Chapter 6 - Room reverberation theory and transfer function

Abstract

Room reverberation theory provides a theoretical basis of sound fields in rooms. Room acoustics has been investigated following geometrical acoustics or wave theory analysis. The geometrical approach represented by the reverberation time is useful for the design of acoustic space from the macroscopic perspective of sound space. In contrast, the wave theory approach, such as modal analysis, explores fine structures of sound fields and the distribution of eigenfrequencies. Spatial- and frequency-band averaged behavior of sound waves in rooms can be expressed according to the geometrical acoustics. This chapter derives a hybrid formulation of geometrical and wave theory representations of room reverberation. On the other hand, the linear-system theory can unify the two types of approaches, where impulse responses in rooms can be formulated according to the geometrical acoustics, and modal analysis based on the wave theory gives the frequency responses in the sound fields in rooms. The transfer function is defined by the z−transform for the impulse response of a discrete system's well develop audio-engineering technologies, such as room reverberation simulators or equalizers of the sound transmission path in a room. Decomposition of the transfer function into the minimum-phase and all-pass components forms the theoretical basis for the development of audio engineering on room acoustics. This chapter describes the transfer function in terms of poles and zeros, as well as the frequency characteristics of reverberation in rooms.