B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

352 PRINCIPLES OF DIGITAL DATA TRANSMISSION
Fi g
ure 7. 16
(a) The minimum
bandwidth pulse
that satisfies the
duobinary pulse
criterion and
(b) its spectrum.
p(i)
1-
(a)
\P(f) \
7.3.5 Pulse Relationship between Zero-ISi,
Duobinary, and Modified Duobinary
(b )
Now we can establish the simple relationship between a pulse P a (t) satisfying the first Nyquist
criterion (zero ISi) and a duobinary pulse P b (t) (with controlled ISI). From Eqs. (7.23) and
(7.37), it is clear that P a (kT b ) and P b (kT b ) only differ for k = 1. They have identical sample
values for all other integer k. Therefore, one can easily construct a pulse P b (t) from p a (t) by
This addition is the "controlled" ISi or partial-response signaling that we deliberately introduced
to reduce the bandwidth requirement. To see what effect "duobinary" signaling has on
the spectral bandwidth, consider the relationship of the two pulses in the frequency domain:
P b (f) = P a lf)[l + e - jZ11'fTb]
IP b (f) \ = IP a lf) I J2(1 + cos (2nfT b )2 lcos (.7TfT b ) I
(7.40a)
(7.40b)
We can see that partial-response signaling is actually forcing a frequency null at 2nfT b = .7T or,
equivalently f = 0.5/T b . Therefore, conceptually we can see how partial-response signaling
provides an additional opportunity to reshape the PSD or the transmission bandwidth. Indeed,
duobinary signaling, by forcing a frequency null at 0.5/T b , forces its essential bandwidth to
be at the minimum transmission bandwidth needed for a data rate of 1/T b (as discussed in
Sec. 6.1.3).