## 2 Materials and Methods  
### Data  
High-speed videos (HSVs) of the vocal folds with a frame rate of 4000 frames per second are obtained by inserting a laryngeal endoscopic camera (HRES ENDOCAM 5562) through the mouth into the pharynx [21]. Subjects are instructed to produce sustained phonation of vowels for a duration of two seconds while the vocal fold vibrations are filmed. Audio files are recorded simultaneously using a head worn microphone. The audio files are synchronized with the captured video files. The voice samples are annotated by three expert annotators with regard to presence or absence of vocal fry. Based on the annotations, the corresponding video frames of the HSVs are cropped and used for GAW extraction. The GAWs are extracted using a seeded region growing segmentation algorithm [22]. Seven GAWs annotated as vocal fry contain amplitude modulations without long phases. They are used as a positive group. Eight euphonic i.e., normophonic GAWs are used as a negative group. The vocal fry GAWs are further distinguished into two categories based on the cyclicity of the GAWs by visual inspection. Three out of seven amplitude modulated GAWs are observed to be acyclically modulated. These GAWs are termed as Acyclically Amplitude Modulated Pulse train (AAMP). The remaining four vocal fry GAWs are observed to have a cyclic modulator. These cyclic GAWs are further subclassified based on the number of pulses in each modulator cycle, one of which is characterized by double-pulsing, i.e., alternation of pulse magnitudes, timing, and/or shapes. This type is termed as Cyclically Amplitude Modulated Pulse train-2 (CAMP = 2). The other cyclically modulated type is characterized by more than two pulses per cycle. This type is termed as Cyclically Amplitude Modulated Pulse train = 4 (CAMP = 4). Along with the natural GAWs, 1200 synthetic GAWs are used. Of the synthetic GAWs, 300 belong to the euphonic group and the remaining 900 are vocal fry GAWs, with each of the vocal fry type having 300 GAWs. Synthetic GAWs are generated using parameter distributions obtained from estimated parameters of the natural GAWs. Regularity and symmetry of vocal fold vibration is analyzed using phonovibrograms (PVGs). A PVG displays the deflections of the vocal folds from the glottal axis represented as the color intensities [23]. The brighter the color intensity, the farther away are the vocal folds from the glottal axis. Figure 1 shows PVGs of the GAWs shown in Figure 2, i.e., of the amplitude modulated vocal fry and euphonic types of vocal fold vibration. A negligible anterior-posterior asymmetry of vocal folds is observed in the PVG belonging to CAMP = 4 in Figure 1a. Here, each modulator cycle contains four pulses where the borders of one of the modulator cycles is marked by two vertical green lines. The vibration pattern is described as an increase in the amplitude of the vocal fold vibration for four consecutive glottal pulses followed by a sudden decrease in amplitude. In contrast, the anterior-posterior phase difference is observed in PVGs of CAMP = 2, AAMP, and the euphonic type. In Figure 1b, the anterior-posterior phase difference in every second pulse of the vocal folds results in a period-doubled GAW, as shown in Figure 2b. Figure 3 shows an overview of the analysis and synthesis combined with parameter distribution fitting. First, the analyzer models the natural GAW \(y(t)\) (input) using an analysis-by-synthesis approach, which is described in Section 2.2. A Fourier synthesizer is used to obtain the modelled GAWs \(\hat{y}(t)\). The modelling error \(E\) is obtained from the root  
Figure 1: Phonovibrogram (PVG) representation of vocal fold kinematics of the GAWs shown in Figure 2: (**a**) CAMP = 4, (**b**) CAMP = 2, (**c**) AAMP and (**d**) euphonic type. Figure 2: Glottal area waveforms (GAWs) extracted by segmentation of the high-speed videos (HSVs): (**a-c**) vocal fry and (**d**) euphonic voice.