U-LAW and A-LAW definitions
---------------------------
[Adapted from information provided by [email][email protected][/email] (Rick
Duggan) and [email][email protected][/email] (David Perry)]
u-LAW (really mu-LAW) is
sgn(m) ( |m |) |m |
y= ------- ln( 1+ u|--|) |--| =< 1
ln(1+u) ( |mp|) |mp|
A-LAW is
| A (m ) |m | 1
| ------- (--) |--| =< -
| 1+ln A (mp) |mp| A
y=|
| sgn(m) ( |m |) 1 |m |
| ------ ( 1+ ln A|--|) - =< |--| =< 1
| 1+ln A ( |mp|) A |mp|
Values of u=100 and 255, A=87.6, mp is the Peak message value, m is
the current quantised message value. (The formulae get simpler if you
substitute x for m/mp and sgn(x) for sgn(m); then -1 <= x <= 1.)
Converting from u-LAW to A-LAW is in a sense "lossy" since there are
quantizing errors introduced in the conversion.
"..the u-LAW used in North America and Japan, and the
A-LAW used in Europe and the rest of the world and
international routes.."
References:
Modern Digital and Analog Communication Systems, B.P.Lathi., 2nd ed.
ISBN 0-03-027933-X
Transmission Systems for Communications
Fifth Edition
by Members of the Technical Staff at Bell Telephone Laboratories
Bell Telephone Laboratories, Incorporated
Copyright 1959, 1964, 1970, 1982
