[time-nuts] Modified Total Deviation measurement

Magnus Danielson magnus at rubidium.dyndns.org
Mon Jan 18 06:16:50 UTC 2010


Hi Dick,

Dick Moore wrote:
> Hi Magnus -- Any possibility that there is some math package subroutine error of some kind? In yours or theirs?

Well, wherever the error is, for a known series of 1000 frequency 
samples (or equalent 1001 time samples) I expect the error to be 
algorithmic rather than math-support. Programming in crisp C gives me 
the floating-point processor and only the sqrt may be affected and 
numbers sits nicely there, no great cancelation in the big sums (they 
sum up squared values) so no, it is not very likely.

The modified total deviation involves taking 3*m samples out of the 
sequence, calculate the frequency of those samples, compensate the 
samples, mirror them up and down in non-inverting even mirroring to 9*m 
samples, preform the tripple-diff of the second derivate and average 
over m samples. A couple of sums, averaging and scaling terms. There are 
many small details that could go wrong. For instance, I can't understand 
how the Hadamard Total Deviation for m=1 is equal to the Hadamard 
Deviation for m=1. The inner sums comes out differently for 
back-of-printout pen-and-paper analysis. Something is fishy here. Either 
I am quite stupid or...

Cheers,
Magnus



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