EE3008 Assignment I
Consider the following bipolar signal
s
(
t
) using rectangular pulses with amplitudes
±
0.5 volts
and transmitting rate 10 kb/sec.
(a)
Determine the value of
T
above and answer the follows.
1)
Find and plot the energy spectrum of the first pulse in Fig.1.
2)
Find the expression of 
S
(
f
)
2
, the energy spectrum of
s
(
t
). (No need to plot.)
3)
Fine the power spectrum of
s
(
t
) (Hint: It is 
S
(
f
)
2
divided by 6
T
).
4)
Now assume that
K
pulses are transmitted and the signs of these pulses are
randomly selected from +1 and 1. Find the power spectrum of
s
(
t
) for
K
→∞
and
plot it. (Hint: Read Tutorial 2.)
A matched filter receiver diagram is shown in the figure below. The frequency domain
response of the filter is
4
4
4
10
(
)
10
sinc(
10
)
j
f
H
f
f
e
π
π
−
−
−
−
×
×
=
×
×
×
×
volts/Hz.
( )
m t
( )
r t
(b)
Determine the impulse response
h
(
t
) of the filter.
(c)
Consider the noisefree case, i.e.,
r
(
t
)=
s
(
t
).
1)
Determine
and
plot
the
filter
output
m
(
t
)
for
s
(
t
)
in
Fig.1.
(Hint:
( )
( )
( )
( )
t
t
T
m t
r t
h t
r u du
−
=
∗
=
∫
)
2)
Plot the power of
m
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 Fall '08
 PingLi
 Signal Processing, Volt, Estimation theory, 2T 3T 4T

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