## 4 Data Analysis and Post-Processing  
Data analysis has been realized by using the software Adobe Audition CC, which illustrates contemporarily all the RIRs given by the 25 microphones, as reported in Figures 4 and 5. Both Figures 4 and 5 illustrate the direct sound recorded by all the microphones, as shown in a hyperbolic shape on the left of the screen. Based on the geometrical organization of the microphones, channel 13 is the closest to the sound source and hence it represents the first receiver recording the signal. As long as the other microphones are equidistant from the source (located symmetrically with respect to the main axis crossing the sound source, microphone 13 and the sample), the direct sound is recorded with a variable time delay, slightly increasing towards the extreme microphones (i.e., channel 1 and 25). The main characterization factor between the analysis undertaken for Room A and B is the reflected signals. In particular, for Room A the early reflections result was confused with that of the late reflections, while for Room B the early reflections are clearly identified at the center of the screen, with different energy intensities. This phenomenon is mainly due to the volume sizes of the rooms where the surveys have been performed: the small dimensions of Room A create an overlap of the early and late reflections, causing the windowing process as difficult to be carried out; in Room B the volume size was large enough to make a distinction between all types of reflections, in line with the standard. Section 5 shows and comments on how the results in Room A have been compromised by the vertical walls, albeit minimally--an outcome that is considered successful for the tests performed in Room B. Following the standard requirements, time windowing is a necessary process undertaken to select the early reflections related to each channel and discard the late or reverberant sound coming at a second stage. The windowing operation was implemented by using the software Adobe Audition 3.0. The plugin Aurora, suitable for all the versions of Adobe Audition, has been utilized to convert the sound wave from a time domain to a frequency domain through an FFT, in order to obtain all the sound levels at different frequencies and, hence, to calculate the diffusion coefficient. To estimate the values of the absorption (\(\alpha\)) and scattering (\(s\)) coefficients, a numerical model was required to compare the results. One of the assumptions applied to the model consists of the theoretical behavior that the digital entities should assume, to be considered ideal surfaces. This assumption is important to acquire an exhaustive comparison between the model and the curves obtained experimentally. The construction of the theoretical model follows the rules described by literature in previous studies [19]. Given the sound levels at each band of frequency, as recorded by the 25 microphones, the absorption (\(\alpha\)) and scattering (\(s\)) coefficients have been calculated by assuming the following:  
Figure 5: Example of a polar plot of RIR data measured inside Room B: direct sound on the left, early reflections in the center and late reflections on the right. * The direct sound was calculated by following the theory of sound propagation in free field conditions, as indicated in Equation (5); \[L_{p}=L_{w}-10 Log\Big{(}4\pi r^{2}\Big{)}=L_{w}-20 Log(r)-11\ \ [\text{dB}]\] (5)
* The reflected soundwave in the specular zone is obtained by the contribution of the specular reflected wave and the diffused reflected wave, as indicated in Equation (6); \[L_{diff+spec}=L_{w}-10 Log\Bigg{(}\left(\frac{S_{panet}}{4\pi r_{1}^{2}}\right) \frac{(1-\alpha)s}{2\pi r_{2}^{2}}\Bigg{)}+10 Log(\frac{(1-s)(1-\alpha)}{4\pi \big{(}r_{1}^{2}+r_{2}^{2}\big{)}^{2}})\] (6)
* The reflected soundwave out of the specular zone is given by the contribution of the diffuse energy only, as indicated in Equation (7).