|Thesis abstract: |
In this thesis we propose a novel approach to wave field analysis and synthesis based on the geometric description of a sound field. Under the hypothesis of homogeneous medium, wave propagation can be approximated by means of acoustic rays that originate from a point source and spread in all the directions. The interaction with the environment causes the rays to reflect over the obstacles following the geometrical acoustic laws. Contiguous bundle of rays can be represented as acoustic beams that split and branch during the propagation as they encounter reflectors. An acoustic wave field can be seen as the superposition of acoustic beams, each characterized by the origin (source), direction and angular aperture. Due to the projective nature of rays, the most suitable tool for their representation is projective geometry, which gives also a compact and efficient description of more complex acoustic entities such as sources, receivers, reflectors and beams.
As far as the wave field analysis is concerned, projective geometry makes it possible to convert standard acoustic measurements (TOAs, TDOAs, DOAs) into homogeneous quadratic constraints, which all share the same mathematical formulation. This way, through the combination of multiple constraints it is possible to formulate a cost function whose form is equivalent for several estimation problems, ranging from standard ones (e.g. acoustic source localization), to novel ones such as the inference of the geometry of the environment.
As far as the sound field synthesis is concerned, the geometric description of a wave field leads to developing a methodology that aims at reproducing a complex wave field by superimposing elementary beams rendered by means of a loudspeaker array. The knowledge of the map of the environment, which can be estimated in the analysis stage, can be exploited to compensate for the environment hosting the loudspeakers, thus making the rendering system environment-aware. In particular, the reverberations (in terms of early reflections) are seen as determined by a set of image loudspeakers, which are inserted into the model and contribute to the reproduction of the wave field.
This thesis also includes various novel validation methodologies for the proposed techniques. As far as wave field analysis is concerned, we show that it is possible to predict the accuracy of estimation algorithms as a linear mapping between the error on the measurements and the estimation error. As for the sound field synthesis, we propose a methodology for assessing the quality of wave fields reproduced by real loudspeakers. The wave field is sampled over a circle with a pair of rotating microphones and extrapolated by means of the circular harmonic decomposition. The deviation between the extrapolated and the expected wave fields are then evaluated by means of standard (MSE-based) and novel (modal analysis) metrics. In this thesis we also show the results of some simulations and experiments of room compensation and virtual environment rendering.
The solutions proposed in this thesis find potential application in a wide range of fields, including advanced telecommunications (telepresence), immersive gaming, distributed music production, spatial audio at home.