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ECE 351, Systems I
Feb. 23, 2009
OSU, Winter 2009
Solutions  Problem Set 4
Problem 1
(a)
FALSE.
The system is BIBO stable for all

a

<
1. Thus it is unstable for
a
>
1.
(b)
TRUE
by de±nition of causality.
(c)
FALSE.
One cannot write the impulse response in the form
h
[
n
] =
cδ
[
n
] for the given
values of
a
and
b
.
(d)
TRUE.
Here
x
2
(
t
) is a pulse with a span between (0
,
1). If
x
1
(
t
) is ²ipped and shifted by
1, the area under it between 0 and 1 is 0.
(e)
FALSE.
If
x
1
(
t
) is ²ipped and shifted by 2, there remains no overlap with
x
2
(
t
). Thus the
convolution at
t
= 2 is 0.
(f)
FALSE.
If
x
1
(
t
) is ²ipped and shifted by 1
/
2, the overlap with
x
2
(
t
) is between 0 and 1
/
2.
The area of the corresponding triangular region is 1
/
4.
(g)
FALSE.
An LTI system cannot give a nonzero response at a frequency, not induced by
the input.
(h)
FALSE.
x
(
t
) is periodic with a period
T
=
1
250
= 4 msec.
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