[time-nuts] Best method to convert phase measurements into frequency?

[Erik Kaashoek]

One of the intended use cases of my DMTD is to measure minute frequency 
differences to enable the frequency tuning of clocks against a 
reference. A typical frequency display update for this use case would be 
at most every second.
As the DMTD can only measure phase this phase has to be converted into 
frequency. The advice I received was to make  many short duration phase 
measurements and use a linear regression on those phase measurements to 
calculate the frequency at the display update interval.
A typical display of the measured frequency using linear regression over 
100 phase measurements and the noise of the phase measurements (green 
trace) can be found here: 
http://athome.kaashoek.com/time-nuts/DMTD/freq_capture.png

An alternative method would be to measure the phase at the required 
display update frequency and convert the measured phase and the 
previously measured phase and the measurement interval into the frequency.
But what method delivers the most accurate frequency? Linear regression 
accuracy improves with the number of measurements involved but the 
accuracy of the phase measurements decreases with shorter phase 
measurements.
To determine accuracy, both methods where used to measure two 10 MHz 
clocks with a 10 microHz frequency difference over a period of 100 
seconds. Using these 100 measurements the ADEV was calculated and 
compared for a tau of 1 second.
The method using linear regression and 100 phase measurements every 
second had an ADEV at 1 second of 2.1e-13, the method using a single 
phase measurement every second had an ADEV at 1 second of 1.2e-13.
At first it seems the second method has an advantage but as its using 
the phase measurement of the previous second it uses twice the 
measurement data so in practice I feel there is no difference.
Is this to be expected?