A monte-carlo study on the convergence of Multipole-Matched audio Rendering

Multipole-Matched Rendering (MMR) is a novel method to render spatial audio in a sweet spot around a listener´s head. It is based on matching multipole expansions of a virtual and several actual sound sources using the Singular-Value Decomposition of a matrix. A critical parameter of the algorithm is the number of radial modes used in the multipole expansion. It is computationally expensive to determine convergence based on actual sound source renderings. This paper shows that in order to detect convergence of the algorithm when increasing the number of radial modes, looking at the difference of the matrix condition numbers of two subsequent computations is sufficient. A Monte- Carlo experiment has been designed to verify this. Results show that using the condition number is a valid and efficient way to determine convergence and additionally give a heuristic estimate on the number of radial modes required for convergence in a typical immersive environment setup.