Waveform Quantization and Compression - Digital Signal Processing: Fundamentals and Applications - page 503

µ -law expander

1

0.8

0.6

0.4

0.2

0

-0.2

-0.4

-0.6

-0.8

-1

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

yq

FIGURE 11.5

Characteristics for the m-law expander.

1 þ 255 j3:6j
j5j max

ln

y ¼ signð3:6Þ ¼0:94

lnð1 þ 255Þ

As shown in Figure 11.4 , the range of y is 2, thus the quantization step size is calculated as

2
2 3 1 ¼ 0:286 and

y ¼ 0:94

D ¼

0:286 ¼3:28 D

From quantization characteristics, it follows that the binary code is 011 and the recovered signal is

y q ¼3 D ¼0:858.
Applying the m-law expander leads to
x q ¼ j5j max signð0:858Þ ð1 þ 255Þ j0:858j 1
255

¼2:264

Thus the quantization error is computed as
e q ¼ x q x ¼2:264 3:6 ¼ 1:336 volts

b. Similarly, for x ¼ 0:5, we get

1 þ 255 j0:5j
j5j max

ln

y ¼ signð0:5Þ ¼ 0:591

lnð1 þ 255Þ