Communications Toolbox

Companding a Signal

In certain applications, such as speech processing, it is common to use a logarithm computation, called a compressor, before quantizing. The inverse operation of a compressor is called an expander. The combination of a compressor and expander is called a compander.

The compand function supports two kinds of companders: µ-law and A-law companders. Its reference page lists both compressor laws.

Example: A µ-Law Compander

The code below quantizes an exponential signal in two ways and compares the resulting mean square distortions. First, it uses the quantiz function with a partition consisting of length-one intervals. In the second trial, compand implements a µ-law compressor, quantiz quantizes the compressed data, and finally compand expands the quantized data. The output shows that the distortion is smaller for the second scheme. This is because equal-length intervals are well suited to the logarithm of sig, but not well suited to sig itself.

• Mu = 255; % Parameter for mu-law compander
  sig = -4:.1:4;
  sig = exp(sig); % Exponential signal to quantize
  V = max(sig);
  % 1. Quantize using equal-length intervals and no compander.
  [index,quants,distor] = quantiz(sig,0:floor(V),0:ceil(V));
  
  % 2. Use same partition and codebook, but compress
  % before quantizing and expand afterwards.
  compsig = compand(sig,Mu,V,'mu/compressor');
  [index,quants] = quantiz(compsig,0:floor(V),0:ceil(V));
  newsig = compand(quants,Mu,max(quants),'mu/expander');
  distor2 = sum((newsig-sig).^2)/length(sig);
  [distor, distor2] % Display both mean square distortions.
  
  ans =
  
      0.5348    0.0397
  

Optimizing DPCM Parameters

Arithmetic Coding