All-pole Modelling of Noisy Speech with the Weighted Sum of the Line Spectrum Pair

The autocorrelation function of the all-pole filter given by conventional linear prediction (LP) matches exactly the autocorrelation function of the input signal between indices 0 and m, when the prediction order equals m. A recently developed technique, Weighted Sum of the Line Spectrum Pair (WLSP), yields a stable all-pole filter of order m, whose autocorrelation function coincides to that of the input signal between indices 0 and m-1. By sacrificing the exact matching of the autocorrelation at index m, WLSP models the autocorrelation of the input at the indices above m more accurately than conventional LP. In the current paper, the performance of WLSP in spectral modelling of noisy speech is analysed. It is shown that WLSP models the formant structure of noisy vowels more accurately than the conventional LP of the same prediction order.