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interweaving them. Figure 5.10 shows t he T DM of two PAM signals. In this manner,
we c an multiplex several signals o n t he same channel by reducing pulse widths.
Another method of t ransmitting several baseband signals simultaneously is
frequency-division multiplexing (FDM), discussed in Sec. 4.8-4. In FDM various
signals are multiplexed by sharing t he c hannel bandwidth. T he s pectrum of each
message is s hifted t o a specific b and n ot occupied by a ny other signal. T he information o f various signals is l ocated in nonoverlapping frequency bands of t he channel
(Fig. 4.45). In a way, T DM a nd F DM a re t he duals of each other. 332 5 Sampling 5.1 T he S ampling Theorem 333 Pulse Code Modulation (PCM)
P CM is t he m ost useful a nd widely used of all t he pulse modulations mentioned.
Basically, P CM is a m ethod of converting a n analog signal into a digital signal ( AID
conversion). A n a nalog signal is c haracterized by t he fact t hat its amplitude can
take on any value over a continuous range. Hence, analog signal can take on an
infinite number of values. In contrast, a d igital signal amplitude can take on only
a finite n umber of values. An analog signal can be converted into a digital signal
by means of sampling a nd q uantizing (rounding off). Sampling an analog signal
alone will n ot y ield a digital signal because a sampled analog signal can still take on
any value in a continuous range. I t is digitized by rounding off its value t o one of
t he closest permissible numbers (or q uantized l evels), as i llustrated in Fig. 5.l1a.
T he a mplitudes of t he analog signal f (t) lie in t he range ( -V, V ). T his range is
p artitioned i nto L subintervals, each of magnitude ~v = 2 V / L . Next, each sample
amplitude is a pproximated by t he m idpoint value of t he s ubinterval in which the
sample falls (see Fig. 5 .l1a for L = 16). I t is clear t hat each sample is approximated
t o one of t he L n umbers. Thus, t he signal is digitized with quantized samples taking
on a nyone of t he L values. Such a signal is known as a n L -ary d igital s ignal.
From a practical viewpoint, a binary digital signal ( a signal t hat c an t ake on
only two values) is very desirable because of its simplicity, economy, a nd ease of
engineering. W e can convert a n L -ary signal into a binary signal by using pulse
coding. Figure 5 .l1b shows such a code for t he case of L = 16. T his code, formed
by binary representation of t he 16 decimal digits from 0 t o 15, is known as the
n atural b inary c ode ( NBC). O ther possible ways of assigning a binary code
exist. Each of t he 16 levels t o b e t ransmitted is assigned one binary code of four
digits. Thus, e ach sample in this example is encoded by four binary digits. To
t ransmit t his b inary d ata, we need to assign a distinct pulse shape t o each of t he
two binary s tates. O ne possible way is t o assign a negative pulse t o a b inary 0 and
a positive pulse t o a b inary 1 so t hat each sample is now t ransmitted by a group of
four binary pulses (pulse code), as depicted...
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