Let us consider the source signal \(\rm x(n)\) shown at the top of Fig.4.1. A simple approach to linear prediction is to just use the previous sample \(\rm x(n - 1)\) as the prediction for the current sample: \(p(n) = x(n - 1)\cdot\) This prediction is, of course, not perfect, so there is prediction error or residue \(r(n) = x(n) - p(n) = x(n) - x(n - 1)\) which is shown at the bottom of Fig. 4.1. The dynamic range of the residue is obviously much smaller than that of the source signal. The variance of the residue is 2.0282, which is much smaller than 101.6028, the variance of the source signal. The histograms of the source signal and the residue, both shown in Fig. 4.2, clearly indicate that, if the residue, instead of the source signal itself, is quantized, the quantization error will be much smaller.
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