Inverse Problems and Sound Reproduction
Philip A. Nelson, Filipo Fazi, Keith Holland, and Takashi Takeuchi
A brief tutorial introduction will be given to the field of inverse problems. It transpires that several aspects of multi-channel sound reproduction can be analysed by using the theoretical framework provided by an extensive mathematical literature on this topic. An attempt will be made to explain important concepts such as ill-conditioning, regularisation and their implications in practical terms for the design of sound recording and reproduction systems. Such ideas can be most readily described with
reference to the design of systems of relatively low order, but extend naturally to systems with a multiplicity of channels, and ultimately, to systems consisting of continuous distributions of sources and sensors. The analytical tools available also fit naturally into the framework of spherical acoustics.