Analysis of the Maximum Prediction Gain of Short-Term Prediction on Sustained Speech

Signal prediction is widely used in, e.g., economic forecasting, echo cancellation and in data compression, particularly in predictive coding of speech and music. Predictive coding algorithms reduce the bit-rate required for data transmission or storage by signal prediction. The prediction gain is a classic measure in applied signal coding of the quality of a predictor, as it links the mean-squared prediction error to the signal-to-quantization-noise of predictive coders. To evaluate predictor models, knowledge about the maximum achievable prediction gain independent of a predictor model is desirable. In this manuscript, Nadaraya-Watson kernel-regression (NWKR) and an information theoretic upper bound are applied to analyze the upper bound of the prediction gain on a newly recorded dataset of sustained speech/phonemes. It was found that for unvoiced speech a linear predictor always achieves the maximum prediction gain within at most 0.3 dB. On voiced speech, the optimum one-tap predictor was found to be linear but starting with two taps, the maximum achievable prediction gain was found to be about 2 dB to 6 dB above the prediction gain of the linear predictor. Significant differences between speakers/subjects were observed. The created dataset as well as the code can be obtained for research purpose upon request.