Digital Companding
- compression happens at the transmit end after the input sample has
been converted to a linear PCM code
- recent digitally compressed PCM systems use a 12-bit linear code
and an 8-bit compressed code
- this companding process closely resembles µ = 255 analog
compression curve with set a of 8 straight-line segments
i. slope of each segment is half of the previous segment
- the 8-bit compressed code consists of a
i. sign bit
ii. 3-bit segment identifier
iii. 4-bit magnitude code
Compression process
1. Analog signal – sampled, converted to linear 12-bit sign magnitude code
2. The sign bit in 12-bit code is transferred directly to MSB of 8-bit code
3. Segment is determined by the number of leading 0s in the 11 bit
magnitude portion – subtract the number of 0s from 7 ( # of 0s <= 7)
4. This segment is converted to 3-bit binary number (segment identifier)
5. 4-bit magnitude bits which is the quantization interval is substituted to the
least significant 4 bits of the 8-bit code
1
Sign bit
1 = (+)
4-bit
3-bit segment
quantization
identifier
interval
000-111
0 = (-)
abcd
0000-1111
ENCODED PCM
Segment
12-bit Linear code
8-bit compressed
code
0
1
2
3
4
5
6
7
S0000000abcd
S0000001abcd
S000001abcdx
S00001abcdxx
S0001abcdxxx
S001abcdxxxx
S01abcdxxxxx
S1abcdxxxxxx
s000abcd
s001abcd
s010abcd
s011abcd
s100abcd
s101abcd
s110abcd
s111abcd
Compression- ratio of possible transmit codes & possible recovered
codes
In each segment, only 16 12-bit codes can be recovered.
Segments 2 –7 are subdivided into smaller subsegments
16 subsegment each
2
Segment 0 = 16 codes
Segment 1 = 16 codes
Segment 2 = 32 codes
Segment 3 = 64 codes
Segment 4 = 128 codes
Segment 5 = 256 codes
Segment 6 = 512 codes
Segment 7 = 1024 codes
Compression
1:1
1:1
2:1
4:1
8:1
16:1
32:1
64:1
No. codes per subsegment
1
1
2
4
8
16
32
64
DECODED PCM
8-bit compressed
12-bit Linear code
code
s000abcd
s001abcd
s010abcd
s011abcd
s100abcd
s101abcd
s110abcd
s111abcd
S0000000abcd
S0000001abcd
S000001abcd1
S00001abcd10
S0001abcd100
S001abcd1000
S01abcd10000
S1abcd100000
Segment
0
1
2
3
4
5
6
7
Note: Most significant of the truncated bits is reinserted at the decoder as 1.
The remaining truncated bits are reinserted as 0s.
This is to minimize the magnitude of error introduced by the compression
and expansion process.
3
Percentage Error introduced by digital compression:
% error =
| Tx _ voltage  Rx _ voltage |
x 100
Rx _ voltage
EXAMPLES
Determine the 12-bit linear code, the 8-bit compressed code, and the recovered
12-bit code for a resolution of 0.01V and analog sample voltages of
a. 0.05V
b. 0.32V
c. 10.23V
(Answers for these problems are located at the back of the book, but you have
to compute and find out how to come up with those values)
For the following 12-bit linear PCM codes, determine the 8-bit compressed
code to which they be converted
12-bit linear code
1000 1111 0010
0000 0100 0000
0001 1111 1000
1111 1111 0010
0000 0010 0000
A 12-bit linear sign-magnitude PCM code is digitally compressed into 8 bits.
For a resolution of 0.016V determine the following quantities for the
indicated input voltages: 12-bit linear PCM code, 8-bit compressed code,
decoded 12-bit code, decoded voltage, and percentage error. Vin = -6.592
V, +12.992 V, and –3.36 V.
4