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This study presents a new technique called weighted-sum line spectrum pair (WLSP) where an all-pole filter is defined by using a sum of weighted line spectrum pair polynomials. The WLSP yields a stable all-pole filter of order m, whose autocorrelation function coincides with that of the input signal between indices 0 and m-1. By sacrificing the exact matching at index m, the WLSP models the autocorrelation of the input signal at the indices above m more accurately than conventional linear prediction (LP). Experiments with vowels show that, in comparison to the conventional LP, WLSP yields all-pole spectra that model formants with an increased dynamic range between formant peaks and spectral valleys.