[time-nuts] Continuous timestamping reciprocal counter question

[Magnus Danielson]

Hi Fred,

On 05/14/2011 12:12 PM, Tijd Dingen wrote:
> Thanks for the sanity check! :)
>
> I was indeed hoping to be able to get away with "not every Nth edge" since that simplifies thing.

There are many things you can get away with, just how much trouble you 
want to verify it versus doing the proper thing is another issue.

> On the subject of extracting frequency out of the dataseet, for now I use ordinary least squares. What other approaches do you know of that are used for this particular applicaction?

Linear regression is being used as well as block-averaged time-stamps.

The later method using say 200 time-stamps divides them into the first 
and second half, you average the time-stamps, subtract the first half 
average from the second half average and divides by the time between the 
first samples (or equivalent time).

Just using a time sequence of 200 time-stamps you get 199 direct in 
sequence pairs forming 199 frequency estimates. Sounds cool, now we can 
average those 199 frequency estimates... well... the sad thing is that 
you essentially cancels the 198 measures and end up with only using the 
first and last samples. The sqrt(N) averaging of the above block 
averager is lost in this simple variant and still they have about the 
same computing complexity. So, frequency estimation algorithms can look 
good until you find out that their degrees of freedom may vary greatly. 
These to algorithms differs about N/2 in degrees of freedom..

I wanted to illustrate how good or bad algorithms can be on the same 
amount of data.

I have not looked on detail performance comparison between these 
algorithms lately. However, they should not be used naively together 
with AVAR and friends since they attempt to do the same thing, so the 
resulting filtering will become wrong and biased results will be produced.

Cheers,
Magnus