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To determine an encoder for such a quantizer, you must supply not only a partition and codebook as described in Representing Partitions and Representing Codebooks, 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.
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