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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
44
1
0
( ) 10
sinc(
10
)
j
f
Hf
f e
π
−
−−
−
×
×
=×
××
×
volts/Hz.
()
mt
rt
(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
tT
m
tr
t
h
t
r
u
d
u
−
=∗=
∫
)
2)
Plot the power of
m
(
t
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This note was uploaded on 01/11/2011 for the course EE 3008 taught by Professor Pingli during the Fall '08 term at City University of Hong Kong.
 Fall '08
 PingLi
 Volt

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