# Echo Analysis in Iberian Bullfighting Arenas Through Objective Parameters and Acoustic Simulation 1
###### Contents  
* 1 Introduction
* 2 The transmission of sound between two points in a room is formally represented by the impulse response of the transmission path. This impulse response is composed of direct sound and the numerous repetitions of the original sound impulse caused by reflections of the sound signal at the boundaries of the room. With respect to the direct sound, each of these reflections is specified by its level and its time delay. Since our ear is also sensitive to the direction of incidence of sound, this description must be completed by indicating the direction from which each reflection reaches the receiving point. There may be differences in the spectrum, since the various components of the impulse response, strictly speaking, are not exact replicas of the original sound signal due to the frequency-dependent reflection coefficients of the wall faces. Two subjective effects of the reflected components of sound are known: the first occurring, under certain conditions, when said reflection can become an \"echo\" that is heard as a signal repeated over time that appears to come, subjectively, from another place than where the sound is located. This effect is due to the numerous acoustic signals delayed in time through a reflection on a surface, which reach the listener with sufficient energy compared to other sounds or reflections. This phenomenon can frequently be observed outdoors with sound reflections off the walls of houses or at the edge of forests. In closed spaces, these experiences are less common, since echoes therein are fortunately usually masked by the reverberation of the room. Whether a reflection will become an echo or not depends on its delay with respect to the direct sound, its relative level, the nature of the sound signal, and the presence of other reflections that eventually mask the reflection in question [1]. The other subjective effect refers to humans' ability to locate sound sources in closed spaces. Obviously, it is the sound signal that reaches the listener first that subjectively determines the direction from which the sound comes ([PERSON], law of the first wave front [2]). The enormous amount of information that characterises the impulse response must be condensed into certain parameters that summarise the situation in a subjectively meaningful way. This is carried out primarily by comparing the energies contained in the different parts of the impulse response. This procedure is not only an expedient dictated by practical limitations but is also justified by the limited ability of human hearing to distinguish between all the countless repeated sound signals. A reflection is not subjectively perceived as something separate from direct sound, as long as its delay and relative strength do not exceed certain limits. Its only effect is to make the sound source appear somewhat larger and increase the apparent loudness of the direct sound. Since these \"early reflections\" support the sound source, they are considered useful. Reflections that reach the listener with a longer delay are perceived as echoes in unfavourable cases; in favourable cases, they contribute to the reverberation of the room. In principle, any reverberation harms the intelligibility of speech because it blurs its temporal structure and mixes the spectral characteristics of successive phonemes or syllables. Therefore, \"late reflections\" are considered harmful from the perspective of speech transmission. From our everyday experience with outdoor echoes, but even more precisely from the results of [PERSON] [3] and similar findings, it can be concluded that the critical delay time separating useful reflections from harmful ones lies in the range from 50 to 100 ms. Typically, early reflections arriving within 50 ms relative to the direct sound improve the signal received by the listener. However, any early reflection that arrives after 50 ms can be perceived as a separate sound, with a disturbing effect. This is called an echo and gives the impression that the sound is repeated.