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Fig. 4.8
Possible method
to obtain a random sampling
pulse
pulses might occur too close together. However, such issues usually make no
difference biologically.
If it should happen that not even one sampling pulse occurs in a given cycle of
T
o
, more cycles of T
o
are needed to assure that at least one random pulse has
occurred. It may be noted that biological systems generally take the time they need;
and in particular, they do not need to be fast. For example, a delay of a few cycles of
T
o
would not hurt the random masking of cues during a memory search, as done in
the Cue Editor of a future chapter. Cue editing is done in the background and not in
real time, so does not need to be fast.
As a note of little importance, but worth mentioning, when a multivibrator
operates at f
0
, the lowest frequency, the probability of a false is high, but the
probability of a false does not quite 100 % unless f
0
can be made to be zero. To
make probability of a false be 100 % for finite f
0
, sampling could be synchronized
with multivibration. Then sampling may be made to occur only between
and T
o
.
When frequency is at f
0
this would guarantee a false with a probability of 100 %.
Essentially the first pulse at the beginning of the period T
o
is ignored.
τ
Non-ideal Sampling
Non-ideal sampling is accomplished by a single pulse whose width is not zero but
whose width
as in Fig.
4.9
. To assure that the highest frequency always gives an
ideal true with 100 % probability, let
δ
.
The probability of seeing a true as an output (after adjusted sampling) is
δ ¼
2
τ
P
2
τ
f
x
100
%:
(4.5)
Note that a lower frequency for f
x
lowers the probability of a true. The probabil-
ity fraction of seeing a false is the complement of seeing a true:
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