Doppler-variant modeling of the vocal tract

A common technique to deploy linear prediction to non-stationary signals is time segmentation and local analysis. Variations of a process within such a segment cause inaccuracies. In this paper, we model the temporal changes of linear prediction coefficients (LPCs) as a Fourier series. We obtain a compact description of the vocal tract model limited by the predictor order and the maximum Doppler frequency. Filter stability is guaranteed by all-pass filtering, deploying the human ear's insensitivity to absolute phase. The periodicity constraint induced by the Fourier series is counteracted by oversampling in the Doppler domain. With this approach, the number of coefficients required for the vocal tract modeling is significantly reduced compared to a LPC system with block-wise adaptation while exceeding its prediction gain. As a by-product it is found that the Doppler frequency of the vocal tract is in the order of 10 Hz. A generalization of the algorithm to an auto-regressive moving average model with time-correlated filter coefficients is straight forward.