SDA Operator’s Manual
Automatic Renormalization of the Q-scale
This is the heart of the (patent pending) method for analysis of EDF, yielding best estimates of
the underlying PDFs defining the measured system’s behavior.
The procedure is straightforward: create the symmetric EDF for each side of the distribution.
The method can be described in steps as:
1. Forming a set of elements to be fitted, which are 3 values each, a vertical (Q-scale) value, a
horizontal coordinate (for the case of time variable jitter, but the method is extensible to
vertical noise analysis or, in fact, any variable), and an associated error. Statistically, the error
of the input variable
ρ
n
is furnished as the square root of the total population of observations
his value may be
interpreted as the mean-value associated with the noise/jitter contributor with sigma equal to
the reciprocal of the slope obtained from the best linear fit, and amplitude (area) equal to the
best normalization factor itself.
4. Under the assumption of symmetric noise/jitter contributions a single ideal normalization may
be obtained and used, however, ideally both extremes of the EDF must be treated
.
(the same sum) contributing to the estimate (of EDF in this case). Upper and lower values of
BER are obtained for these variations, and an error inversely proportional to the error is
assigned to the data point.
2. Varying the Q-Scale normalization factor over a range of plausible values, the “best” fit to
linear behavior is determined.
3. Using this value to correctly scale the probability, an intercept (with Q
norm
(BER)=0) is obtained
for both the right-hand side and the left-hand side of the CDF(Q
norm
(BER). T
independently, yielding strengths (ρ
norm
) and sigmas (reciprocal slope) to characterize the
extremal behavior of each side of the EDF distribution. In this case we show only an example
of one side of the EDF
SDA-OM-E Rev H 393
To Next Page
Loading...
Need help?
General