The source-filter approach in singing and its implication on inverse-filtering techniques
Résumé
From an acoustical and signal point of view, human phonation is commonly described by the source-filter theory (Fant, 1960). The vocal-tract contribution to the radiated voice sound is assumed to be linear and independent from the glottal source properties. Therefore, it can be estimated and removed, which is the basic principle for inverse-filtering techniques. This linear approach has successfully been applied to speech and singing analysis, coding, and synthesis. Yet, its adequacy for modelling the singing voice seems questionable, as singers are trained to find the best match between their phonatory and articulatory gestures. Using physical measures of vocal-tract resonance frequencies, the possibilities and limitations of formant-estimation and inverse-filtering techniques are investigated. Three different cases are explored: - f0 far below first-resonance R1 (e.g. bottom part of male singer's tessitura) - f0 near R1 (e.g. vowel /u/ for tenors, top part of soprano's tessitura) - a multiple of f0 near R1 (e.g. 2*f0 near R1 in Bulgarian Female singing) The harmonics influence on formant-frequency estimation is discussed. It is shown that, in some cases, the formant estimate is biased by the harmonic nearby. By reconstructing the vocal-tract transfer function from the measured resonance frequencies, examples of inverse-filtered glottal-flow pulses are given. Ripples, which could result from source-tract interaction, are observed on the inverse-filtered glottal-flow pulses, even during the closed phase.