LeCroy SDA, Operator'S Manual

Page: 389 / 397

SDA Operator’s Manual
To the point of all of this, in telecommunications or data communications, the relative rate of bit
errors is called BER
11 .
Extrapolation of the Distribution Tails (Extremes)
Historical Note: Before this approach was taken by LeCroy, the extrapolation was applied to the histogram
tails, whereas now the extrapolation is applied to the EDF; in fact, to each half of the EDF, as previously
described.
While the EDF is well defined in the central region of the histogram, where events are populous, it
is poorly defined at the extremes. This is of course the nature of the problem of analyzing jitter,
since we are most interested in learning about the nature of those most rare (timing error) events.
So we strive to obtain an estimation of how this extremal behavior is even beyond where we have
real observed data. To this end we strive to fit the data at the extremes of the EDF to plausible
mathematical forms (suggested by the underlying physics). One such mathematical form is the
“error function” which is closely related to the CDF of a Gaussian distribution.
The Error Function erf(x), Inverse Error Function erf
-1
(x) and Related Functions
Where the error function itself is
And the complementary error function
But more importantly, the inverse error function
erf-1(x) is the inverse function (neither reciprocal
nor complementary). This function gives the displacement x , for which a given value is the error
function of that displacement. (See http://mathworld.wolfram.com/InverseErf.html for more detail
on the inverse error function.)
And
for -1< z >1
SDA-OM-E Rev H
389
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Sometimes called bit error ratio, BER is the relative rate of bit errors compared to the bit rate, often expressed as a
power of ten. For example: the BER is “ten to the minus 15th.”