0195136047.pdf

15.3 DIGITAL COMMUNICATION SYSTEMS 715

L≤Lb= 2 Nb (15.3.11)

ifLlevels span the message variations. For example, in Figure 15.3.1(b),Nb=3 andL=8;
the binary code word 010 represents 0( 23 −^1 )+ 1 ( 21 )+ 0 ( 20 ) = 2 V, and 110 represents
1 ( 23 −^1 )+ 1 ( 21 )+ 0 ( 20 )=6 V. Thus, binary code words withNb =3 are shown in Figure
15.3.1(b).

EXAMPLE 15.3.2

A symmetrical fluctuating message, with|f(t)|max= 6 .3 V andKCR=3, is to be encoded by
using an encoder that employs an 8-bit natural binary code to encode 256 voltage levels from
− 7 .65Vto+ 7 .65 V in steps ofδv= 0 .06 V. FindL,f^2 (t), andS 0 /Nq.

Solution

From Equation (15.3.6),

L=

2 |f(t)|max

δv

=

2 × 6. 3

0. 06

= 210

From Equation (15.3.8),

f^2 (t)=

|f(t)|^2 max

KCR^2

=

6. 32

9

= 4 .41 V^2

From Equation (15.3.9),
(
S 0
Nq

)

=

3 L^2

KCR^2

=

3 × 2102

9

=14,700 or 41.67 dB

Digital Signal Formatting

After quantization and coding the samples of the message, a suitable waveform has to be chosen
to represent the bits. This waveform can then be transmitted directly over the channel (if no carrier
modulation is involved), or used for carrier modulation. The waveform selection process is known
as formatting the digital sequence. Three kinds of waveforms are available:

1. Unipolar waveform,which assigns a pulse to code 1 and no pulse to code 0. The duration
   of a pulse is usually chosen to be equal toTb, if binary digits occur eachTbseconds (the
   bit interval’s duration).


2. Polar waveform,which consists of a pulse of durationTbfor a binary 1 and a negative
   pulse of the same magnitude and duration for a 0. This yields better system performance
   in noise than the unipolar format, because of the wider distinction between the two values.


3. Manchester waveform,which transmits a pulse of durationTb/2 followed by an equal
   magnitude, but negative pulse of durationTb/2 for each binary 1, and the negative of this
   two-pulse sequence for a binary 0. Even when a long string of 0s or 1s may occur in the
   digital sequence, the advantage of this format is that it never contains a dc component.

Figure 15.3.5 illustrates these formats for a sequence of binary digits. Figure 15.3.1 (b) shows
the polar format corresponding to the coding in that case. Since it is important that a digital system