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Backward adaptive prediction in differential pulse code modulation (DPCM) systems is represented as a problem of spectral analysis within a closed loop. Using this spectral analysis approach, the backward adaptive all-pole predictor in classic DPCM is shown to perform well, given good initial conditions and a slowly varying DPCM system input. However, when it loses track, the all-pole predictor is shown to have a tendency to track itself rather than changes in the input signal transfer function. The use of a pole-zero predictor improves the situation since the backward adaptation of the zeros is clearly dependent upon the input signal transfer function and thus should respond to changes or nonstationarities in the DPCM system input. The backward adaptation of the poles in the pole-zero predictor is able to track changes in the system input through variations in the predictor zeros. The results provide additional motivation for including zeros in backward adaptive predictors for DPCM.