Statistical properties of linear prediction analysis underlying the challenge of formant bandwidth estimation

Formant bandwidth estimation is often observed to be more challenging than the estimation of formant center frequencies due to the presence of multiple glottal pulses within a period and short closed-phase durations. This study explores inherently different statistical properties between linear prediction (LP)-based estimates of formant frequencies and their corresponding bandwidths that may be explained in part by the statistical bounds on the variances of estimated LP coefficients. A theoretical analysis of the Cramér-Rao bounds on LP estimator variance indicates that the accuracy of bandwidth estimation is approximately twice as low as that of center frequency estimation. Monte Carlo simulations of all-pole vowels with stochastic and mixed-source excitation demonstrate that the distributions of estimated LP coefficients exhibit expectedly different variances for each coefficient. Transforming the LP coefficients to formant parameters results in variances of bandwidth estimates being typically larger than the variances of respective center frequency estimates, depending on vowel type and fundamental frequency. These results provide additional evidence underlying the challenge of formant bandwidth estimation due to inherent statistical properties of LP-based speech analysis.