Analysis of Glottal Inverse Filtering in the Presence of Source-Filter Interaction

The validity of glottal inverse filtering (GIF) to obtain a glottal flow waveform from radiated pressure signal in the presence and absence of source-filter interaction was studied systematically. A driven vocal fold surface model of vocal fold vibration was used to generate source signals. A one-dimensional wave reflection algorithm was used to solve for acoustic pressures in the vocal tract. Several test signals were generated with and without source-filter interaction at various fundamental frequencies and vowels. Linear Predictive Coding (LPC), Quasi Closed Phase (QCP), and Quadratic Programming (QPR) based algorithms, along with supraglottal impulse response, were used to inverse filter the radiated pressure signals to obtain the glottal flow pulses. The accuracy of each algorithm was tested for its recovery of maximum flow declination rate (MFDR), peak glottal flow, open phase ripple factor, closed phase ripple factor, and mean squared error. The algorithms were also tested for their absolute relative errors of the Normalized Amplitude Quotient, the Quasi-Open Quotient, and the Harmonic Richness Factor. The results indicated that the mean squared error decreased with increase in source-filter interaction level suggesting that the inverse filtering algorithms perform better in the presence of source-filter interaction. All glottal inverse filtering algorithms predicted the open phase ripple factor better than the closed phase ripple factor of a glottal flow waveform, irrespective of the source-filter interaction level. Major prediction errors occurred in the estimation of the closed phase ripple factor, MFDR, peak glottal flow, normalized amplitude quotient, and Quasi-Open Quotient. Feedback-related nonlinearity (source-filter interaction) affected the recovered signal primarily when f was well below the first formant frequency of a vowel. The prediction error increased when f was close to the first formant frequency due to the difficulty of estimating the precise value of resonance frequencies, which was exacerbated by nonlinear kinetic losses in the vocal tract.