Differential Encoding

Simple example of transform coding mentioned earlier and instance of this approach.

Here:

• The difference between the actual value of a sample and a prediction of that values is encoded.
• Also known as predictive encoding.
• Example of technique include: differential pulse code modulation, delta modulation and adaptive pulse code modulation -- differ in prediction part.
• Suitable where successive signal samples do not differ much, but are not zero. E.g. Video -- difference between frames, some audio signals.
• Differential pulse code modulation (DPCM) simple prediction:

  f_predict(t_i) = f_actual(t_i-1)

  i.e. a simple Markov model where current value is the predict next value.

  So we simply need to encode:

  $$\Delta f(t_i) = f_{actual}(t_{i}) - f_{actual}(t_{i-1})$$

  If successive sample are close to each other we only need to encode first sample with a large number of bits:

  Actual Data: 9 10 7 6

  Predicted Data: 0 9 10 7

  $\Delta f(t)$: +9, +1, -3, -1.

• Delta modulation is a special case of DPCM: Same predictor function, coding error is a single bit or digit that indicates the current sample should be increased or decreased by a step.

  Not Suitable for rapidly changing signals.

• Adaptive pulse code modulation -- Fuller Markov model: data is extracted from a function of a series of previous values: E.g. Average of last n samples. Characteristics of sample better preserved.