Digital Signal Processing Reference
In-Depth Information
6.29.
For the system of Figure P6.28, with
c
1
(t) = cos(v
c
t)
and
c
2
(t) = sin(v
c
t),
sketch
Y(v)
and
Z(v).
Identify all amplitudes and frequencies of importance.
6.30.
In QAM [8], it is possible to send two signals on a single channel, which effectively
doubles the bandwidth of the channel. QAM is used in the uplink (path from the house
to the service provider) in today's 56,000 bits/second modems, in DSL modems, and in
Motorola's Nextel cellular phones.
A block diagram of a QAM system is shown in Figure P6.30. Assume that
f
1
(t)
and
f
2
(t)
have bandwidth
v
0
,
where
v
0
V
v
c
and
v
c
is the carrier frequency.
g
1
(
t
)
LPF
2
e
1
(
t
)
f
1
(
t
)
0
(
t
)
Communication
Channel
cos(
c
t
)
cos(
c
t
)
g
2
(
t
)
LPF
2
e
2
(
t
)
f
2
(
t
)
0
sin(
c
t
)
sin(
c
t
)
Figure P6.30
You will find the trigonometric identities in Appendix A useful for solving this problem.
We form the following signals, as shown in Figure P6.30:
f(t) = f
1
(t)cos v
c
t + f
2
(t) sin v
c
t
g
1
(t) = f(t) cos v
c
t
g
2
(t) = f(t) sinv
c
t
(a)
Determine the signal
(b)
Determine the signal
(c)
As shown in Figure P6.30,
g
1
(t).
g
2
(t).
g
1
(t)
and
g
2
(t)
are filtered by ideal low-pass filters, with
cutoff frequency of
2v
0
and unit amplitude, to form the output signals
e
1
(t)
and
e
2
(t).
Determine
e
1
(t)
and
e
2
(t).
6.31.
The triangular pulse waveform shown in Figure P6.31 modulates a sinusoidal carrier
signal
c(t) = cos(10
6
pt)
by DSB/SC-AM modulation techniques.
(a)
Sketch the resulting modulated signal,
(b)
Derive the frequency spectrum of the modulated signal.
(c)
Sketch the frequency spectrum, S(v).
s(t) = m(t)c(t).
