Generation of diffuse acoustic modes using prolate spheroidal wave functions

In a diffuse field, the undamped eigenvalues of a diffuse wave field with uncertain local wave scattering properties conform to those of a Gaussian Orthogonal Ensemble (GOE) matrix, while the mode shapes are Gaussian random fields. With the GOE based Monte Carlo (GOE-MC) approach, the probability distribution of the response in a diffuse field can be obtained by computing realizations for the natural frequencies and mode shapes of the diffuse system component. This paper focuses on the generation of diffuse acoustic modes, which is based on an eigenvalue decomposition of the covariance matrix. The corresponding eigenvalue problem can be solved numerically, but this is computationally expensive, especially if the number of source, receiver, or interface points increases. An analytical solution based on prolate spheroidal wave functions is therefore presented. This approach is numerically validated for (correlated) point sources in a diffuse room and experimentally validated for a PMMA plate radiating sound into an adjacent room.