EE3210 Assignment 5: Fourier Transform
Due: (before lecture) Nov 18, 2009
(Marks will be deducted for late submission.)
1.
The input and the output of a stable and causal LTI system are related by the
differential equation
)
(
9
)
(
3
)
(
8
)
(
6
)
(
2
2
t
x
dt
t
dx
t
y
dt
t
dy
dt
t
y
d
+
=
+
+
.
a)
Find the frequency response of this system.
b)
Find the impulse response of this system.
c)
What is the response of this system if
[
]
)
(
)
(
3
t
u
e
e
t
x
t
t
−
−
+
=
.
2.
Consider a discrete-time LTI system whose input x[n] and output y[n] are related
by the following difference equation:
]
[
]
1
[
4
1
]
[
n
x
n
y
n
y
=
−
−
.
Suppose that the input signal is given by:
⎟
⎠
⎞
⎜
⎝
⎛
−
+
=
6
5
cos
2
]
[
π
π
n
n
x
.
a)
Determine the frequency response of the system.
b)
What is the fundamental frequency of
x
[
n
]? Determine its Fourier series
coefficients, {
a
k
}.
c)
Find the Fourier series representation of the output

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