noted that the breakpoints between the different sloped in 
ADEV and MDEV is expected to differ, so direct translation of these is 
not recommended.

Cheers,
Magnus