# Development of Parameters towards Voice Bifurcations
## 1 Introduction
Another mode of biphonia occurs later at \(t_{0}=0.7\): (**a**) time-domain plots each over 100-ms window; (**b**) normalized power spectral density estimates (periodogram with Hamming window; only showing below 1 kHz, range \(-50\) to 0 dB) in decibel scale. Vertical dotted lines indicate the estimated harmonic frequencies by [PERSON]’s pitch estimator [16]. There are objective parameters that explicitly target the spectral features of Type-II voice. In the context of digital telephone systems, subharmonic-to-harmonic ratio [17; 18] was introduced to improve the pitch determination performance and was later applied to assess the pathological subharmonics [19]. The Degree of Subharmonics (DSH) parameter in the Multi-Dimensional Voice Program (MDVP) [20] measures the percentage of time the subharmonic is present. [PERSON] et al. [21] devised the Diplophonia Diagram, which characterizes the signal under study by the residuals of two modeling outcomes using single harmonic series vs. two harmonic series. [PERSON] and [PERSON] [22] proposed a tandem of cepstrum peak prominence measures to quantify the degree of presence of subharmonics and demonstrated an 82.2% correct classification of rough vs. non-rough voice. [PERSON] et al. [23] studied the relationship between cycle-to-cycle variability in the fundamental frequency \(F_{0}\) and percentage of low \(F_{0}\) estimates on connected speech to the perceived roughness. [PERSON]'s work is unique among others because it focuses on the frequency measure rather than measures based on signal strength or power. This remark from their work is noteworthy: \"Because the presence of subharmonics is the main source of both pitch perception and \(F_{0}\) detection errors, it seems reasonable to exploit errors in \(F_{0}\) detection for quantitative measurement of pathologic voices.\" For Type-I voice, \(F_{0}\) detection error seldom happens (assuming clean signal) while Type II induces error because of the strong non-harmonic content residing near the first harmonic (relative to the second harmonic frequency). In the case of biphonia, there exist two different \(F_{0}\)s that are close in both frequency and power. This leads to the seed idea for this paper: the spectral peak characteristics are vastly different between Type-I and Type-II voices, and analyzing the relative positions of the peaks may result in differentiating Type-I and Type-II signals. We apply this idea towards detecting mid-phonon bifurcations, especially between Type I and Type II. The voice type detection scheme can also be devised from Type-III signals, namely by deploying the methods based on dynamical systems analysis and chaos theory. There are a number of studies available, exploring different methodologies, e.g., correlation dimensions [4; 5; 24; 25; 26], Lyapunov exponent [4; 25], diffusive chaos [6], nonlinear energy difference ratio [7], recurrence quantification measures [27; 28], and intrinsic dimension [5]. To detect mid-phonon bifurcations, these methods are challenged by their data duration requirements. Typical analysis durations range from 0.2 to 2 s, while the bifurcations could occur at a more frequent rate, as shown in Figure 1.