[time-nuts] On some pitfalls of the dual mixer timedifferencemethod of horology

[Dr Bruce Griffiths]

Poul-Henning Kamp wrote:
> In message <000001c6e54b$d13299a0$03b2fea9 at athlon>, "Ulrich Bangert" writes:
>   
>> Hello Paul-Henning,
>>
>> www.tmo.jpl.nasa.gov/progress_report/42-121/121G.pdf
>>
>> definitely uses no FFT but uses a theoreme from geometry to estimate the
>> signal's frequency and the rest is a two dimensional non-linear fit for
>> amplitude and phase. But i am starting to understand how a FFT might be
>> helpfull too.
>>
>> Does it involve finding the maximum of the frequency spectrum by
>> interpolating between frequency bins and then find the matching
>> (interpolated) phase bin?
>>     
>
> That would depend on your sampling rate.
>
> If you sample a 1Hz signal 96k times a second, interpolation between
> bins would probably just be a waste of time.
>
> Alternatively, you could apply a really steep band-pass filter around
> 1 Hz.  Something like an 1131 pole FIR filter, and then find
> the zero crossing geometrically using the three points around the
> zero line.
>
>   
You are still left with the problem of apportioning the measured 
instability between the 2 oscillators/signals being compared.
Unless you know one of them is significantly less noisy than the other 
it is not possible to accurately apportion the instability between them.
A 3 cornered hat where 3 oscillators are compared using 3 mixers can 
help if the instabilities of all 3 oscillators are statistically 
independent.
It is also better if all 3 oscillators have similar instabilities.

A comparison of N oscillators using 0.5*N(N-1) mixers is even better.

Bruce