![]() ![]() The algorithms could also be extended to deal with multiple-speaker signals. used Doctor Speech (Tiger DRS Inc)26 and one study9 used Praat (Paul Boersma. With the use of a complete production model, the proposed systems provide robust formant tracks which can be used in various applications. This result was not surprising because FFT and LPC are standard procedures. Zeros that are outside the unit circle are reflected into it. The results are comparable to state-of-the-art formant tracking algorithms. Behaviour For each LPC frame, the zeros of the linear prediction polynomial are extracted. ![]() Two algorithms are proposed, with two different strategies: first, a simplification of the underlying model, with a parameter estimation based on variational methods, and second, a sparse decomposition of the signal, based on Non-negative Matrix Factorization methodology. In this paper, we propose a Factorial Hidden Markov Model combined with a vocal source/filter model, with parameters naturally encoding the $f_0$ and $f_p$ tracks. However, directly estimating the formant frequencies, or equivalently the poles of the AR filter, allows to further model the smoothness of the desired tracks. Many works assume an auto-regressive (AR) model to fit the spectral envelope, hence indirectly estimating the formant tracks from the AR parameters. Tracking vocal tract formant frequencies ($f_p$) and estimating the fundamental frequency ($f_0$) are two tracking problems that have been tackled in many speech processing works, often independently, with applications to articulatory parameters estimations, speech analysis/synthesis or linguistics. ![]()
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