On the consistent use of space and time conventions in array processing

Processing of microphone arrays of various configurations involves mathematical models of the surrounding sound fields. These models are based on different space and time conventions found throughout the literature. In traditional open array processing, interchanging different space and time conventions can lead to confusion between the arrival and propagation directions. This is relatively easy to observe and adjustments can be made as necessary. However, in the case of spherical arrays, which are a more recent subject of research, the consequences of interchanging between the conventions are not so straightforward. In this paper, an analysis of the misuse of space and time conventions in array processing is presented, with special emphasis on the new results for spherical array configurations. It is shown that, in addition to the reversal of propagation direction, a misuse of notation has the potential of introducing a significant error in the array directivity pattern.