In this paper a mass-spring model is developed that is a hybrid of the two-mass and the longitudinal string models, proposed by Ishizaka and Flanagan [Bell Sys. Tech. J. 51, 1233-1268 (1972)] and Titze [Phonetica 28, 129-170 (1973)], respectively. The model is used to simulate the vibratory motion of both the normal and asymmetric vocal folds. Mouth-output pressure, lateral tissue displacement, phase plots, and energy diagrams are presented to demonstrate the interaction between vocal fold tissue and the aerodynamic flow between the folds. The results of the study suggest that this interaction is necessary for sustained large amplitude oscillation because the flow supplies the energy lost by the tissue damping. Tissue mass and stiffness were varied locally or uniformly. Decreased stress in the longitudinal string tension produced subharmonic and chaotic vibrations in the displacement, velocity and acceleration phase diagrams. Similar vibratory characteristics also appeared in pathological speech data analyzed using time domain jitter and shimmer measures and a harmonics-to-noise ratio metric. The subharmonics create an effect that has been perceptually described as diplophonia.

This paper explores technical issues affecting computed measures of the relative level of noise in the frequency spectrum of a vowel. This type of measure has been proposed for quantification of hoarseness in pathological speakers. An analysis of synthesized vowels was used to test the influence of vowel type, fundamental frequency, perturbation type, perturbation level and quantization. The algorithms were shown to be highly sensitive to errors in pitch-period demarcation, and a dependency on jitter perturbations, fundamental frequency, and vowel type was demonstrated. Relationships between algorithm performance and methods of spectrum estimation were discussed, and approaches for reducing the dependencies were proposed. Finally, a method for achieving a significant reduction in computation time was described.

The harmonics-to-noise ratio (HNR) was proposed for measurement of noise in sustained vowels. A generalized algorithm is described here for removing the dependence on the data offset and for reducing the influence of jitter and shimmer. In addition, a new algorithm is proposed that accommodates periodic perturbations. Formulations are presented that can be computed in a single pass through the data under certain assumptions, thus simplifying the implementation of an efficient analysis program. A mathematical analysis of the effect of small errors in pitch-period demarcation is presented. The analysis indicates that the sensitivity to demarcation errors depends on the preponderance of high-frequency components, and significant underestimation is predicted for /a/ and /i/ data. A method for correcting quantization and demarcation errors in pitch-period markers is described. The method is shown to be effective at reducing demarcation errors for all but the most severely perturbed waveforms. Examples of the use of this method for HNR estimation are provided. Finally, a comparison with recent work by Milenkovic [J. Speech Hear. Res. 30, 529-538 (1987)] is presented.

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