# Speech Intelligibility Analysis and Approximation to Room Parameters through the Internet of Things
## 2 Materials and Methods
### SII Computation  
The SII value ranges between 0 and 1, and it is highly correlated with speech intelligibility under adverse hearing conditions, such as auditory masking, filters, and reverberation [20]. The American National Standards Institute (ANSI) defined the standard SII to evaluate speech intelligibility in background noise. The measurement inputs are clean speech signal and noise, while the output is a scalar number that specifies the amount of speech intelligibility. A key component of the SII measure is the band importance function, which determines the contribution of each frequency band (e.g., the one-third octave bands) to speech intelligibility. This objective measure is based on the SNRs weighted, usually in  
Figure 3: Measurement of parameters in the classroom using the designed system. Detail of sound source location (square mark) and receiver nodes (circular mark).  
the one-third octave bands. The SII measure is calculated by considering the SNR of each frequency band weighted according to its contribution to speech intelligibility. The SII has a bell-shaped band importance function, as we can see in Figure 4, with a value of 0.0083 for the one-third octave frequency band centered at 160 Hz, 0.0898 for the band centered at 2000 Hz, and 0.0185 for the band centered at 8000 Hz.  
The general formula for calculating the SII is:  
\[SII=\sum_{i=0}^{n}I_{i}A_{i} \tag{1}\]  
where \(n\) is the number of individual frequency bands used for computing. Here, there is some flexibility in the definition of the SII standard [20] and it is possible to select the frequency measure bands (ranging from 6 [octave bandwidth] to 18 [critical bandwidth] bands). Generally speaking, the more frequency-specific your measures, the more accurate your computations. The \(I_{i}\) values, also known as the band importance function (BIF), are related to the importance for each frequency band to speech understanding and are based on specific speech stimuli. When they are summed across all bands, they are 1. The standard also allows some flexibility in using the most appropriate BIF for each situation. Finally, the \(A_{i}\) values, or band audibility function (BAF) -also ranging from 0 to 1-, indicate the proportion of speech cues that are audible in a given frequency band and its determination is based simply on the level of the speech, in a given frequency band, relative to the level of noise in that same band. For determining \(A_{i}\) a dynamic range of speech of 30 dB is assumed. Using the basic formula for calculating \(A_{i}\), it is possible to subtract the spectrum level of noise from the spectrum level of the speech (in dB) in a given band, add 15 dB (the assumed speech peaks), and divide by 30. Resulting values greater than 1 or less than 0 are set to 1 and 0, respectively. This value essentially provides the proportion of the 30-dB dynamic range of speech that is audible to the listener.  
Figure 5 provides a complete description of the SII algorithm based on ANSI standard [20], where the BIF are directly defined in the standard and the Equivalent Hearing Threshold levels \(T_{i}\) are the ones used in an average normal audition pattern. This \(T_{i}\) levels will modulate the BAF and combined with BIF, we obtain SII.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Needed for Computation** & **Regulation** \\ \hline RT60 (Reverb. Time 60 dB) & Impulse Response & ISO 3382-2 \\ C50 (Speech Clarity) & Impulse Response & ISO 3382-2 \\ C80 (Music Clarity) & Impulse Response & ISO 3382-1 \\ STI (Speech Transmission Index) & Impulse Response & IEC 60268-16 2003 \\ SII (Speech Intelligibility Index) & Audio signal & ANSI S3.5-1997 \\ \hline \hline \end{tabular}
\end{table}
Table 1: A set of room acoustic parameter, the source needed for computation and regulation if any.  
Figure 4: Band Importance function values for average speech SII calculation.