BME 311
EXAM #2
March 29, 2006
•
Show all work in your blue book.
•
Please start each problem on a new page, and clearly indicate your answers.
•
Write and sign the honor pledge on the cover of your blue book: “I have neither given nor received
unauthorized aid on this exam, nor have I concealed any violations of the Honor Code.”
•
This test is closedbook and closednote. Calculators are allowed.
•
You may find these relations useful:
x
[
n
] =
k
=
N
X
(e
jkω
0
)e
jkω
0
n
c
k
=
X
(e
jkω
0
) =
1
N
n
=
N
x
[
n
]e

jkω
0
n
x
(
t
) =
∞
k
=
∞
X
(e
jkω
0
)e
jkω
0
t
c
k
=
X
(e
jkω
0
) =
1
T
0
T
0
x
(
t
)e

jkω
0
t
d
t
x
(
t
) =
1
2
π
∞
∞
X
(
jω
)e
jωt
d
ω
X
(
jω
) =
∞
∞
x
(
t
)e

jωt
d
t
ax
2
+
bx
+
c
= 0 has roots

b
±
√
b
2

4
ac
2
a
[
x

(
a
+ j
b
)][
x

(
a

j
b
)] = (
x

a
)
2
+
b
2
1. [15] Find the Fourier spectrum for each of the following signals:
(a) The periodic CT signal:
!
4
!
2
0
2
4
0
0.5
1
1.5
x(t)
t
Signal
where
x
(
t
) =
e

t
,
0
< t <
1
0
,
1
< t <
2
.
(b)
y
(
t
) =
e

t
,
0
< t <
1
0
,
otherwise
1
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BME 311
EXAM #2
March 29, 2006
(c) The periodic DT signal:
!
6
!
4
!
2
0
2
4
6
0
0.5
1
1.5
z[n]
n
Signal
2. [20] There are receptors in the airways of the lung that respond to the stretching of the airways’ walls.
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 Winter '06
 Steel
 Digital Signal Processing, Fourier Series, LTI system theory

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