Unformatted text preview: .9: Top: A message signal pro duced using a random data sequence and raisedcosine pulses with β = 0.5. Bottom: Normalized average energy spectrum of m(t) computed
numerically using the following pro cedure: a message signal of length 32768T was generated
using a random sequence of bits. The long message signal was divided into short segments of
length approximately 100T . The energy spectrum of each short segment was computed, and
all spectra were averaged. The average spectrum was normalized so that the area under the
spectrum is 1.0. Note that the shape of the energy spectrum exhibits the raisedcosine shape
of the pulses. Since β = 0.5, the bandwidth of the spectrum is W T = 1 (1 + 0.5) = 0.75.
2 Digital Television (DTV) message signal:
m(t) =
an p(t − nT )
n an ∈ (−3.5, −2.5, −1.5, −0.5, 0.5, 1.5, 2.5, 3.5) 8 possible pulse amplitudes: log2 (8) = 3 bits/pulse Signaling rate T −1 = 10.762238 Mpulses/sec,
or 3 bits/pulse ×10.762238 32.387 Mbits/sec.
About 40 percent of the bits are used to provide forward error
correction, so that actual data rate is approximately 0.60×32.387 =
19.4 Mbits/sec.
Pulses, p(t), are squareroot raisedcosine with β = 0.0575 (5.75%
excess bandwidth).
Pulse bandwidth (and message signal bandwidth) is
W = 21 (1 + β ) = 5.69 MHz.
T 1.5. LINEAR MODULATION 15 2.0
1.0
m(t) 0.0
−1.0
−2.0
0
3.0
2.0
1.0
s(t) 0.0
−1.0
−2.0
−3.0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
t/ T 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
t/ T DSB 0 1 Figure 1.9: Top: message signal representing 20 information bits generated using
raisedcosine pulses with β = 0.1. Bottom: DSB signal, s(t), normalized such that
< s2 (t) >= 1.
The DSB/SC signal, s(t), shown in the lower panel has been normalized to have
a meansquare value of 1.0. Thus, if this signal represents the voltage developed lope ( maxm(t)(t)) + 1) > 0 for all t. The signal s (t) was then normalized to have
( m
a meansquare of 1.0. The normalized signal, s(t), is shown in the bottom plot of
Figure 1.17.
2.0
1.0
m(t) 0.0
−1.0
−2.0
0
3.0
2.0
1.0
s(t) 0.0
−1.0
−2.0
−3.0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
t/ T 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
t/ T DSB, full carrier 0 1 2 3 4 5 Figure 1.17: Top: message signal representing 20 information bits generated using
raisedcosine pulses with β = 0.1. Bottom: DSB with fullcarrier signal, s(t), normalized such that < s2 (t) >= 1. Compare the bottom plot with the corresponding
plot in Figure 1.9.
Figure 1.18 illustrates how the envelope detector demo dulates a fullcarrier DSB
signal. The upper plot shows the result of passing s(t) from Figure 1.17 through a fullwave rectiﬁed s(t)
2.0
1.0
0.0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
t/ T 8 9 10 11 12 13 14 15 16 17 18 19 20
t/ T after lowpass ﬁlter
2.0
1.0
0.0 0 1 2 3 4 5 6 7 Figure 1.18: Upper plot shows s(t), which is the result of passing s(t) through
a fullwave rectiﬁer. The lower plot was obtained by passing the signal shown
in the upper plot through a lowpass ﬁlter with cutoﬀ frequency larger than the
bandwidth of m(t) (W) and smaller than fc − W . The transient at the beginning of
the lower plot is the startup transient of the digital lowpass ﬁlter used to pro duce
the simulated signal. 2.0
1.0
m(t) 0.0
−1.0
−2.0
2.0
1.0
m(t) 0.0
ˆ
−1.0
−2.0
2.0
1.0
s(t) 0.0
−1.0
−2.0
2.0
1.0
s(t) 0.0
−1.0
−2.0
2.0
1.0
s(t) 0.0
−1.0
−2.0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
t/T 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
t/T 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
t/T 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
t/T 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
t/T DSBsc 0 1
USB 0 1
LSB 0 1 2.0
1.0
m(t) 0.0
−1.0
−2.0
3.0
2.0
1.0
s(t) 0.0
−1.0
−2.0
−3.0
3.0
2.0
1.0
s(t) 0.0
−1.0
−2.0
−3.0
3.0
2.0
1.0
s(t) 0.0
−1.0
−2.0
−3.0
3.0
2.0
1.0
s(t) 0.0
−1.0
−2.0
−3.0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
t/T DSBfull carrier 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
t/T 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
t/T 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
t/T 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
t/T DSBsc 0 1
USB 0 1
LSB 0 1 2.0
1.0
m(t) 0.0
−1.0
−2.0
3.0
2.0
1.0
s (t) 0.0
−1.0
−2.0
−3.0
3.0
2.0
1.0
s (t) 0.0
−1.0
−2.0
−3.0
3.0
2.0
1.0
s (t) 0.0
−1.0
−2.0
−3.0
3.0
2.0
1.0
s (t) 0.0
−1.0
−2.0
−3.0 0 1 2 3 4 5 6 7 8 DSBfull carrier: s(t) cos(ωc t) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
t/T 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
t/T 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
t/T 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
t/T DSBsc: s(t) cos(ωc t) 0 1 2 3 4 5 USB: s(t) cos(ωc t) 0 1 2 3 4 5 LSB: s(t) cos(ωc t) 0 1 2 3 4 5 9 10 11 12 13 14 15 16 17 18 19 20
t/T 2.0
1.0
m(t) 0.0
−1.0
−2.0
2.0
1.0
s (t) 0.0
−1.0
−2.0
2.0
1.0
s (t) 0.0
−1.0
−2.0
2.0
1.0
s (t) 0.0
−1.0
−2.0
2.0
1.0
s (t) 0.0
−1.0
−2.0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
t/T
DSBfull carrier: LPF[s(t) cos(ωc t)] 1 2 3 4 5 6 7 8 DSBsc: LPF[s(t...
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 Spring '08
 Staff
 Digital Signal Processing, Signal Processing, Bandwidth, message signal, Superheterodyne receiver

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