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The ETSI noise model that was simulated outputs samples of the time error rather than fractional frequency error. Thus it is necessary to re-cast equation (4.3) in terms of x
. By considering that from equation (3.6),

the above expression (4.3) for TDEV can be expressed in terms of the time error x(t) as

assuming there are N+1 time error samples.
By considering that the samples are spaced by integer multiples of
any particular
in the above equation can be chosen such that
. This results in the equation

To increase the confidence in the estimate and to maximise the data utilisation Wallis and Allan [23] substitute N-3n+1 for N in their expression for the Allan Variance and therefore limit n to values up to
. Performing a similar procedure here yields

By taking the mean the above equation may be estimated as [1]
|  |
(28) |
where xi is the ith sample of the time error function; N is the total number of samples;
is the integration time; and
is the number of sampling intervals. It is this equation (4.4) that was used to calculate TDEV, as is discussed in section B.1.
Next: TDEV in terms of
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Mark J Ivens
11/13/1997