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Sec. 3–6 Intersymbol Interference 189
sampling points and yet have an envelope that decays much faster than 1x so that
clock jitter in the sampling times does not cause appreciable ISI. One solution for the
equivalent transfer function, which has many desirable features, is the raised cosine-rolloff
Nyquist filter.
Raised Cosine-Rolloff Nyquist Filtering
DEFINITION.
The raised cosine-rolloff Nyquist filter has the transfer function
1,
|f| 6 f 1
1
H e (f) = d
2
e 1 + cos c p(|f| - f 1)
df, f 1 6 |f| 6 B
2f ¢
0, |f| 7 B
(3–69)
where B is the absolute bandwidth and the parameters
f ¢ = B - f 0
and
f 1 ! f 0 - f ¢
f 0 is the 6-dB bandwidth of the filter. The rolloff factor is defined to be
(3–70)
(3–71)
r = f ¢
(3–72)
f 0
This filter characteristic is illustrated in Fig. 3–25. The corresponding impulse
response is
h e (t) = -1 [H e (f)] = 2f 0 a sin 2pf 0t cos 2pf ¢ t
bc
(3–73)
2pf 0 t 1 - (4f ¢ t) 2 d
Plots of the frequency response and the impulse response are shown in Fig. 3–26 for rolloff
factors r = 0, r = 0.5, and r = 1.0. The r = 0 characteristic is the minimum-bandwidth case,
|H e (f)|
f f
1.0
0.5
– B – f 0 – f 1 f 1 f 0 B
Figure 3–25
Raised cosine-rolloff Nyquist filter characteristics. (See Example3_14.m.)
f