G.711 Audio Encoding

A law and U law is defined as follows: a law code is a compression/decompression algorithm for pulse coding defined by ITU-T (International Telecommunications Institute of Standards. Most countries in the world adopt the law compression algorithm (including China ). The United States uses the U law Algorithm for pulse encoding. The English definition is roughly as follows:

A-Law and U-law are companding schemes used in telephone network
Get more dynamics to the 8 bit samples that is available with linear
Coding. typically 12 .. 14 bit samples (linear scale) sampled at 8 kHz
Sample are companded to 8 bit (logarithmic scale) for transmission
Over 64 kbit/s data channel. In the processing ing end the data is then
Converter back to linear scale (12 .. 14 bit) and played back.
Converted back
U-law definition
U-Law (pronounced Mu-Law) is
SGN (m) (| M |) | M |
Y = ------- ln (1 + u | -- |) | -- | = <1
Ln (1 + u) (| MP |) | MP |
Another definition for Mu-law I have seen
Ln (1 + 255 | x |)
Output = SGN (x )---------------------
Ln (1 + 255)

X = normalized input (between-1 and 1)
255 = compression Parameter
SGN (x) = sign (+/-) of X

A-law definition
A-LAW is
| A (m) | M | 1
| ------- (--) | -- | = <-
| 1 + ln a (MP) | MP |
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 0-03-0933-x
? Transmission Systems for communications, century th edition,
Members of the technical staff at Bell Telephone Laboratories,
Bell Telephone Laboratories, inreceivated, copyright 1959,196 4,
1970,198 2

The following describes the core of g.711 C code.

# Ifndef _ g711_h _
# DEFINE _ g711_h _


# Ifdef _ cplusplus
Extern "C "...{
# Endif/* _ cplusplus */


Unsigned char linear2ulaw (short pcm_val );
Short ulaw2linear (unsigned char u_val );

Unsigned char linear2alaw (short pcm_val );
Short alaw2linear (unsigned char a_val );

Unsigned char alaw2ulaw (unsigned char a_val );
Unsigned char ulaw2alaw (unsigned char u_val );


# Ifdef _ cplusplus
}
# Endif/* _ cplusplus */


# Endif/* _ g711_h _*/

Generally, law A is used in many projects, so

Unsigned char linear2alaw (short pcm_val );
Short alaw2linear (unsigned char a_val );

Note that the data types used in audio processing are unsigned char and short, where the official code for the ITU-T is fine, in openh323, the Data Types of g.711 codecs all use int and unsigned, which results in data overflow and cannot work properly. I encountered this problem when I did it for the first time, replace the int with short and unsigned char.