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

276 SAMPLING AND ANALOG-TO-DIGITAL CONVERSION
Figure 6. 16
(a) µ-Law
characteristic.
(b) A-Law
characteristic.
t
y
0.8
t 0.6
y
0.2
0.4
0.6 0.8
0 0.2
0.4 0.6 0.8
(a)
(b)
Figure 6. 17
Utilization of
compressor and
expander for
nonuniform
q uantization.
Compressor
nonlinearity
Uniform
quantizer
PCM
channel
Expander
nonlinearity
Nonuniform quantizer
The output SNR for the cases of f.l = 255 and f.l = 0 (uniform quantization) as a function of
m 2 (t) (the message signal power) is shown in Fig. 6.18.
The Compandor
A logarithmic compressor can be realized by a semiconductor diode, because the V - 1
characteristic of such a diode is of the desired form in the first quadrant:
KT ( /)
V = - ln 1 + -
q ls
Two matched diodes in parallel with opposite polarity provide the approximate characteristic
in the first and third quadrants (ignoring the saturation current). In practice, adjustable resistors
are placed in series with each diode and a third variable resistor is added in parallel. By adjusting
various resistors, the resulting characteristic is made to fit a finite number of points (usually
seven) on the ideal characteristics.
An alternative approach is to use a piecewise linear approximation to the logarithmic characteristics.
A 15-segmented approximation (Fig. 6.19) to the eighth bit (L = 256) with 1.1 = 255
law is widely used in the D2 channel bank that is used in conjunction with the Tl carrier system.
The segmented approximation is only marginally inferior in terms of SNR. 8 The piecewise
linear approximation has almost universally replaced earlier logarithmic approximations to
the true f.l = 255 characteristic and is the method of choice in North American standards.