On the measurement of the instantaneous frequency and amplitude of partials in vocal vibrato

In this paper, we analyze some methodological and practical grounds affecting a correct estimation of the instantaneous amplitude (IA) and instantaneous frequency (IF) of the partials of vocal vibrato signals. This particular class of acoustical signals can be described as a set of harmonics, or partials, whose amplitude and frequency vary with time following a particular pattern. The interest in the correct measurement of these two magnitudes stems from the fact that they are widely used to extract more information about the production mechanisms of this vocal effect, and even the singing voice. Focusing on the estimation of these magnitudes from the signal processing point of view, the estimation of the IA and the IF of a partial represents a practical example for the more general problem of the AM-FM decomposition of a bandpass signal, which has received considerable attention by the Time-Frequency community. With this in mind, this work will investigate the most appropriate AM-FM decomposition of the partials, and how it is affected by the reverberation present in recordings. A mathematical description of the effect of reverberation on the measurement will be given. It will be shown that the measurement of the IA and the IF of the partials will be corrupted by reverberation regardless of the employed estimation method