The laws used in compressor of a non-uniform Quantizer are known as compression laws.
two laws are available
- – law.
-law:- A particular form of compression law that is used in practice is the so called – law which is defined by
where – Normalized compressed output voltage.
– Normalized input voltage to the compressor.
and is a positive constant and its value decides the curvature of .
corresponds to no compression, which is the case of uniform quanization, the curve is almost linear as the value of increases signal compression increases.
is the north american standard for PCM voice telephony.
for a given value of , the reciprocal slope of the compression curve, which defines the quantum steps is given by the derivative of with respect to
we see that therefore law is neither strictly linear nor strictly logarithmic.
It is approximately linear at low levels of input corresponding to . and is approximately logarithmic at high input levels corresponding to .
typical value of
A-law :- another compression law that is used in practice is the so called A- law defined by
A=1 corresponds to the case of uniform Quantization. A-law has been plotted for three different values of A. A=1, A=2, A=87.56.
typical value of A is 87.56 in European Commercial PCM standard which is being followed in India.
for both the -law and A-law, the dynamic range capability of the compander improves with increasing and A respectively. The SNR for low-level signals increases at the expense of the SNR for high level signals.
to accommodate these two conflicting requirements (i.e, a reasonable SNR for both low and high-level signals), a compromise is usually made in choosing the value of parameter for the -law and parameter A for the A-law. The typical values used in practice are and .
It is also interested to note that in actual PCM systems, the companding circuitry does not produce an exact replica of the non-linear compression curves shown in the compression law characteristics.