Detrending the Waveforms of Steady-State Vowels

Steady-state vowels are vowels that are uttered with a momentarily fixed vocal tract configuration and with steady vibration of the vocal folds. In this steady-state, the vowel waveform appears as a quasi-periodic string of elementary units called pitch periods. Humans perceive this quasi-periodic regularity as a definite pitch. Likewise, so-called pitch-synchronous methods exploit this regularity by using the duration of the pitch periods as a natural time scale for their analysis. In this work, we present a simple pitch-synchronous method using a Bayesian approach for estimating formants that slightly generalizes the basic approach of modeling the pitch periods as a superposition of decaying sinusoids, one for each vowel formant, by explicitly taking into account the additional low-frequency content in the waveform which arises not from formants but rather from the glottal pulse. We model this low-frequency content in the time domain as a polynomial trend function that is added to the decaying sinusoids. The problem then reduces to a rather familiar one in macroeconomics: estimate the cycles (our decaying sinusoids) independently from the trend (our polynomial trend function); in other words, detrend the waveform of steady-state waveforms. We show how to do this efficiently.