# Development of Parameters towards Voice Bifurcations
## 4 Discussion
### Clinical Applications  
The HDF and BI are short-term parameters, which are meant to be measured repeatedly over each voice sample. With the HDF ability to distinguish Type I and Type II/III, it could be used in the automation of spectrogram visual inspection for clinical assessment. Additionally, these measurements can be further processed to form objective parameters, which are potentially clinically useful indicators for voice quality.  
The clinical value of HDF and BI measurements themselves (or their means over multiple windows) needs to be further investigated. These parameters are designed primarily to detect bifurcations, i.e., to observe the changes in their values in time. They, however, could be significant measures if different biphonic or subharmonic components in voice are perceived differently and found to be contributing to severity of voice quality; for example, period-doubling vs. period-tripling subharmonics and 2:3 biphonia vs. 3:5 biphonia. To the authors' knowledge, there is no known related work in the literature.  
What is likely to be perceivable, on the other hand, is the occurrence rates of non-Type-I voicing and of voice-type switching. This leads us to two viable objective parameters: amount of harmonically disturbed phonation and the rate of bifurcation. The former  
Figure 6: Case 3 periodogram at \(t=0.075\) (7 th window).  
quantifies how much time during phonation the voice exhibited non-Type-I behavior, and the latter how often voice bifurcations occur. The cases in this paper demonstrated promising signs for the HDF to serve these objective parameters. The HDF of Type-I voice is tightly concentrated at zero. This allows reliable detection of non-Type-I short-term phonation, and therefore the HDF is an excellent basis to form an effective parameter to quantify the occurrence rate of non-Type-I voice.  
The alternate parameter, quantifying the occurrences of mid-phonation bifurcations, requires additional analysis: distinguishing the three phonation types and detecting changes within Type II. Both HDF and BI can contribute to this analysis. The HDF and BI measures in each phase-locked Type-II segment are drawn from a fixed set of values, as illustrated in Figure 2. As such, a transition to another Type-II mode is likely to introduce a discontinuity in the HDF or BI measures. To detect transition away from a biphonic segment, the BI is more a reliable solution than the HDF as the BI takes a unique value for each biphonic mode (2.3, 3.5, etc.). Detection of Type III can be achieved by monitoring the variation of the HDF (or BI) over several windows. Further development is required to better understand the implementational limitations, such as noise characteristics and measurements in the windows that bridge two distinctive modes. Additionally, a dedicated classifier for subharmonic periodicity would complement HDF and BI and strengthen bifurcation detection.  
This paper focused on glottal source signals, specifically on the glottal area waveforms from high-speed videoendoscopic data. Other types of source signals, such as the electroglottogram, could use the same algorithm if the first harmonic is the most dominant harmonic. This condition is not satisfied by acoustic signals due to the vocal tract effect. Thus, extending the HDF to general voice signals, especially acoustic signals, requires a frequency selection algorithm that can identify the speaking fundamental frequency. With such an algorithm, the HDF concept can be extended to the assessment of voicing changes in connected speech, which is known to expose dysphonia more than sustained phonation [23].