
The filter sample time is T ¼0.01 h. The parameter a is related to the bandwidth of the
filter v
0
by
a ¼ 2 cos v
0
T
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
(3 cos v
0
T)(1 cos v
0
T)
p
Choose v
0
as the frequency of the ambient temperature (in rad=h), and simulate the filter’s
response over a 24 h period. Plot T
amb
(t), T
s
(t), and T
f
(k) on the same graph.
5.33 Differentiation of noisy analog signals in continuous-time systems is often accom plished by
first removing the high-frequency components. To illustrate, suppose the signal x(t) ¼s(t) þ
n(t) where s(t) ¼2t, t 0, and n(t) ¼0.25 sin 120pt is fed to a differentiator as shown in
Figure