Performance Evaluation of Adaptive Algorithms for Wave Field Analysis/Synthesis Using Sound Field Simulations

Abstract

The main objective of a multi-channel sound reproduction system is to give an optimal acoustical sensation to the listener. These systems are designed to produce sounds that are as natural as possible, so that the listener does not realize that they are generated by a loudspeakers system. For this purpose, the knowledge of only audio temporal information is not sufficient: also spatial information is needed. Furthermore, since the invention of stereophony, it is well known that at least two loudspeakers are needed in order to generate a virtual source that is not spatially localized at the speaker position. However, the stereo reproduction is very limited because the optimal source localization is focused on one point, called sweet spot. Starting from this assumption, in the recent literature, research efforts have focused on reproduction techniques that use an extremely high number of loudspeakers in order to reproduce not only a simple audio source but a complete sound field. Various techniques, able to record and to reproduce the entire sound field, have been proposed in the literature (Berkhout et al., 1993; Daniel et al., 2003; Fazi et al., 2008). One of the most studied techniques is Wave Field Synthesis (WFS) that is directly based on the Huygens’ principle. It has been introduced in the late ’80s by Berkhout, who showed that audio reproduction can be linked to audio holography concepts (Berkhout, 1988). WFS is based on Kirchhoff-Helmholtz integral which permits the calculation of the pressure field inside a volume by knowing pressure and normal particle velocity on the enclosing surface. The underlying idea of WFS is to generate a sound field inside a volume bounded by an array of loudspeakers. Actually, the surface is reduced to a 2D curve positioned on the ear plane. The number of loudspeakers on this curve depends on the desired localization quality. Similarly, Wave Field Analysis (WFA) implements a sound field recording technique based on microphone arrays (Hulsebos et al., 2002). Therefore, this approach allows to record the entire sound field in the recording room (WFA) and subsequently to reproduce it in the listening room (WFS) more or less accurately depending on loudspeakers/microphones number. As it happens in traditional reproduction systems, digital algorithms based on adaptation processing have to be applied inside the WFS/WFA in order for these techniques to be used in real applications (music, cinema, theatre, etc.). Examples of adaptive algorithms that are very useful in real applications are Acoustic Echo Cancellation (AEC), Active Noise Control (ANC), room compensation, etc. (Haykin, 1996). A straightforward implementation of these algorithms in WFA/WFS systems is not feasible due to the dramatically high 25