On the conditioning of the propagation function in a near-field loudspeaker array

This paper presents an algorithm for computing the weights of a loudspeaker array based on a given set of listening locations and their respective desired sound field distribution. We achieve this by introducing the E-norm condition number to control the desired sound field distribution for our application. We show that the conditioning of the problem is determined by this E-norm condition number and that part of the computation of this number is independent of frequency. Exploiting this intrinsic property and through the use of an optimization algorithm, we develop an efficient algorithm for the computation of array weights to achieve desired sound field distribution in the spatial domain. The proposed algorithm can also be used to search for a set of alternative listening locations that give rise to a well-conditioned solution for the loudspeaker weights.