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

7.2 Line Coding 337
Figure 7.7
Split-phase
(Manchester or
twinned-binary)
signal. (a) Basic
pulse p(t) for
Manchester
signaling.
(b) Transmitted
waveform for
binary data
sequence using
Manchester
signaling.
(a)
0 0 1 1 0 1 1 0 0 0 1 1 0
7 nmn mn nnmn r
WU UW UWULJ UW t--+-
I Tb I
(b)
we have
P(0) = i: p(t) dt
Hence, if the area under p(t) is made zero, P(0) is zero, and we have a de null in the PSD. For
a rectangular pulse, one possible shape of p (t) to accomplish this is shown in Fig. 7. 7 a. When
we use this pulse with polar line coding, the resulting signal is known as Manchester code, or
split-phase (also called twinned-binary), signal. The reader can use Eq. (7.13), to show that
for this pulse, the PSD of the Manchester line code has a de null (see Prob. 7.2-2).
7.2.4 On-Off Signaling
In on-off signaling, a 1 is transmitted by a pulse p(t) and a O is transmitted by no pulse. Hence,
a pulse strength ak is equally likely to be 1 or 0. Out of N pulses in the interval of T seconds,
ak is 1 for N /2 pulses and is O for the remaining N /2 pulses on the average. Hence,
1 N
Ro = lim - [
2 N 2
- (1) + (0) ] = -
1
N➔oo N 2 2 2
(7.16)
To compute R n we need to consider the product akak+n · Since ak and ak+n are equally likely
to be 1 or 0, the product akak+n is equally likely to be 1 x 1, 1 x 0, 0 x 1 or O x 0, that is,
1, 0, 0, 0. Therefore on the average, the product akak+n is equal to 1 for N /4 terms and O for
3N / 4 terms and
1 N 3N 1
[ ]
N➔oo N 4 4 4
R n
= lim -(1) + -(0) = -
n 2:: 1 (7.17)
Therefore, [Eq. (7.9)]
(7.1 8a)
(7 .18b)