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Unified Engineering II Spring 2004
Problem S21 (Signals and Systems)
Solution:
1. The signal is plotted below:
-10 -8 -6 -4 -2 0 2 4 6 8 10
0
0.2
0.4
0.6
0.8
1
1.2
Time, t
g(t)
The signal is very smooth, almost like a Gaussian. Therefore, I expect that the
duration bandwidth product will be close to the theoretical lower bound.
2. � �2 �
Δtt2g2(t)dt
2 g2(t)dt
The two integrals are easily evaluated for the given g(t). The result is
7
2 2
t g (t)dt = 2
5
2
g (t)dt = 2
Therefore,
� 7
Δt = 2 5
3. The time domain formula for the bandwidth is
� �2 �
Δωg˙2(t)dt
2 g2(t)dt
The numerator integral is 1
g˙2(t)dt = 2
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