# Interaural Coherence Estimation for Speech Processing in Reverberant Environment
## 3 Numerical Experiment and Results
### Optimal Parameter Determination  
Using the proposed IC estimation methods with \(\text{MAC}_{\text{total}}\), \(L_{\text{T}}\) and \(\beta\) were analyzed according to gender and frequency in various reverberation environments with RT\({}_{60}\). Numerical simulations were conducted to see the tendency of parameters according to gender, frequency, and reverberation time. In total, 3260 male and 1360 female speech samples of the training set were generated assuming a speaking situation in front of the dummy head in three different reverberation environments with 0.37 s, 0.69 s, and 0.79 s of RT\({}_{60}\), as shown in Table 1. STFT with a 25-ms Hamming window, 10-ms hop length, and 512-point fast Fourier transform (FFT), which are commonly used for general speech processing, was applied to the generated reverberant speech. First of all, to determine the \(L_{\text{T}}\) and \(\beta\) for the male speech, MACtotal was calculated at every 1-kHz interval for each STFT-applied 3260 reverberant male speech samples of the training set, and the parameters with the largest MACtotal were determined to be optimal. Since the range of MACtotal was different for each reverberant speech sample, to reduce the effect of different utterances, we calculated a histogram of the optimal parameters for each frequency interval. As an example, the histogram for the 3-4-kHz range of 3260 male speech samples in the reverberation environment of 0.37 s is shown in Figure 1. The optimal \(L_{\text{T}}\) and \(\beta\) values for each speech sample are distributed around the maximum point in the histogram. To determine the same IC estimation equation for various speech, we tried to determine the optimal parameters corresponding to the maximum point of the histogram. \(L_{\text{T}}=7\) and \(\beta=0.75\) for the maximum point could be estimated to be the optimal parameters. Around the optimum value of \(L_{\text{T}}(=7)\) and \(\beta(=0.7\text{-}0.8)\), the MACtotal was insensitive with variation less than or equal to 0.0001, which is small. In the same way, the optimum \(L_{\text{T}}\) and \(\beta\) of the 3260 male speech samples for a total of eight frequency intervals in three different reverberation environments were determined, and the results are shown in Figure 2. With less reverberation and with 0.37 s of RT\({}_{60}\), it is appropriate to use nine time-frequency bins at 0-1 kHz and seven bins at the other intervals, and \(\beta\) decreased from about 0.8 to 0.5 as the frequency increased. As the effects of reverberation increased to 0.69 s and 0.79 s of RT\({}_{60}\), \(L_{\text{T}}\) was nine or 11 bins and \(\beta\) was 0.9 or 1.0. \(L_{\text{T}}\) for all frequency intervals increased as the reverberation time increased, but it can be seen that \(L_{\text{T}}\) had a higher value from 0 kHz to 4 kHz regardless of the reverberation. \(\beta\) had high and steady values with all frequencies in a high reverberation time environment, but it decreased as the frequency increased in 0.37 s and 0.69 s of RT\({}_{60}\). This tendency \begin{table}
\begin{tabular}{c c c} \hline
**Room** & \(\mathbf{d_{\text{LM}}}\) & \(\mathbf{\text{RT}_{60}}\) \\ \hline Office & 1.00 m & 0.37 s \\ Stairway & 2.00 m & 0.69 s \\ Lecture room & 5.56 m & 0.79 s \\ \hline \end{tabular}
\end{table} 
Table 1: Properties of the various rooms. Figure 1: Histogram of 3260 reverberant male speech samples for \(L_{\text{T}}\) and \(\beta\) at 3 kHz to 4 kHz in RT\({}_{60}=0.37\) s based on mean accuracy of coherence (MACtotal). according to frequency and reverberation time can be used to estimate the parameters of male speech in other reverberation environments. Secondly, the same method based on the histogram was used to determine the parameters for the 1360 female speech samples.