Waveform Encoding - Digital Communication: Principles and System Modelling - page 23

Fig. 2.8 Illustration of
uniform quantization and
encoding

Δ 3

( )

q 3 11

Δ 2

( )

q 2 10

( )

Δ 1 q 1 01

( )

q 0 00

Δ 0

to A min is equally divided into 4 regions of width S. The 4 regions are named as
0 to -regions is our defined probable amplitude

level. The levels are called as q-levels or quantization levels. The algorithm of quan-
tization states, 'If the sampled signal amplitude lies within

3 . The middle of each of the

i region, the amplitude
will be quantized (approximated) to the amplitude q i '. Figure 2.8 clearly depicts the
process.
The shaded signal in the above figure is the staircase representation of the quan-
tized signal. Next, each q-level can easily be encoded to through 2 bit encoder or
MUX to get proper digital representation of the input analog signal. After quanti-
zation, the signal x q (

is represented as q 2 , q 3 , q 2 , q 2 , q 3 , q 0 , q 0 , q 0 , q 0 , q 1 .And
after encoding, each level is inferred by a pair of digits in parallel. Next, by employ-
ing a parallel to serial converter, the serial bit stream is obtained which is the
corresponding digital representation of the input analog signal.
There are two types of uniform quantizer namely,

kT S )

(a) Midtread quantizer
(b) Midrise quantizer

Figure 2.9 shows the input-output characteristics of the two types of the uniform
quantizer. In midtread type quantizer, the origin lies in the middle of the tread of
the staircase like graph. In midrise type, the origin the graph lies in the middle of
a rising part of the staircase like graph. It can be noticed that, both midtread and
midrise graphs are symmetric about the origin.

2.2.3 PCM Transmitter and Receiver

2.2.3.1 PCM Transmitter

The entire principle of analog to digital conversion is now unveiled to us. Therefore,
we can just club up all the procedural blocks to construct the PCM transmitter as
shown in Fig. 2.10 . We have already discussed the functioning of the blocks. First
the input analog signal x ( t ) is being passed through a low pass filter of bandwidth