PROBLEM Spring04Q.2.1:
A periodic signal
x
(
t
)
is represented as a Fourier series of the form
x
(
t
)
=
∞
k
=∞
(
δ
[
k
]

2
k
2
+
1
)
e
j
50
π
kt
(a) Determine the fundamental period of the signal
x
(
t
)
, i.e., the minimum period.
T
0
=
sec.
(Give a numerical answer.)
(b) Determine the DC value of
x
(
t
)
. Give your answer as a number.
DC
=
(c) Define a new signal by adding a sinusoid to
x
(
t
)
y
(
t
)
=
14 cos
(
100
π
t
+
π/
2
)
+
x
(
t
)
The new signal,
y
(
t
)
can be expressed in the following Fourier Series with new coefficients
{
b
k
}
:
y
(
t
)
=
∞
k
=∞
b
k
e
j
50
π
kt
Fill in the following table, giving
numerical values
for each
{
b
k
}
in polar form:.
Hint:
Find a simple relationship between
{
b
k
}
and
{
a
k
}
.
b
k
Mag
Phase
b

3
b

2
b

1
b
0
b
1
b
2
b
3
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PROBLEM Spring04Q.2.2:
For each short question, pick a correct frequency
5
(from the list on the right only) and enter the number in
the answer box
6
:
Question
(a) If the C/D converter output is
x
[
n
]
=
A
cos
(
0
.
75
π
n
)
, when the
input signal is defined by:
x
(
t
)
=
A
cos
(
1900
π
t
)
, then deter
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 Spring '08
 JUANG
 Digital Signal Processing, Fourier Series, Signal Processing, ideal ctod converter

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