VII. __EXAMPLE OF TIME-DOMAIN SIGNAL PROCESSING
AND ANALYSIS__

We will analyze in some detail a commercial
portable clock, Serial No. 102. This cesium
was measured against another commercial cesium
whose stability was well-documented and verified
to be better than the one under test. Plotted
in figure 7.1 are the residual time deviations
after removing a mean frequency of 4.01 parts
in 10^{13}. Applying the methods described in section
IV and section V, we generated the s _{y}(t ) diagram shown in figure 7.2.

One observes that the last two points are
proportional to t ^{+1} and one is suspicious of a significant frequency
drift.

If one calculates the drift knowing that
s _{y}(t ) is equal to the drift times t /%2 a drift of 1.22 x 10^{-14} per day is obtained. A linear least squares
to the frequency was removed and sections
IV and V were applied again. The linear least
squares fit showed a drift of 1.23 x

10^{-14} per day, which is in excellent agreement
with the previous calculated value obtained
from s _{y}(t ). typically, the linear least squares will
give a much better estimate of the linear
frequency drift than will the estimate from
s _{y}(t ) being proportional to t ^{+1}.

Figure 7.3 gives the plot of the time
residuals after removing the linear least
squares and figure 7.4 is the corresponding
s _{y}(t ) vs. t diagram. From the 33 days of data, we have
used the 90% confidence interval to bracket
the stability estimates and one sees a reasonable
fit corresponding to white noise frequency
modulation at a level of 4.4 x 10^{-11} t ^{-}2. This seemed excessive in terms of the typical
performance of this particular cesium and
in as much as we were doing some other testing
within the environment, such as working on
power supplies and charging and discharging
batteries, we did some later tests.

Figure 7.5 is a plot of s _{y}(t ) after the standard had been left alone
in a quiet environment and had been allowed
to age for about a week. One observes that
the white noise frequency modulation level
is more than a factor of 4 improved over
the previous data. This led us to do some
studies on the effects of the power supply
on the cesium frequency as one is charging
and discharging batteries, which proved to
be significant. One notices in figure 7.4
that the s _{y}(t ) values plotted are consistent within the
error bars with flicker noise frequency modulation.
This is more typical of the kind of noise
one would expect due to such environmental
perturbations as discussed above.

Figure 7.1
Careful time- and/or frequency-domain analyses
can lead to significant insights into problems
and their solutions and is highly recommended
by the authors. The frequency-domain techniques
will be next approached.

Figure 7.2

Figure 7.3

Figure 7.4