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The pitch-predictor contributes greatly to the efficiency of current analysis-by-synthesis speech coders by mapping the past reconstructed signal into the present. However, for good performance, it is required that its parameters are updated often (one every 2.5-7.5 ms). A slower update rate of the pitch-predictor delay results in time misalignment between the original signal and the pitch-predictor contribution to the reconstructed signal and the pitch-predictor contribution to the reconstructed signal. The authors introduce a new procedure, that allows a slow update rate of the pitch-predictor parameters without this problem. In this method the original signal is modified in a closed-loop fashion such that the parameter values obtained by interpolation of open-loop estimates form the optimal encoding of the modified signal. This new paradigm is a generalization of the familiar analysis-by-synthesis principle. The generalized analysis-by-synthesis principle can be used for interpolation of both the pitch-predictor delay and gain. The authors compare, by means of a subjective test, speech signals encoded with different versions of the code-excited linear predictor delay and gain. They compare, by means of a subjective test, speech signals encoded with different versions of the code-excited linear predictor (CELP) coder. The comparison shows that a pitch predictor exploiting the present interpolation strategy, with an update rate of 50 Hz, provides a subjective speed quality similar to a conventional pitch predictor where the parameters are updated for every pitch cycle.