Communications Toolbox

Implementing Differential Pulse Code Modulation

The quantization in the section Quantizing a Signal requires no a priori knowledge about the transmitted signal. In practice, you can often make educated guesses about the present signal based on past signal transmissions. Using such educated guesses to help quantize a signal is known as predictive quantization. The most common predictive quantization method is differential pulse code modulation (DPCM).

The functions dpcmenco, dpcmdeco, and dpcmopt can help you implement a DPCM predictive quantizer with a linear predictor.

DPCM Terminology

To determine an encoder for such a quantizer, you must supply not only a partition and codebook as described in Representing Quantization Parameters, but also a predictor. The predictor is a function that the DPCM encoder uses to produce the educated guess at each step. A linear predictor has the form

y(k) = p(1)x(k-1) + p(2)x(k-2) + ... + p(m-1)x(k-m+1) + p(m)x(k-m)

where x is the original signal, y(k) attempts to predict the value of x(k), and p is an m-tuple of real numbers. Instead of quantizing x itself, the DPCM encoder quantizes the predictive error, x-y. The integer m above is called the predictive order. The special case when m = 1 is called delta modulation.

Representing Predictors

If the guess for the kth value of the signal x, based on earlier values of x, is

• y(k) = p(1)x(k-1) + p(2)x(k-2) +...+ p(m-1)x(k-m+1) + p(m)x(k-m)
  

then the corresponding predictor vector for toolbox functions is

• predictor = [0, p(1), p(2), p(3),..., p(m-1), p(m)]
  

Note    The initial zero in the predictor vector makes sense if you view the vector as the polynomial transfer function of a finite impulse response (FIR) filter.

Example: DPCM Encoding and Decoding

A simple special case of DPCM quantizes the difference between the signal's current value and its value at the previous step. Thus the predictor is just y(k) = x (k - 1). The code below implements this scheme. It encodes a sawtooth signal, decodes it, and plots both the original and decoded signals. The solid line is the original signal, while the dashed line is the recovered signals. The example also computes the mean square error between the original and decoded signals.

• predictor = [0 1]; % y(k)=x(k-1)
  partition = [-1:.1:.9];
  codebook = [-1:.1:1];
  t = [0:pi/50:2*pi];
  x = sawtooth(3*t); % Original signal
  % Quantize x using DPCM.
  encodedx = dpcmenco(x,codebook,partition,predictor);
  % Try to recover x from the modulated signal.
  decodedx = dpcmdeco(encodedx,codebook,predictor);
  plot(t,x,t,decodedx,'--')
  distor = sum((x-decodedx).^2)/length(x) % Mean square error
  
  distor =
  
      0.0327
  
  
  

Optimizing Quantization Parameters

Optimizing DPCM Parameters