**1. Introduction**

Reverberation results from pairing a sound source with an acoustic space. After emanating from the source, a sound wave will interact with its environment, undergoing reflection, diffraction and absorption. Thus, a listener will receive filtered replicas of the original wavefront (echoes) arriving from various directions at different times, causing the impression that the original sound persists in time. According to the so-called precedence effect, the direct sound allows a listener to determine the position of the sound source, while early reflections are generally not perceived as distinct auditory events [1–3]. As stated by Wallach et al. [1], the maximum delay after which a reflection is no longer 'fused' with the direct sound depends on the signal, being around 5 ms for single clicks and as long as 40 ms for complex signals such as speech or music [4]. Nevertheless, early reflections can broaden the perceived width of the source and shift its apparent position, as shown experimentally by Olive and Toole [5]. Furthermore, they can modify the signal's spectrum due to phase cancellation and subsequent comb filtering, as shown by Bech in his study on small-room acoustics [6]. Such phenomena can alter the perception of the room on a higher level. For example, Barron and Marshall [7]

argued that the timing, direction of arrival, and spectra of early lateral reflections contribute to the sense of 'envelopment'—defined as the 'subjective impression of being surrounded by the sound'. The time delay between the direct sound and the first distinct echo has also been shown to be a relevant feature: in the case of small rooms, Kaplanis et al. [8] found that it was correlated with the perception of environment dimensions and 'presence'—or 'sense of being inside an enclosed space and feeling its boundaries'—while in the case of concert halls, Beranek [9] linked it to a sense of 'intimacy'.

As time passes and the sound waves that emanated from the source continue interacting with the environment, the temporal density of echoes increases, and the resulting sound field becomes more diffuse. At this point, temporal and spatial features of individual echoes become less relevant, and late reverberation can be characterised as a stochastic process. An important parameter used to define such process is the reverberation time (RT), or the 'duration required for the spaceaveraged sound energy density in an enclosure to decrease by 60 dB after the source emission has stopped' [10], which is generally proportional to the volume of the room. Yadav et al. [11] suggested that RT contributes to the perception of environment dimensions most significantly in large spaces, whereas early reflections have greater importance in small rooms. Although late reverberation is often modelled as diffuse and isotropic (i.e., with an even distribution of energy across directions from the listeners' point of view). Alary et al. [12] showed that this assumption may not always hold and directionality should be taken into account, especially for asymmetrical spaces, such as a corridor.

When reproduced binaurally (e.g., through headphones), it has been shown that reverberation increases the sense of externalisation, i.e., the illusion of virtual sound sources being outside the head, when compared to anechoic sounds [13, 14]. It has been suggested that this effect can be achieved even by just adding the early reflections [13], while the contribution of late reverberation (>80 ms) is smaller in comparison [15]. Previous studies have looked into the contribution of both monaural and binaural cues to the externalisation of reverberant binaural signals. Monaural cues have been shown to have limited importance by Hassager et al. [16] and Jiang et al. [17], who argued that spectral detail is not as critical in the reverberant sound as it is in the direct sound. Regardless, it has been reported that applying spectral correction (headphone equalisation) to binaural signals could increase externalisation and other subjective attributes when employing headphones with limited reproduction bandwidth [18, 19]. Binaural cues, on the other hand, have been shown to be critical: Leclere et al. [14] suggested that reverberation increases externalisation of a binaural signal as long as interaural differences are introduced. This is supported by Catic et al. [15], who reported a considerable decrease in externalisation when the reverberant part of auralised speech was presented diotically. Such effects have been linked to specific binaural cues, such as interaural level differences (ILDs) and interaural coherence (IC). Recent studies have reported correlations between the level of externalisation and the amount of temporal fluctuations of ILDs and IC in the binaural signals [14, 15, 20]. Moreover, Li et al. [21, 22] highlighted the importance of reverberation specifically in the contralateral ear signal, showing a stronger contribution to externalisation than its ipsilateral counterpart, which is explained by the fact that reverberation is proportionally louder on the contralateral side due to the head shadow effect. Finally, according to the 'room divergence effect', externalisation of simulated binaural signals increases when the rendered reverberation matches the listener's expectations given their prior knowledge of the room [23–25]. Head movements and vision also play an important role in spatial audio perception [26], but they are not covered here—for a thorough review on sound externalisation, the reader is referred to Best et al. [27].

*Reverberation and its Binaural Reproduction: The Trade-off between Computational… DOI: http://dx.doi.org/10.5772/intechopen.101940*

In summary, reverberation greatly influences how a listener perceives an auditory scene by providing information on the room characteristics, the size and location of the sound sources and, in the case of binaural simulations, affecting the level of externalisation. Consequently, it should be modelled carefully when producing realistic acoustic simulations, although this can prove to be a challenging task in real-time systems with limited resources. The next sections of this chapter will address the issue of balancing computational efficiency and perceptual quality when simulating reverberation.
