
NOTE
The Sigma vs. Tau function uses the Carrier Frequency
defined in the Instrument Parameters display for it
computation. If Sigma vs. Tau is being computed for a
Result File loaded from memory, be sure that the same
Carrier Frequency used for the measurement is entered
into the Instrument Parameters display.
Allan Variance
David Allan of the National Bureau of Standards recognized that
(T
y
2
(r) is also a function of N and T for some noise processes.
Therefore, he proposed the following:
Let N = 2, T =
T,
Allan Variance = (jy(2,T,r, f
h
) = v%(Tj
h
)
[°l(Tjh))
(Y
k+1
- Y
k
y
Cutler
2
has shown that:
W(N, T, r, A)
>
= & fh
SyifY-^^
sin
2
{-KNJT)
N
2
sin
2
(TrfT)
df
D.
W. Allan, "Statistics of atomic frequency standards/ Proc. IEEE, vol. 54, pp. 221-230,
February 1966.
L. Cutler and C. Searle, "Some aspects of the theory and measurement of frequency
fluctuations in frequency standards," Proc. IEEE, vol. 54, pp. 135-154, February 1966.
rev.05SEP89
Sigma vs. Tau 4-11
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