Waveform Quantization and Compression - Digital Signal Processing: Fundamentals and Applications - page 508

EXAMPLE 11.4
In a digital companding system , decode each of the following 8-bit compressed PCM codes into a 12-bit linear
PCM code.
a. 10000101
b. 01001101
Solution:
a. Using Table 11.4 , we notice that S ¼ 1, A ¼ 0, B ¼ 1, C ¼ 0, and D ¼ 1, and the code is in segment 0. Decoding
leads to 1 0 0 0 0 0 0 0 0 1 0 1, which is identical to the 12-bit PCM code in (a) in Example 11.3. We expect
this result, since there is no compression for segment 0 and segment 1.
b. Applying Table 11.4 , it follows that S ¼ 0, A ¼ 1, B ¼ 1, C ¼ 0, and D ¼ 1, and the code resides in segment 4.
Decoding achieves 0 0 0 0 1 1 1 0 1 1 0 0. As expected, this code is the approximation of the code in (b) in
Example 11.3. Since segment 4 has compression, the last 3 bits in the original 12-bit linear code, that is,
XXX ¼ 010 ¼ 2 in decimal, are discarded during transmission or storage. When we recover these three bits,
the best guess should be the middle value: XXX ¼ 100 ¼ 4 in decimal for the 3-bit coding range from 0 to 7.

Now we apply the m 255 compander to compress 12-bit speech data as shown in Figure 11.10 ( a).
The 8-bit compressed code is plotted in Figure 11.10 ( b). Plots (c) and (d) in the figure show the 12-bit

(a)

1000

0

-1000

0 200 400 600 800 1000 1200 1400 1600 1800 2000

(b)

100

0

-100

0 200 400 600 800 1000 1200 1400 1600 1800 2000

(c)

1000

0

-1000

0 200 400 600 800 1000 1200 1400 1600 1800 2000

(d)

40

20

0

-20

-40

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Sample number

FIGURE 11.10
The m 255 compressor and expander: (a) 12-bit speech data; (b) 8-bit compressed data; (c) 12-bit decoded
speech; (d) quantization error.