563489578934

(
192
Baseband Pulse and Digital Signaling Chap. 3
where Y(f) is a real function that is even symmetric about f = 0; that is,
Y(-f) = Y(f), |f| 6 2f 0
and Y is odd symmetric about f = f 0 ; that is,
Y(-f + f 0 ) =-Y(f + f 0 ), |f| 6 f 0
(3–76a)
(3–76b)
Then there will be no intersymbol interference at the system output if the symbol rate is
D = f s = 2f 0
(3–77)
This theorem is illustrated in Fig. 3–27. Y(f) can be any real function that satisfies the
symmetry conditions of Eq. (3–76). Thus, an infinite number of filter characteristics can be
used to produce zero ISI.
Y(f)
0.5
– 2f 0 – f 0 f 0 2f 0
–0.5
f
(
f
––
2f 0
1.0
– f 0 f 0
f
1.0
f
H e (f)= –– +Y(f), |f|