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ENEE 241 02*
HOMEWORK ASSIGNMENT 6
Due Wed 02/13
(i) (5 pts.)
Compute the sum of the two discretetime sinusoids:
x
1
[
n
] = cos(2
πn/
5 +
π/
3)
and
x
2
[
n
] = cos(8
πn/
5 +
π/
4)
(
Hint
: Start with reducing the angular frequency of
x
2
[
n
] to a value between 0 and
π
, then use
phasors.)
(ii) (5 pts.)
Consider the frequency
f
0
= 50 Hz and the sampling rate
f
s
= 200 samples/sec. List
all the aliases of
f
0
with respect to
f
s
in the frequency range 0.0 to 1.0 kHz.
(iii) (5 pts.)
The discretetime sinusoid
x
[
n
] = 2
.
5cos((2
π/
5)
n
+0
.
9) is obtained by sampling the
continuoustime sinusoid
x
(
t
) at a rate of 200 samples per second. If it is known that the frequency
of
x
(
t
) is in the range 300 to 400 Hz, write an equation for
x
(
t
).
(iv) (5 pts.)
(
Unrelated to part (i)
) Consider the two continuoustime signals
x
1
(
t
) = cos(2
πt
)
and
x
2
(
t
) = cos(3
πt
)
The two signals are sampled at the same rate
f
s
= 1
/T
s
to produce the sequences
x
i
[
n
] =
x
i
(
nT
s
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 Spring '08
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