## 3 Results and Discussions
(**a**) Room 2; (**b**) Room 1; (**c**) Room 3; (**d**) Room 5; (**e**) Room 4; (**f**) Room 12.  
coherence function as defined in Equation (7) was evaluated. The signals were divided into 100 segments, each segment with a Hamming window of equal bandwidth, in addition a 50% overlap between segments was used. A total of 129 discrete Fourier transform (DFT) points were set, and a frequency range for the estimation of magnitude-squared coherence from 0 to Fs/2 (Fs = 44,100 Hz). Fs is the sampling frequency, that is the number of samples per second. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Frequency, Hz**} \\ \hline  & **125** & **250** & **500** & **1000** & **2000** & **4000** \\ \hline T\({}_{30}\), room 1 (s) & 0.60 & 0.63 & 0.64 & 0.77 & 0.75 & 0.74 \\ T\({}_{30}\), room 2 (s) & 0.85 & 0.90 & 0.92 & 1.06 & 1.09 & 0.93 \\ T\({}_{30}\), room 3 (s) & 2.40 & 2.50 & 2.60 & 2.75 & 2.80 & 2.45 \\ T\({}_{30}\), room 4 (s) & 0.73 & 0.75 & 0.79 & 0.67 & 0.69 & 0.57 \\ T\({}_{30}\), room 5 (s) & 0.69 & 0.73 & 0.77 & 0.87 & 0.86 & 0.78 \\ T\({}_{30}\), room 6 (s) & 0.65 & 0.68 & 0.70 & 0.82 & 0.84 & 0.75 \\ T\({}_{30}\), room 7 (s) & 0.63 & 0.65 & 0.68 & 0.75 & 0.83 & 0.80 \\ T\({}_{30}\), room 8 (s) & 0.83 & 0.85 & 0.90 & 0.81 & 0.70 & 0.60 \\ T\({}_{30}\), room 9 (s) & 0.38 & 0.39 & 0.40 & 0.51 & 0.43 & 0.39 \\ T\({}_{30}\), room 10 (s) & 0.59 & 0.65 & 0.69 & 0.71 & 0.64 & 0.59 \\ T\({}_{30}\), room 11 (s) & 0.34 & 0.35 & 0.37 & 0.50 & 0.52 & 0.52 \\ T\({}_{30}\), room 12 (s) & 0.70 & 0.72 & 0.74 & 0.86 & 0.83 & 0.74 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Reverberation time in the octave band measured in some of the rooms used in this study (s). Figure 6: Magnitude-squared coherence estimation for the signals recorded in twelve rooms. Each curve refers to the same reproduced signal (white noise) and is calculated as function of the power spectral densities, and the cross power spectral density, as reported in Equation (6). After calculating the coherence function for the signals recorded in the selected rooms, the records were labeled by associating each sequence with the value of the reverberation time in octave bands as reported in Table 3. At the end, a dataset with 720 observations and 131 features was obtained. The 720 observations refer to the signals recorded in the twelve rooms, while the 131 features represent the components at different frequencies of the magnitude-squared coherence. At this point, the processed dataset can be used to train an algorithm based on supervised learning. The reverberation time prediction model developed is based on a multi-level artificial neural network, feed-forward type, with 1 hidden layer (with 10 neurons) and an output that represents the reverberation time. In feed-forward networks, information moves in one direction only, forward, from the input nodes, through the hidden nodes until it reaches the output nodes, without creating loops in the network. To provide the system with the ability to generalize, the data were divided into three groups, the selection was performed randomly [42; 43]. This selection divides the data randomly into three subsets as follows:  
* 70% of the available observations were used to create a training set. This subset is used by the network during training where the connection weights are adjusted according to the error made on the output production. This set contains 504 observations. * 15% of the available observations are used to create a validation set. It is a set of examples used to optimize the parameters of a classifier to find the \"optimal\" number of hidden drives or to determine a checkpoint for the back-propagation algorithm. This set contains 108 observations. * 15% of the available observations are used to create a test set. This is a set of examples used only to evaluate the performance of a fully trained classifier to estimate the error rate after choosing the final model. This set contains 108 observations.