ECE 402: Communications Engineering
Homework 5 (Fall 2009)
Due: Tuesday 10/27
1.
(a)
Suppose that binary data are transmitted by unipolar signaling with the triangular pulse wave
forms:
x
0
(
t
) = 0
, x
1
(
t
) = Λ(
t/T
). Assuming that the data consist of i.i.d., equally likely binary
digits, find the PSD and spectral efficiency of the modulated signal. Assume the pulse duration
is
T
(i.e., the pulses overlap).
(b)
Repeat for polar signaling:
x
0
(
t
) =

Λ(
t/T
)
, x
1
(
t
) = Λ(
t/T
).
2. Suppose we want to send data at a rate of 16 Mbps over a cable of bandwidth 8 MHz using
M
ary
PAM baseband modulation with a rectangular pulse shape.
If we take the null bandwidth of the
signal power spectral density to be equal to the cable bandwidth, what value of
M
and what baud
rate should we choose? Repeat the problem for a cable of bandwidth 4 MHz.
3. In 4ary pulse position modulation (4PPM), two data bits are transmitted by sending one of the
following four signals:
0
T
4
T
2
T
3
4
T
0
( )
x
t
A
0
T
4
T
2
T
3
4
T
1
( )
x t
A
0
T
4
T
2
T
3
4
T
2
( )
x
t
A
0
T
4
T
2
T
3
4
T
3
( )
x
t
A
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 Fall '08
 Townsend
 pulse position modulation, 4PAM signal constellation, PAM baseband modulation, triangular pulse waveforms

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