# Prosody-Based Measures for Automatic Severity Assessment of Dysarthrie Speech
## 2 Acoustic Measures  
### Prosody-Based Measures  
The prosody-based features we use in our experiments are based on the findings from previous acoustic studies on dysarthric speech. In general, these values are irregular in speakers with dysarthria in comparison to the average healthy speakers. Prosodic features are grouped into 3 categories: pitch, speech rate, and rhythm. Compared to the study in Reference [36], which only uses 11 measures from the 3 prosodic categories, we include a wider range of 23 prosody-based measures as shown in Table 1. Pitch and speech rate are extracted using the Python library parselmouth, which provides a Pythonic interface to the internal Praat code [47]. Rhythm metrics are collected using the software Correlatore 2.3.4 [48].  
The acoustic representation of pitch is known as fundamental frequency (F0), which is the lowest frequency of a periodic waveform. F0 is measured for all voiced segments of an utterance. The pitch feature set includes mean, median, minimum, and maximum F0 along with the standard deviation, 25%, and 75% quantiles.  
The speech rate refers to the speed-related measurements of speech such as speaking rate (syllables per second) and articulation rate (syllables/per second without pause). The current study includes seven speech rate measures per utterance: number of syllables, number of pauses, full utterance duration, speaking duration (excluding pauses), speaking rate, articulation rate, and balance. Balance refers to the ratio of speaking duration to utterance duration.  
In linguistics, rhythm corresponds to the duration-based division of speech units into relatively equal pieces. Duration-based measures of vocalic and intervocalic segments are proposed as correlates of rhythm in the speech signal [49; 50; 51]. The first group of 3 rhythm metrics is proposed in Reference [49]: the proportion of vocalic intervals (%V) and the standard deviations of consonantal (\(\Delta\)C) and vocalic (\(\Delta\)V) intervals.  
In Reference [50], the influence of speech rate on \(\Delta\)C and \(\Delta\)V is addressed. Delta values can be normalized by dividing the delta into the mean duration of vocalic or consonantal intervals, then multiplying that by 100. The normalized delta values are known as the 'Varcos' and can be  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Pitch** & **Speech Rate** & **Rhythm** \\ \hline \multicolumn{3}{c}{\%V} \\ F0 mean & \# of syllables & Delta-V \\ F0 median & \# of pauses & Delta-C \\ F0 min & Utterance duration & Varco-V \\ F0 max & Speaking duration & Varco-C \\ F0 std & Speaking rate & VrPVI \\ F0 quantile 25 & Articulation rate & CrPVI \\ F0 quantile 75 & Balance & VnPVI \\  & & CnPVI \\ \hline \hline \end{tabular}
\end{table}
Table 1: The full set of prosody-based measures.  
measured for both vowel and consonant intervals. Varco-C and Varco-V can be calculated as shown in Equations (1) and (2), respectively:  
\[\text{Varco}-\text{C}\ =\ \frac{\Delta\text{C}\ast 100}{mean(C)} \tag{1}\]  
\[\text{Varco}-\text{V}\ =\ \frac{\Delta\text{V}\ast 100}{mean(V)} \tag{2}\]  
The next group of rhythm metrics is calculated using the pairwise variability index (PVI), where the temporal succession of the vocalic or consonantal intervals are taken into consideration [51]. The influence of speech rate variation can be controlled by calculating the normalized PVI, which calculates the mean absolute normalized difference between durations of neighboring interval pairs. Both rPVI and nPVI are defined in Equations (3) and (4), where \(d_{k}\) is the length of the \(k\)th vocalic or consonantal segment and \(m\) is the number of segments. The raw PVI can be calculated for vowel intervals (VrPVI) or consonant intervals (CrPVI). Similarly, the normalized PVI can also be calculated for vowel intervals (VnPVI) or consonant (CnPVI) intervals.  
\[\text{rPVI}\ =\ \sum_{k-1}^{m-1}\abs{d_{k}-d_{k+1}}/(m-1) \tag{3}\]  
\[\text{nPVI}\ =\ 100\ \ast\ \sum_{k-1}^{m-1}\abs{\frac{d_{k}-d_{k+1}}{\frac{d_{k} +d_{k+1}}{2}}}/\ (\text{m}-1) \tag{4}\]