A short review of signals and systems for spatial audio

Processing of one-dimensional signals for all kinds of applications is based on the mature theory of signals and systems. On the other hand, processing methods for acoustical signals have been developed in quite diverse application fields like seismic engineering, sonar, audio engineering, and communication acoustics. Similar techniques and algorithms appear under different names and with different notation. This short course tries to unify some of the general concepts of acoustical signal processing. First, it covers some basics from multidimensional signals and systems. By considering the acoustic wave equation as description of a special multidimensional system, its solutions can be represented in various domains regarding time, space, and their associated frequency domains. Spatial descriptions in various coordinate systems and their corresponding Fourier transforms are discussed.