# Perceptual Similarities between Artificial Reverberation Algorithms and Real Reverberation
## 2 Background
### Delay Network Reverberation  
The traditional approach to synthesizing reverberation is based on delay networks combining feedforward paths to render early reflections and feedback paths to synthesize late reverberation [32]. One of the earliest and most famous reverberation algorithms was presented by [PERSON] in 1961 [5]; it has a simple structure consisting of four parallel comb filters and two series all-pass filters, as shown in Figure 1[27]. Natural reverberation consists of random closely-spaced impulse responses of exponentially decaying amplitude [33]. The first two conditions can be achieved by ensuring that the delay of each comb filter has no common divisor, and exponential decay can be achieved by making their reverberation times equal [5; 8; 34; 35; 36; 37]. The reverberation time of the comb filters is equal to the overall reverberation time. Therefore, according to [PERSON]'s recommendation [5; 27], the maximum to minimum delay ratio of the four comb filters is approximately 1.5 (especially between 30-45 ms) and the gain of the comb filters are adjusted to obtain the desired reverberation time. The two all-pass filters have delays of approximately 5 ms and 1.7 ms, respectively, and their gains are both adjusted to 0.7. In this study's implementation of Schroeder reverberation, the reverb time (\(RT_{60}\)) is a user-oriented and adjustable parameter (range 0.1-5 s). The filter delays (\(T\)) are set according to [PERSON]'s recommendations [5; 27], and the filter gains (\(g\)) are calculated from the delay time (\(T\)) and the reverberation time (\(RT_{60}\)) through Equation (1) [5]. The parameter values of each filter are presented in Table 1[38]. \[g=0.001^{(T/RT_{60})} \tag{1}\]  
[PERSON] enhanced the [PERSON] reverberation algorithm in 1979 [6] through four critical modifications, as shown in Figure 2[39]. The first improvement was a Finite Impulse Response (FIR) delay line inserted in order to simulate the early reflections of the RIR. Another modification was inserting a one-pole low-pass filter into the feedback loop of each comb filter to simulate the absorption of sound by air in order to decrease the reverberation time at high frequencies, making the sound appear more real. Here, this is called the low-pass-feedback (LPF) comb filter. The third improvement was to increase the number of comb filters from four to six in order to obtain higher echo and modal density, especially for longer reverberation times. Finally, [PERSON] replaced the all-pass filter near the output with a delay filter to ensure that the late reflections arrive at the output a little later than the early reflections. [PERSON] proposed parameters for all filters in his study [6]. As in [PERSON]'s reverberation algorithm, the random and closely spaced characteristics of pulses can be realized by ensuring that the delay of each comb filter has no common \begin{table}
\begin{tabular}{c c c} \hline \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 \hline \end{tabular} Note 1: Reverb time (\(RT_{60}\)) is a user-oriented and adjustable parameter (range 0.1–5 s).  
\end{table} 
Table 1: The parameter values of the [PERSON] reverberation algorithm [38]. divisor, while the exponential attenuation can be realized by making its reverberation time (\(RT_{60}\)) equal. Here, adjustments have been made to the parameters of the original low-pass comb reverberation filter. As in the Schroeder reverberation algorithm, the filter gain (\(g\)) is calculated from the delay time (\(T\)) and reverb time (\(RT_{60}\)) through Equation (1). The FIR parameter values are presented in Table 2[6]. The low-pass feedback gain values for all low-pass feedback comb filters are 0.9, and the values of the late reverberation filters are shown in Table 3[6].