# Late Reverberation Synthesis Using Filtered Velvet Noise +
## 1 Introduction  
Artificial reverberation research started in the 1960s, when [PERSON] developed the first methods to simulate the room effect with a computer [1; 2]. His methods plus numerous other approaches, which were introduced thereafter, have been reviewed by [PERSON] [3] and recently in a series of two papers by [PERSON] et al. [2; 4].  
Concert halls and listening rooms are often considered to be linear and time-invariant systems. Therefore, it should be possible to fully reproduce their sonic characteristics by replicating the impulse response, which is measured between a source and a listening point. A room impulse response (RIR) is often divided into three phases: the direct (or dry) sound, early reflections, and the late reverberation. This paper focuses on the modeling of the late reverberation, which is noise-like and contains the contribution of a large number of reflections.  
Convolution with a measured RIR is a popular technique resulting in very realistic reverberation [2; 4; 5]. However, convolution is computationally intensive, and modification or parameterization of the measured RIR can be cumbersome. Partitioned fast convolution methods [6; 7; 8; 9] reduce the computational complexity considerably compared to direct convolution and avoid most of the delay introduced by the basic fast convolution, which corresponds to a full-scale FFT(Fast Fourier transform)-based implementation. [PERSON] suggested that the late part of the RIR can be well characterized as exponentially decaying white noise [10]. This observation led to useful applications whenRubak and [PERSON] used a finite-impulse response (FIR) filter with random coefficients in a recursive reverberation algorithm [11; 12]. [PERSON] and [PERSON] developed an improved algorithm in which a random coefficient FIR filter is cascaded with a lowpass comb filter [13]. They also introduced velvet noise, which is smooth-sounding [PERSON] random noise [13]. Later, [PERSON] et al. [14] and [PERSON] et al. [15] investigated alternative recursive reverberator structures using velvet noise.  
This paper focuses on room reverberation modeling using velvet noise, extending our previous work [16; 17]. The RIR is divided into short segments and each of them is approximated as a filtered velvet noise (FVN) sequence. The coloration filters and their associated gain account for the spectral shape and level of each RIR segment, so together they enable the approximation of a given frequency-dependent decay behavior in the time domain. Finally, cascaded Schroeder allpass filters are used to obtain a smooth, wideband, noise-like response. This approach is thus orthogonal to the modal filter bank idea, which divides the RIR into slices in the frequency dimension [18; 19], and to [PERSON]'s idea of estimating the reverberation time across frequency bands [20] and calibrating a feedback delay network reverberator [21; 22]. Such methods are best suited for exponentially decaying responses.  
This FVN approach leads to a parametric representation and computationally efficient RIR synthesis, since convolution with velvet noise is economical to implement[PERSON] A novel idea is proposed to cascade the coloration filters, so that the effect of all filtering operations of the previous stages are accounted for by using differential filters in the subsequent stages.  
The rest of this paper is organized as follows: Sections 2 and 3 discuss velvet noise and the basic version of the FVN method, respectively, and Section 4 describes a new differential filtering strategy and an impulse response segmentation strategy for it[PERSON] Section 5 shows how well the algorithm can synthesize the impulse response of a real concert hall, and how the synthetic response can be modified. Section 6 compares the computational complexity and memory usage with other algorithms, and Section 7 presents a subjective evaluation of the proposed method. Section 8 concludes this paper.