A method for calculating reverberation time from musical signals

by Martin Hansen

The following document is the abstract of the Report "A method for calculating reverberation time from musical signals" from The Acoustics Laboratory, Technical University of Denmark.
(Now "Department of Acoustic Technology")


The reverberation time is the oldest measure in room acoustics and accordingly several methods and many improvements of them have been developed to determine this quantity. Sabine, as the first to investigate reverberation time, used organ pipes to excite the room and his hearing to determine when the sound had become inaudible. Although he did not have other equipment, this was very appropriate because the investigations in room acoustics are closely related to human beings' perception of music (or speech). The commonly used method nowadays, using loud impulses from pistol shots or noise radiated into the room by loudspeakers, makes it difficult to measure reverberation times in rooms that are occupied with an audience. On the other hand, the audience changes the reverberation time and it is therefore not possible to measure the relevant reverberation time without audience. This is the reason, why room acousticians have always been interested in methods to measure the reverberation time with audience in the hall. The maximum length method (Schroeder, 1979) provides a possibility of measuring the reverberation time while a concert is being played and with an audience present because it is possible to measure with the maximum length sequence noise at an inaudible level. On the other hand this makes it necessary to use a long measuring time in order to achieve enough dynamic in the decay curve.

Concert halls and lecture rooms are built for the purpose of an optimal performance of music or speech. In addition to a number of room acoustical criteria that have been developed to describe the acoustical qualities of a room with respect to human listeners, it is well-known that a room requires the right value of the reverberation time to provide good musical or speech reception. Whether a hall has the right value of the reverberation time or not is judged in the situation when it is occupied with audience and with music or speech as the sound signal being heard. A listener can perceive the reverberance of a hall when he listens to music or speech and even an untrained listener can judge whether the reverberation time is too long or too short. Among musically trained people there is agreement about the need of different reverberation times for optimal performance of music of different styles.

This leads to the idea that the information about the reverberation time of the room must be integrated into the reverberated music or speech signal in some way. In earlier approaches (Polack, 1982; Simon, 1987; Eilemann, 1989) it was also tried to use music as the source signal for investigations on the properties of rooms. These works were based on comparisons of two signals, one signal recorded very close to the sound source and one further away in the room. The method proposed in this work is in contrast based on the autocorrelation function of a reverberated musical signal. The autocorrelation function is highly related to the correlation length of a signal. It is shown that the reverberation time may be defined as the correlation length of the impulse response function. A room with a long reverberation time will force the reverberated music signal to have a larger correlation length than a room with a smaller reverberation time. This effect can be used to determine the reverberation time from real music played in the hall (Hansen, M. and Püschel, D., 1992; Hansen, M. and Püschel, D.,1993)

In the first part of this work a short theoretical consideration is given of why it is possible in principle to determine the reverberation time from the autocorrelation function of a room impulse response function instead of from the impulse response itself. The measurement and the comparison between this method called autocorrelation function method and well-known methods and the results obtained using only reverberated music are presented in the following sections.

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