# Late Reverberation Synthesis Using Filtered Velvet Noise +
## 8 Conclusion and Future Prospects  
This paper discussed the modeling of the late part of a measured room impulse response using filtered velvet-noise sequences. The idea here is to divide the impulse response into many non-overlapping segments of variable length and to approximate each segment using a spectral coloration filter and a sparse FIR filter having its coefficients taken from a velvet-noise sequence. The summed output of these filtering stages is further processed with a cascade of a few Schroeder allpass filters to increase the density and to smooth out the transitions between the segments. In this configuration, velvet-noise convolution can provide a smooth response even with very low pulse densities. Moreover, the sparsity of the velvet noise may vary along the reverberation tail so that towards the end, where the bandwidth gets narrow, the sequences are sparser. To obtain a realistic \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sound Type** & **Drums** & **Chords** & **Singing** & **Average** \\ \hline Identification & 99\% & 76\% & 84\% & 86\% \\ Quality rating & 2.1 & 3.9 & 3.3 & 3.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Identification of FVN approximation of reverberated sounds in the listening test. Figure 16: User interface of the ABX test with the 5-point difference rating used in the listening test. The verbal descriptions associated with each quality level appear on the right. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Concert Hall** & **Pori** & **Cologne Philharmonic** & **Vienna Musikverein** & **Average** \\ \hline Identification & 84\% & 85\% & 88\% & 86\% \\ Quality rating & 3.3 & 3.0 & 3.0 & 3.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Identification of the FVN approximation of different RIRs in the listening test. model of a target RIR, the coloration filters can be designed by applying linear prediction to the variable-length RIR segments. Additionally, this paper contributed a method to improve the computational efficiency of the FVN reverberation algorithm: the idea is to link the coloration filters so that each of them receives as the input the output of the previous stage. This way each segment only requires a differential coloration filter, which reduces the bandwidth sufficiently with respect to the previous stages. Instead of being a high-order IIR filter, each differential coloration filter is a second-order notch filter. The performance of the proposed algorithm was demonstrated with a modeling example, and the results showed that the algorithm is able to accurately model the overall characteristics of the target concert hall impulse response. The design procedure yields a flexible parametric approximation of the late part of the target impulse response, allowing for variations such as time-scale modification. Furthermore, the proposed reverberation algorithm is computationally efficient, providing a major advantage over the direct convolution: in the example case of 2-s RIR modeling, the proposed method reduces the computational cost by over 99.6% compared to direct convolution, and it is in this respect comparable to the best FFT-based partitioned convolution methods. Results of a subjective test were also reported, showing that the FVN approximations are often perceptually different from the original, but that the difference between the original RIR and its FVN approximation is considered small. The difference is easiest to observe when the audio signal contains transients, such as in drum sounds. However, the FVN method was observed to be equally well-suited for approximating long and short RIRs, as there was not much difference in the identification of different RIRs. The proposed method can be used to implement convolution reverberation in which instead of directly using the measured impulse response, its FVN model is implemented. This allows the possibility for parametric control of the impulse response characteristics.