Weighted Pressure and Mode Matching for Sound Field Reproduction: Theoretical and Experimental Comparisons

TL;DR

This paper compares weighted pressure and mode matching methods for sound field reproduction, both theoretically and experimentally, highlighting their differences and relationships through advanced mathematical analysis.

Contribution

It introduces a generalized framework for sound field reproduction methods using weighting matrices and establishes the theoretical connection between pressure and mode matching.

Findings

Weighted pressure matching is a special case of weighted mode matching.

Experimental results compare the effectiveness of both methods.

Theoretical analysis shows the relationship via infinite-dimensional harmonic analysis.

Abstract

Two sound field reproduction methods, weighted pressure matching and weighted mode matching, are theoretically and experimentally compared. The weighted pressure and mode matching are a generalization of conventional pressure and mode matching, respectively. Both methods are derived by introducing a weighting matrix in the pressure and mode matching. The weighting matrix in the weighted pressure matching is defined on the basis of the kernel interpolation of the sound field from pressure at a discrete set of control points. In the weighted mode matching, the weighting matrix is defined by a regional integration of spherical wavefunctions. It is theoretically shown that the weighted pressure matching is a special case of the weighted mode matching by infinite-dimensional harmonic analysis for estimating expansion coefficients from pressure observations. The difference between the two methods are discussed through experiments.