# Perceptual Similarities between Artificial Reverberation Algorithms and Real Reverberation
## 2 Background
### Delay Network Reverberation
[PERSON] proposed a set of reverberation algorithms aimed at simulating the reverberation effects of different room sizes [7]. These algorithms share three similar structures for different sizes of room (small, medium, and large) with different reverberation times [40]. These three reverberator structures are shown in Figures 3-5, respectively [7,27], and their corresponding reverberation time ranges are presented in Table 4[7]. The structures of these three algorithms mainly include all-pass filters (simple and nested), delay filters, and a first-order low-pass filter. In this study's implementation of the Gardner reverberation, the delay length of each filter is adjusted somewhat to better match the correct reverberation time. The corresponding parameter values for each filter are presented in Table 5[7]. \begin{table}
\begin{tabular}{c c} \hline
**Gardner Reverberator Structures** & **Reverberation Time Ranges (s)** \\ \hline Small-size-room reverberator structure & \(0.38\leq RT_{60}\leq 0.57\) \\ Medium-size-room reverberator structure & \(0.58\leq RT_{60}\leq 1.29\) \\ Large-size-room reverberator structure & \(1.30\leq RT_{60}<\infty\) \\ \hline \end{tabular}
\end{table} 
Table 4: The corresponding reverberation time ranges for each Gardner reverberator [7]. \begin{table}
\begin{tabular}{c c c} \hline
**Tap** & **Delay (s)** & **Gain** \\ \hline  
\hline \end{tabular}
\end{table} 
Table 2: The parameter values of the early FIR of the Moorer reverberation algorithm [6]. \begin{table}
\begin{tabular}{c c c} \hline
**Filter** & **Delay (s)** & **\(RT_{60}\) (s)** \\ \hline LPF COMB1 & 0.04 & \(RT_{60}\) \\ LPF COMB2 & 0.041 & \(RT_{60}\) \\ LPF COMB3 & 0.043 & \(RT_{60}\) \\ LPF COMB4 & 0.055 & \(RT_{60}\) \\ LPF COMB5 & 0.059 & \(RT_{60}\) \\ LPF COMB6 & 0.061 & \(RT_{60}\) \\ ALLPASS1 & 0.007 & 0.09683 \\ DELAY & 0.0017 & - \\ \hline \end{tabular} Note1: Reverb time (\(RT_{60}\)) is a user-oriented and adjustable parameter (range 0.1–5 s).  
\end{table} 
Table 3: The parameter values of the the late reverberation filters of the Moorer reverberation algorithm [6]. Figure 4: The structure of the Gardner reverberation algorithm for medium size room [7]. Figure 5: The structure of the Gardner reverberation algorithm for large size room [27]. Figure 3: The structure of the Gardner reverberation algorithm for small size room [7]. Feedback Delay Network (FDN) was proposed by [PERSON] in 1992 [8]. It consists of N-dimensional delay lines and a feedback matrix, as shown in Figure 6[10; 27; 41]. As a novel and versatile reverberator design structure, it provides separate and independent control of the energy storage, damping, and diffusion components of the reverberator [42]. Compared with parallel comb filters, this feedback structure can generate much higher echo density given a sufficient number of non-zero feedback coefficients and delay lengths [41]. In this paper, we adopt four-dimensional delay lines. In this structure, following [PERSON]'s advice [5], the delay length (\(m_{i}\)) of each delay line is derived from a prime power exponential delay Equations (2) to (5). The gain (\(g_{i}\)) for each delay line is calculated from a given reverberation time (\(RT_{60}\)) and sample rate (\(Fs\)) by Equations (6) to (8) according to [PERSON]'s [10] suggestion. The feedback matrix (\(A\)) is implemented by a fourth-order Hadamard matrix.