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University of Southern California
MingHsieh Department of Electrical Engineering
Homework 4, EE 200L, Fall 2008, Ali Zadeh
____________________________________________________________________________________
(1)
Consider the following DiscreteTime LinearTime Invariant (DTLTI) system with impulse response h(n)
x(n)
y(n)
h(n)=½ [
δ(
n
29
–
δ
n
129]
(a)
Using Convolution sum, find the output response y(n) when the input signal x(n) is a unit step function.
<
≥
=
=
0
0
0
1
n
,
n
,
)
n
(
u
)
n
(x
(b)
Using Convolution sum, find the output response y(n) when the input signal x(n) is :
)
n
(u
)
n
(
Cos
)
n
(u
)
(
)
n
(x
n
π
=

=
1
(c)
Find the output response y(n) when the input signal x(n) is :
)
n
(u
)
(
e
e
e
)
n
(u
)
n
(x
n
n
)
(i
n
)
(i
n
)
(i
1
4
3
3
3
2
4
3
2
4

+
+
+
+
=
π
π
π
(d)
Find the frequency response of the system H(
ϖ
) using complex exponential input signal.
(e)
Find the frequency response of the system using impulse response h(n). Does this match the answer in part (c)?
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This note was uploaded on 12/02/2008 for the course BME 423 taught by Professor D'argenio during the Fall '06 term at USC.
 Fall '06
 D'Argenio
 Biomedical Engineering

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