**Digital Companding**

Digital Companding involves
compression in the transmitter after the input sample has been converted to a
linear PCM code and then expansion in the receiver prior to PCM decoding.
Digitally compressed PCM codes use a 12 –bit linear PCM code and convert into
8-bit Compressed PCM Code.

Digitally Companded PCM System

**Algorithm for 12-bit to 8-bit Digital Compression**

The 8-bit compressed code consist of sign bit, three bit
segment identifier and 4-bit magnitude code that specifies the Quantization
interval.

8-bit μ-255 compressed code format

As shown in table below, bit
positions designated with X are truncated during compression and subsequently
lost. Bits Designated as A,B,C,D are transmitted as it is and its value ranges
from (0000-1111). The sign bit is also transmitted as it is.

**Algorithm for Encoder**

1. The analog signal is sampled
and converted to linear 12-bit Sign Magnitude code.

2. Sign bit is transmitted
directly as it is to 8 bit compressed code.

12-bit to 8-bit Digital Companding
μ-255 Encoding and Decoding Table

3. Segment
number in the 8-bit code is determined by number of 0’s in the 12-bit code.

4. Subtract
number of 0’s in 12-bit code from 7 that is the segment number of 8-bit code
and converted it into three bit binary number. eg. As shown in table if there
are four 0’s in the 12-bit code(s0000ABCDXX)
then (7-4)=3 that is the segment number of 8-bit code and binary
equivalent of 3 is 011 so 8 bit code is s011ABCD.

5. Bits
Designated as A,B,C,D are transmitted as it is and its value ranges from
(0000-1111). These bits represent Quantization interval.

**Algorithm for Decoder**

Here we have to
expand code from 8-bit to 12-bit.

1. The most
significant bit of the truncated bit is reinserted as logic 1.

2. Remaining
truncated bits are reinserted as logic 0.

3. Suppose we
have code (s100ABCD), transmit sign bit and (A,B,C,D) bits as it is, now
segment bit is 100 whose decimal equivalent is 4. Now subtract (7-4) that is 3,
so insert three 0’s after sign bit and in truncated bits insert 1 for most
significant truncated bit and 0 for the rest truncated bits.

Every function
performed by PCM encoder and Decoder is accomplished with single integrated
chip known as codec. It includes antialiasing filter, sample and Hold circuit
and A-D converter in transmitter section and D-A converter, a Hold circuit and
bandpass filter in the receiver section.

**Analog Companding**

Analog Compression is implemented
using specially designed diodes inserted in the analog path in a PCM
transmitter prior to Sample and Hold Circuit. Analog expansion is also
implemented using diodes that are placed just after low pass filter in PCM
receiver.

Figure shows the
basic process of analog companding. In the transmitter, the dynamic range of
analog signal is compressed, sampled and then converted to linear PCM code. In
the receiver, PCM code is converted to PAM signal, filtered and then expanded
back to original dynamic range.

**μ-Law Companding**

In USA and
Japan, μ law companding is used. The compression characteristics for μ-law is

V

_{max}= Maximum uncompressed analog input amplitude
V

_{in}= Amplitude of input signal at particular instant of time
μ = Parameter
used to define the amount of compression

V

_{out}= Compressed output amplitude (volts)
The diagram
shows μ- law compression characteristics. It shows compression curves for
several values of μ. Higher the μ, more the compression. For μ = 0, the curve
is linear (no compression). In recent PCM system, it uses 8-bit PCM code and
μ=255.

μ-Law
Compression Characteristics

**A-Law Companding**

In Europe, the
ITU-T has established, A-law companding to be used to approximate true
logarithmic companding. For an intended dynamic range, A-Law companding has
slightly flatter SQR than μ-Law. A-Law companding is inferior to μ-Law in terms
of small signal quality (ideal channel noise). The compression Characteristics
A-Law companding is

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