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186
Baseband Pulse and Digital Signaling Chap. 3
w in (t)
Flat-top
pulses
Transmitting
filter
H T (f)
Channel (filter)
characteristics
H C (f)
w c (t) Receiver
filter
H R (f)
w out (t)
Recovered rounded
pulse (to sampling
and decoding
circuits)
Figure 3–24
Baseband pulse-transmission system.
Consider a digital signaling system as shown in Fig. 3–24, in which the flat-topped multilevel
signal at the input is
w in (t) = p an
a n h(t - nT s )
(3–58)
where h(t) = ß(tT
s ) and a n may take on any of the allowed L multilevels (L = 2 for binary
signaling). The symbol rate is D = 1T s pulsess. Then Eq. (3–58) may be written as
w in (t) = an
a n h(t) * d(t - nT s )
= c an
a n d(t - nT s )d * h(t)
(3–59)
The output of the linear system of Fig. 3–24 would be just the input impulse train convolved
with the equivalent impulse response of the overall system; that is,
w out (t) = c an
a n d(t - nT s )d * h e (t)
(3–60)
where the equivalent impulse response is
(3–61)
Note that h e (t) is also the pulse shape that will appear at the output of the receiver filter when
a single flat-top pulse is fed into the transmitting filter (Fig. 3–24).
The equivalent system transfer function is
where
h e (t) = h(t) * h T (t) * h C (t) * h R (t)
H e (f) = H(f)H T (f)H C (f)H R (f)
(3–62)
H(f) = cßa t bd = T (3–63)
T s a sin pT sf
s pT s f
b
Equation (3–63) is used so that flat-top pulses will be present at the input to the transmitting
filter. The receiving filter is given by
H e (f)
H R (f) =
(3–64)
H(f)H T (f)H C (f)
where H e (f) is the overall filtering characteristic.