[time-nuts] Allan variance by sine-wave fitting
d.schuecker at avm.de
d.schuecker at avm.de
Thu Nov 23 07:34:03 EST 2017
Hi,
just my two cents on sine wave fitting.
A undamped sine wave is the solution of the difference equation
sig(n+1)=2*cos(w)*sig(n)-sig(n-1)
This is a linear system of equations mapping the sum of the samples n+1 and
n-1 to the sample n. The factor 2*cos(w) is the unknown. The least-squares
solution of the overdetermined system is pure linear algebra, no nonlinear
fitting involved. The trick also works for a damped sine wave. Care must be
taken for high 'oversampling' rates, it works best for 4samples/sinewave,
ie near Nyquist/2.
Cheers
Detlef
DD4WV
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