# Perceptual Similarities between Artificial Reverberation Algorithms and Real Reverberation
## 2 Background
### Hybrid Moorer-Schroeder Implementation
#### 2.4.2 The Binaural Optimised Structure of Reverberation Algorithms  
In order to realise binaural audio, all reverberation algorithms mentioned in Sections 2.3 and 2.4.1 were optimised with two channels to generate binaural reverberation, as shown in Figure 13. Here, the mono input is the output of the above seven reverberation algorithms. First, the above mono structures are regarded as the left channel of the binaural reverberation algorithm, and the difference between right channel and left channel is achieved through a random constant as the delay parameter (_Delvar_). The parameter _Delvar_ is set to 0.1 in this paper, though it can be adjusted. The filter delay parameters for the right channel reverberation structure are implemented by Equation (13):  
\[\delta\_right=\delta\_left\times(1+\Delta) \tag{13}\]  
where \(\delta\_right\) is the delay parameter for all filters in the right channel, \(\delta\_left\) is the delay parameter for all filters in the left channel, and \(\Delta\) is the random delay parameter mentioned above. \begin{table}
\begin{tabular}{c c c} \hline
**Filter** & **Delay (s)** & **\(RT_{60}\) (s)** \\ \hline COMB1 & 0.0297 & \(RT_{60}\) \\ COMB2 & 0.0371 & \(RT_{60}\) \\ COMB3 & 0.0411 & \(RT_{60}\) \\ COMB4 & 0.0437 & \(RT_{60}\) \\ ALLPASS1 & 0.005 & 0.09683 \\ ALLPASS2 & 0.0017 & 0.03292 \\ \hline \end{tabular}
\end{table} 
Table 9: Parameter values of the the late reverberation filters of the HMS reverberation algorithm for small rooms. Figure 11: The structure of the low-pass feedback comb filter in the large-room HMS reverberation algorithm. Figure 10: The structure of the low-pass filter in the large-room HMS reverberation algorithm. Figure 9: The structure of the HMS reverberation algorithm, where the part A is the FIR delay line for simulating early reflections and the part B that is composed of different filters is to simulate late reverberation. Next, the Interaural Cross-correlation Coefficient (IACC) of the left channel and the right channel are matched with a measured BRIR through a channel correlation parameter (_corr_scale_) as Equation (14). Interaural Cross-Correlation is a measure of the difference between the signals received by a person's two ears that measures the spaciousness of the listening room and the listener's envelopment [46]. Large IACC values correspond to greater degrees of envelopment and a more enjoyable overall listening experience in auditoriums [47]. \[Imp\_IACC=Imp+Imp\_flipped\times corr\_scale \tag{14}\]  
where \(Imp\) is the output binaural impulse response (two columns) from reverberation algorithms, \(Imp\_flipped\) is the flip column of the output binaural impulse response around the vertical axis in the left-right direction, \(Imp\_IACC\) is the output binaural impulse response after matching IACC, and \(corr\_scale\) is the channel correlation parameter mentioned above. The minimum phase reconstructed version of the 0 degree azimuth and 0 degree elevation HRIR from Subject D1 of the SADIE II database is added as the direct sound component [48]. The minimum-phase version is taken to ensure the energy of the impulse response is moved to the start of the filter, implemented via the reps function in MATLAB. The timbre of the reverberation is then matched to the measured BRIR. Timbre matching is performed separately for the left and right channels, and is only performed on the reverberation, not on the direct sound. IRs from the reverberators are extracted and the root mean square value in Equivalent Rectangular Bandwidth (ERB) bands is compared to the measured IR using a 4096 tap ERB linear phase filter bank with 24 bands. The difference in each band is then computed and the algorithmic reverb is scaled by the difference. Outputs from the filterbank are then summed and the direct sound is added. Finally, the direct-to-reverberant (D/R) energy ratio of the impulse response generated by the reverberation algorithm is matched with the measured BRIR.