Compression and Expansion

• To improve the perceived quality of quantized speech signals, a process called compression is used.
• For compression, the samples are passed through a nonlinear compression function before A/D conversion.
• The effect is that quantization is not uniform: resolution is finer for small amplitudes and coarser for large amplitudes.
• After D/A conversion the compression is undone by passing the output of the D/A converter through the inverse function.
• In the American phone system, the $\mu$-law compression function is used:
  
  $$y = \frac{\ln(1+\mu x)}{\ln(1+\mu)}.$$
  
  

  

Figure: $\mu$-law compression function.