Multivariate-state Hidden Markov Models for Simultaneous Transcription of Phones and Formants

A multivariat,e-state HMM an HMM with a vector state variable can be used to find jointly optimal phonetic and formant transcriptions of an utterance. The complexity of searching a multivariate state space using the BaumWelch algorithm is substantial, but may be significantly reduced if the formant frequencies are assumed to be conditionally independent given knowledge of the phone. Operating with a known phonetic transcription, the multivariatestate model can provide a maximum a posteriorz formant trajectory, complete with confidence limits on each of the formant frequency measurements. The model can also be used as a phonetic classifier by adding the probabilities of all possible formant trajectories. A test system is described which requires only nine trainable parameters per formant per phonetic state: five parameters to model formant transitions, and four to model spectral observations. Further simplifications were achieved through parameter tying.