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EE 2200 / Spring 2010: Section THREE
1
ECE 2200 / Spring 2010
SECTION Three (Week 4: Feb 1518)
1. The continuoustime sinusoid
x
(
t
) = 4
.
5
sin
(16
.
6
πt
)
is to be sampled at
f
s
to produce the discretetime sinusoid
x
[
k
]=
M
cos(
γk
+
θ
)
(i) For
f
s
= 15 Hz, determine
M
,
γ
, and
θ
. Has
x
(
t
) been undersampled or
oversampled?
(ii) For
f
s
=7
.
5 Hz, determine
M
,
γ
, and
θ
. Has
x
(
t
) been undersampled or
oversampled?
(iii) For
f
s
= 22
.
5 Hz, determine
M
,
γ
, and
θ
. Has
x
(
t
) been undersampled or
oversampled?
2. Consider the discretetime sinusoid
y
[
n
] = 11
.
8 cos(0
.
21
πn

π/
5)
generated by sampling
y
(
t
)=
M
cos(2
παt
+
θ
)
at a sampling rate of 4200 Hz. Determine three di±erent continuoustime sinusoids
y
(
t
) with frequencies all less than 5.8 kHz that could have produced
x
[
n
]. Specify
your three possibilities with unique triples of
M
,
α
and
θ
.
3. Sketch the spectrum of
x
(
t
) = sin
3
(470
)
Clearly label the frequencies and complex amplitudes of each component. Deter
mine the minimum sampling rate that can be used to sample
x
(
t
) without aliasing
any of its components.
4. Consider the three zerophase cosines of di±erent frequencies
x
1
(
t
) = cos(2
π
8500
t
)
x
2
(
t
) = cos(2
π
24500
t
)
x
3
(
t
) = cos(2
π
31000
t
)
For each
x
i
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 Spring '05
 JOHNSON

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