Quadratic Programming Approach to Glottal Inverse Filtering by Joint Norm-1 and Norm-2 Optimization

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This study proposes an approach for glottal inverse filtering of acoustic speech signals using quadratic programming (QPR). The method aims to jointly model the effect of vocal tract and lip radiation with a single filter whose coefficients are optimized using QPR. This optimization is based on the principles of closed phase analysis, where the contribution of the glottal source is attenuated in optimizing the inverse model of the vocal tract. By expressing the optimization problem in terms of the output of a filter, we can apply physically motivated optimization such as flatness of the closed phase. The proposed method was objectively evaluated using a synthetic Liljencrants–Fant model based test set of sustained vowels, as well as a real speech test set where the glottal flow estimates’ closed phases were compared in terms of their flatness. The results based on synthetic speech indicate that the proposed method is robust to changes in $f_0$ , and state-of-the-art quality results were obtained for high-pitched voices, when $f_0$ is in the range 330–450 Hz. The results based on real speech indicate that the proposed method produces glottal flow estimates that have flatter closed phases with less formant ripple in comparison to estimates computed with known reference methods.