# Perceptual Similarities between Artificial Reverberation Algorithms and Real Reverberation
## 2 Background
### Hybrid Moorer-Schroeder Implementation
#### 2.4.1 The Basic Mono Structure of the HMS Reverberation Algorithm  
The reverberation structures of the algorithm are shown in Figure 9. The filter coefficients in the dashed boxes change according to the reverberation time range shown in Table 4, and the lower limit of the time range for small-size-room reverberator is 0. The structures of the HMS algorithm mainly include an FIR delay line, comb filters, low-pass-feedback comb filters, all-pass filters, delay filters, and first order low-pass filters. The large-room HMS reverberation algorithm was modified by inserting a one-pole low-pass filter following the FIR delay line in the Moorer reverberation algorithm [6] to filter the high-frequency noise to smooth the audio [43]. Another all-pass filter was inserted between the all-pass filter and the delay filter to increase the number of echoes from the comb filter output and ensure that their phase characteristics cause minimal interference [27; 44]. Meanwhile, a further low-pass filter was added following the parallel low-pass-feedback comb filters to further reduce the high-frequency noise and simulate the air absorption [6; 43]. The parameter values of the FIR are the same as those for the Moorer reverberation algorithm shown in Table 2[6]. The gain values of low-pass filters 1 and 2 are 0.6 and 0.3, respectively. The low-pass feedback gain values for all low-pass feedback comb filters are 0.9. The parameter values of the other late reverberation filters are presented in Table 8. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Filter** & **Delay (s)** & \(\mathbf{RT_{60}}\) **(s)** \\ \hline LPF COMB1 & 0.082 & \(RT_{60}\) \\ LPF COMB2 & 0.093 & \(RT_{60}\) \\ LPF COMB3 & 0.113 & \(RT_{60}\) \\ LPF COMB4 & 0.123 & \(RT_{60}\) \\ LPF COMB5 & 0.145 & \(RT_{60}\) \\ LPF COMB6 & 0.203 & \(RT_{60}\) \\ ALLPASS1 & 0.005 & 0.09683 \\ ALLPASS2 & 0.0017 & 0.03292 \\ DELAY & 0.02/0.01 & - \\ \hline \hline \end{tabular} Note1: Reverb time (\(RT_{60}\)) is a user-oriented and adjustable parameter (range 0.1–5 s). Note2: DELAY value 0.02 is for large size room and 0.01 is for medium size room.  
\end{table} 
Table 8: Parameter values of the the late reverberation filters of the HMS reverberation algorithm for large and medium room sizes. Figure 8: Structure of Direction Feedback Delay Network (DFDN) [10]. The medium-room HMS reverberation algorithm was achieved by setting the gain (g) and delay coefficients (\(z^{-1}\)) of low-pass filter 2 to zero in the large-room HMS reverberation algorithm, as shown in Figure 10, effectively removing it from the algorithm. A study by [PERSON] et al. [45] indicated that the attenuation constant of air is usually important only in large rooms or at high frequencies; thus, further simulation of high frequency noise attenuation and air absorption is not necessary in medium and small rooms. The parameter values of the FIR are same as those for the Moorer reverberation algorithm shown in Table 2[6]. The gain value of low-pass filter 1 is 0.55. The gain value of the low-pass feedback of all low-pass-feedback comb filters is 0.9. The parameter values of the other late reverberation filters are presented in Table 8.  
The small-room HMS reverberation algorithm was improved by adding a Finite Impulse Response (FIR) delay line and a one-pole low-pass filter following the FIR delay line before the Schroeder reverberation algorithm [5]. Therefore, as in the medium-room HMS algorithm, the coefficients of low-pass filter 2 were set to zero in the large-room HMS algorithm, as shown in Figure 10. Furthermore, all gain (g and \(g_{L}\)) and delay coefficients (\(z^{-m}\) and \(z^{-1}\)) of low-pass-feedback comb filters 5 and 6 were set to zero, as shown in Figure 11, disabling low-pass-feedback comb filters 5 and 6.