1. COMPANDING - is the process of compressing and then expanding
with companded system, the higher amplitude analog signals are compressed - (amplified less than the lower- amplitude signals) prior to transmission and then expanded ( amplified more than the lower amplitude signals in the receiver).

2. TYPES OF COMPANDING 1. Analog Companding a.  - Law b. A - Law
2. Digital Companding

3. PCM SYSTEM WITH ANALOG COMPANDING

4. Vmax ln(1 + µ{Vin /Vmax})
µ-LAW COMPANDING
Vmax ln(1 + µ{Vin /Vmax})
Vout =
ln(1 + µ)
Where:
Vmax = maximum uncompressed analog input amplitude (volts)
Vin = amplitude of the input signal at particular instant of time (volts)
µ = parameter used to define the amount of compression(unitless)
Vout = compressed output amplitude (volts)

5. µ-LAW CHARACTERISTIC

6. A-LAW COMPANDING
In Europe, the ITU-T has established A-law companding to be used to approximate true logarithmic companding
AVin /Vmax
Vin 1
Vout =
0 ≤ ≤
Vmax
Vmax A
1 + lnA
1 + ln(AVin /Vmax) 1
Vin
Vout = ≤ ≤ 1
Vmax A
Vmax
1 + lnA

7. DIGITALLY COMPOUNDED PCM SYSTEM

8. µ-255 COMPRESSION CHARACTERISTIC
- µ-law companding is a system that divides the analog signal range into fifteen segments each eventually encoded into eight-bit digital value.

9. 13 SEGMENT SCALE

10. µ-255 COMPRESSION CHARACTERISTIC

11. 8-BIT COMPRESSED CODE FORMAT

12. µ-255 ENCODING TABLE

13. µ-255 DECODING TABLE

15. PROCESS OF DIGITAL COMPRESSION
Digitally, the 12-bit values are encoded into 8-bit compressed code as follows:
1. Retain the sign bit as the first bit of the 8-bit code.
2. Count the number of zeros until the occurrence of the first 1 bit. Subtract the zero count from 7. This is the segment number.
3. The first occurrence of 1 is assumed during the expanding process, so it is set aside during compression.
4. Copy the next four bits (ABCD) into the 8-bit compressed code.

16. EXAMPLE
Code the 12-bit code into an 8-bit compressed µ-law code.

17. EXAMPLE
Determine the 12-bit linear code, the eight-bit compressed code, the decoded 12-bit code, the quantization error, and the compression error for a resolution of 0.01 V and analog sample voltages of
(a) V
(b) V
(c) V

18. PROCESS OF DIGITAL EXPANSION
Expanding back digitally, reverses the process:
1. Retain the sign bit.
2. Take the segment number, subtract from 7 and add that many 0s.
3. Make the next bit a 1.
4. The next bits are ABCD values.
5. Add a 1 and sufficient 0s to complete the 12-bit value.

19. WORK Examples
For the following 12-bit linear PCM codes, determine the eight-bit compressed code to which they would be converted: a b c d e

20. WORK
For the following 8-bit compressed codes,determine the expanded 12-bit code. a b c d e f

21. WORK
A 12-bit linear sign-magnitude PCM code is digitally compressed into 8 bits. For a resolution of V, determine the following quantities for the indicated input voltages:
a. 12-bit linear PCM code
b. eight-bit compressed code
c. decoded 12-bit code
d. decoded voltage
For Vin = V, V, V

22. PCM problems
Determine the signal-to-quantization noise ratio in dB, if an audio signal with a bandwidth of 3.2 kHz is converted to PCM signal by sampling at 8 kilosamples/sec and with a data rate of 64 kbps.

23. Line Encoding