ACOUSTIC COUPLING IN PHONATION AND ITS EFFECT ON ...

25an all-pole system, this instability is easily solved without affecting its magnituderesponse [32,88,136–138].Many researchers have opted for the covariance method since the smaller temporalwindows allow for estimation of the vocal tract filter within the closed phased portionof the vocal fold cycle. An estimate in this portion is thought to be a more accuraterepresentation since it discards the changes in vocal tract formants product of sourcefilterinteractions that are more predominant during the open cycle. A number ofmethods have been proposed for the detection of the closed phase portion of the cycle,including a multi-channel method that uses electroglottography (EGG) [139,140] anda formant frequency modulation scheme that searches for the stable regions of thefirst formant [31], among others [33,34].In spite of the presence of source-filter interactions, it has been suggested thatseparability between source and filter is still possible [139]. This can be achieved intwo ways, by assuming that: 1) the source is independent and that the vocal tractwill have different formants and bandwidths during the open and closed phase, or2) that the vocal tract is time-invariant as in the closed phase and that the glottalsource contains the formant frequency and bandwidth changes from the previouscase. The latter explains the vowel dependent ripples normally observed during theopen phase of the glottal waveform [6]. In addition, linear prediction applied to awhole period (or more) will contain formant frequency and bandwidth errors [139].This evidently means that the estimation of the properties of the vocal tract (e.g.,formant frequencies and bandwidths) obtained via autocorrelation and covariancemethods will differ. In fact, closed phase inverse filtering (CPIF) using the covariancemethod has been shown to provide better estimates of the glottal waveform than thoseobtained with the autocorrelation method [34, 138]. In particular, better estimatesare those that preserve the source-filter interactions observed during the open phasewhen removing the vocal tract filtering effect. However, it is unclear how the CPIFscheme handles incomplete glottal closure, where subglottal coupling is present andthere is no true closed phase. It is possible that CPIF incorrectly suppresses ripples