All-pole modeling technique based on the Weighted Sum of the LSP polynomials

With the order of prediction equal to m, conventional linear prediction (LP) yields an all-pole filter that matches exactly the autocorrelation function of the input signal between indices 0 and m. This study presents a new technique, Weighted-Sum Line Spectrum Pair (WLSP), where an all-pole filter is defined by using a sum of weighted LSP polynomials. 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 autocorrelations at index m, WLSP models the autocorrelation of the input signal at the indices above m more accurately than conventional LP. The current paper presents mathematical properties of WLSP together with preliminary results on modeling of vowels. The results indicate that WLSP, in comparison to conventional LP is able to yield all-pole filters that model especially the upper formants with a larger dynamic range between formant peaks and spectral valleys.