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

TL;DR

This paper analyzes the theoretical maximum prediction gain in short-term speech prediction, revealing that simple linear predictors are nearly optimal for unvoiced speech, while more complex predictors significantly improve gain for voiced speech.

Contribution

It introduces a method to evaluate the upper bound of prediction gain in speech, applying kernel regression and information theory to a new dataset, and compares predictor performances.

Findings

Linear predictor achieves near-maximum gain for unvoiced speech.

Two-tap predictors improve gain by 2-6 dB for voiced speech.

Significant speaker-dependent differences in prediction gain.

Abstract

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.