Calculation of true glottal flow and its components

An iterative numerical algorithm is presented for camputing the true glottal flow given the glottal area function and lung pressure. The effectsofglottalinertance and suband supraglottal impedance are discussed. It is sham that the effect of glottal inertance is small and that it is adequate t o consider subglott a l and supraglottal systems by one-formant loads only. An equivalentcircuitfor the glott is considering the nonlinear and time-varying pressure-flw relation is derived. In addition to the dynamic glottal resistance, there exists a hypothetical inductance in the equivalent circuit which is minly responsible fortheskewing of the source pulses under load. An analytical equation for the min p l s e shape of the true glottal f l w is derived as the source residue. Theroleof ripple conponents in the true glottal f l w is discussed. 1 . Introduct ion The volume velocity of a i r flow through the glott is , the glottal pilses, is the min source of voiced sounds. Glottalairflaw as w e l l as vocal folds vibratory patterns my be affected by changes in subglottal pressure and supraglottal articulations. In the classical approach for the synthesis of voiced sounds,viz., the source-filter modeling philosophy (Fant 1960), the interaction betthe volum velocity source and the physiological parameters is assumed to be linearly separable. This approach is q i r i c a l but the implementation of synthesis is sinple. CXI the other hand, an integrated vocal cord, vocal tract mdel (Flanagan 1968, 1972) preserves inherent constraints between the a i r f lw through the glottis and suband supraglottal states. This approach is sophisticatedbutthepract ical implementation in synthesis becorres highly complex. Fromgeneralexperience in speech analysis we expect the source-filter interaction to be minly confined to the f i r s t formant. A pragmtic model for synthesis my l i e in-between these t m extreme modeling philosophies, the simple formant analog and the conplete interactive VT-rodel. Recent studies by Fant (1979, 1980, 1981) are airred the developmt of a pragmtic m e 1 for the voice source. The present study is also in the m direction. The success of an interactive source-filter model depends on its ability t o represent the complex three-dimensional mvements of the vocal folds by m s of analytical equations. The early mrk of van den Berg (1957) provided us with insight in the glottal impedance and aerodynamic forces within the glott is during * P a r t s of this paper were presented a t the 102nd meeting of the Acoustical Society of America, Dec. 1-4, 1981, Miami Beach, FL, USA by G. Fant