ECE 101 – Linear Systems Fundamentals
Problem Set # 6 Solutions
December 1, 2009
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Speed Problems
9.1
a.
b.
c.
d.
e.
f.
Note : In e. and f., we use the fact that
9.3
The ROC is given by
.
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x(t) is a sum of two signals. The ROC of the first signal
is
}. The
ROC of the second signal is
}.
The ROC of the sum is atleast
Therefore for the ROC to be
we need to have
and there is no restriction
on the imaginary part of
β
.
9.6
A.
Since x(t) has a pole, it cannot be of finite duration.
B.
Since x(t) has a pole at 2 and it is absolutely integrable (ROC includes the imaginary
axis), its ROC cannot be right sided. Hence x(t) could be leftsided.
C.
x(t) cannot be rightsided as reasoned in B.
D.
x(t) can be twosided, if it has atleast one more pole on to the left of the imaginary axis.
9.10
A.
The poles are both on the real axis. If we move on the imaginary axis starting from the
origin, the denominator of the transfer function will be smallest in magnitude at the origin
and increase monotonically as we move away from the origin. Thus the magnitude of the
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 Spring '09
 Highpass filter, Bandpass filter, Lowpass filter, imaginary axis

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