0195136047.pdf

15.3 DIGITAL COMMUNICATION SYSTEMS 711

originalf(t) could be exactly reconstructed at all times, with no error by the receiver. However,
since the exact samples cannot be conveyed, they must be converted to discrete samples in a
process known asquantization.

Quantization

Let Figure 15.3.1(a) illustrate a messagef(t) with values between 0 and 7 V. A sequence of
exact samples taken at uniform intervals of time is shown: 1.60, 3.70, 4.75, 3.90, 3.45, and
5.85 V. Quantization consists of rounding exact sample values to the nearest of a set of discrete
amplitudes calledquantum levels. Assuming the quantizer to have eight quantum levels (0, 1,
2,... , 7 V), a sequence ofquantized samples(2, 4, 5, 4, 3, and 6 V) is shown in Figure 15.3.1(a).
Obviously, the scheme is not limited to messages with only nonnegative voltages. The quantizer
is said to beuniformwhen thestep sizebetween any two adjacent quantum levels is a constant,
denoted byδvvolts. Quantizers with nonuniform step size are also designed for improved system
performance. AnL-level quantizer can have even or oddL. A quantizer is said to be saturated or
overloaded when

|f(t)|>

(

L− 2

2

)

δv+δv=

L

2

δv (15.3.2)

Figure 15.3.2 shows the output quantum levels versus input voltage characteristic (stairstep in
shape) of anL-level quantizer, when the message signal has both positive and negative amplitudes
of the same maximum magnitude. Case (a) corresponds toLbeing an even integer, when the
midrisercan be observed; and case (b) corresponds toLbeing an odd integer, when themidtread
can be seen.

V

t

t

f(t)

Ts 3 Ts 5 Ts 6 Ts

Quantized samples

Binary code words (Nb = 3)

(a)

Polar format

(b)

−A

A

2 Ts 4 Ts

2454

00 00 11111100110 0 10

36

5.85

3.45

3.90

3.70

1 1.60

0

2

3

4

5

6

7

4.75

Figure 15.3.1(a)Analog messagef(t) with

exact and quantized samples.(b)Coding and

waveform formatting of quantized samples.