Communications Blockset

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.

This blockset supports two kinds of companders: µ-law and A-law companders. The reference pages for the A-Law Compressor, A-Law Expander, Mu-Law Compressor, and Mu-Law Expander blocks list the relevant expander and compressor laws.

Example: Using a µ-Law Compander

This example quantizes an exponential signal in two ways and compares the resulting mean square distortions. To create the signal in the MATLAB workspace, execute these commands:

• sig = -4:.1:4;
  sig = exp(sig'); % Exponential signal to quantize
  

Now, the model in the following figure performs two computations. One computation uses the Sampled Quantizer Encode block with a partition consisting of length-one intervals. The second computation uses the Mu-Law Compressor block to implement a µ-law compressor, the Sampled Quantizer Encode block to quantize the compressed data and, finally, the Mu-Law Expander block to expand the quantized data.

To open the completed model, click here in the MATLAB Help browser. To build the model, gather and configure these blocks:

• Signal From Workspace, in the DSP Blockset DSP Sources library
• Set Signal to sig.
• Mu-Law Compressor
• Set Peak signal magnitude to max(sig).
• Mux, in the Simulink Signals & Systems library
• Sampled Quantizer Encode, in the Source Coding library
• Set Quantization partition to 0:floor(max(sig)).
• Set Quantization codebook to 0:ceil(max(sig)).
• Set Sample time to 1.
• Terminator, in the Simulink Signals & Systems library
• Demux, in the Simulink Signals & Systems library
• Mu-Law Expander
• Set Peak signal magnitude to ceil(max(sig)).
• Two copies of To Workspace, in the Simulink Sinks library
• Set Variable name to nocompander and withcompander, respectively, in the two copies of this block.
• Set Save format to Array in each of the two copies of this block.

Connect the blocks as shown above. Also, from the model window's Simulation menu, choose Simulation parameters; then in the Simulation Parameters dialog box, set Stop time to 80. Run the model, then execute these commands:

• distor = sum((nocompander-sig).^2)/length(sig);
  distor2 = sum((withcompander-sig).^2)/length(sig);
  [distor distor2]
  
  ans =
  
      0.5348    0.0397
  

This output shows that the distortion is smaller for the second scheme. This is because equal-length intervals are well suited to the logarithm of the data but not as well suited to the data itself.

Implementing Differential Pulse Code Modulation

Selected Bibliography for Source Coding