LeCroy SDA, Operator'S Manual

Page: 388 / 397

For this case (jitter) the observed distribution is the histogram of time interval error (TIE) values,
obtained through analysis of either clock or NRZ data waveforms acquired by a digital recording
instrument (like a digital oscilloscope).
Integrating the PDFs
The Cumulative Distribution Function (CDF or c.d.f.) expresses the probability that an observation
will fall between
and the value x .
Of course this is a purely theoretical value. We can, however, calculate the Empirical Distribution
Function (EDF or e.d.f.) by summing the histogram from the left extreme to some value
x .
Now, for our purposes and in keeping with tradition for discussions of jitter, we make a small
change of representation. We are interested in variations in timing (jitter) before and after the
mean timing value (or, to left or right of the mean). As such, and in order to view the timing errors
in a symmetric fashion, we paste together two halves, the right-hand and the left-hand parts of
the EDF, where the left-hand part is summed from the left (increasing bin index, starting with
leftmost bin) and the right-hand part is summed from the rightmost bin with decreasing bin index,
noting that these are approximations of the right-hand and left-hand parts of the “bathtub curve.”
In practice, these two functions are joined at the median of the histogram (the bin containing the
median, or the bin for which 50% of the total population is in that bin or those with lower index,
and consequently 50% of the total population also falls within that bin and those bins with higher
index.
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