EE 200 – Fall 2009 (Weber)
Homework 2
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EE 200, Homework #
Show intermediate steps whenever possible.
1.
Define
x
(
t
) as
x
(
t
) = 5 cos(
ωt
+
3
2
π
) + 4 cos(
ωt
+
2
3
π
) + 4 cos(
ωt
+
1
3
π
)
a.
Express
x
(
t
) in the form
x
(
t
) =
A
cos(
ωt
+
φ
) by finding the numerical values of
A
and
φ
.
b.
Plot all the phasors used to solve part (a) in the complex plane.
2.
If a function is periodic with period
T
0
, then
x
(
t
) =
x
(
t
+
kT
0
) for integer values of
k
. For each of the
following continuous functions, is the function periodic, and if so what is the period? If it is not periodic,
explain why.
a.
x
1
(
t
) = sin(2
πt
) + sin(
√
2
πt
)
b.
x
2
(
t
) = sin(2
√
2
πt
) + sin(
√
2
πt
)
3.
A continuoustime signal
x
is given by
x
(
t
) = 2 cos(68
πt
) + 5 sin(170
πt
)

7 cos(306
πt

π/
6)
where
t
is in seconds.
a.
Determine the fundamental frequency of
x
(
t
) and specify the units.
b.
What is the period of
x
(
t
)?
c.
Convert the expression for
x
(
t
) from sin and cos functions to complex exponentials and determine
the amplitudes (
a
0
, a
1
, a
2
, . . .
) for the Fourier series expansion of
x
(
t
). Your
a
k
values should be in
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 '08
 ZADEH
 Exponential Function, Fourier Series, Weber, Complex number, Fourier series expansion

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