1. PCM stands for Pulse Code Modulation
PCM Quantizer
PCM stands for Pulse Code Modulation

2. Properties A-law: European standard
𝜇-law: (u-law) North American and Japanese Standard
ITU Standardization 1972
Bit rate: 64 kBit/sec
Compression ratio: 2 = (128 kBit/sec)/(64 kBit/sec)
Non-uniform quantizer
Finer quantization around “0” to represent consonants more accurately

3. Companding: A nonlinear function is applied to the input
U(x) = sgn(x) ln(1 + μ |x|) / ln (1 + μ)
where the input x: -1≤ x ≤ 1
and μ =255
The nonlinear function is discreatized to 8 “chords” .

4. Digital Implementation
Linear to u-law compressed data:
Before chord determination, the sign of the original integer is removed and a bias of 33 is added to the
absolute value of the integer. Due to the bias, the magnitude of the largest valid sample is reduced to 8159 and
the minimum step size is reduced to 2/8159. The added bias enables the endpoints of each chord to become
powers of two, which in turn simplifies the determination of the chord and step.

5. Decoding U-1(y) = sgn(y) (1 / μ) [(1+ μ)|y| - 1] where -1 ≤ y ≤ 1
Decoding Example:
(1 1 1 a b c d)2 becomes (1 a b c d )2
(1 1 0 a b c d)2 becomes (0 1 a b c d )2

6. A-law companding
A-law is the CCITT recommended companding standard used across Europe.
F(x) =sgn(x)A|x|/(1+lnA) for 0 ≤|x|<1/A
= sgn(x) (1+ln A|x|) /(1 + lnA) for 1/A ≤ |x| ≤ 1
where A=87.6 in Europe), and x is the normalized input.
Linear for 0 ≤|x|<1/A

7. A-law companding curve

8. MATLAB
Matlab has built-in mu-law and A-law functions!