Efficient synthesis of large room impulse responses in the modal domain

An efficient methodology for synthesising large-scale room impulse responses (RIRs) is presented, operating entirely in the modal domain. The approach proceeds in two stages: an analysis phase, wherein modal parameters are extracted from measured RIRs using a frequency-domain sub-band implementation of the PolyMAX algorithm; and a synthesis phase, based on time-stepping of a second-order modal equation discretised via a low-dispersion finite difference scheme. The procedure yields a structured parametric model consisting of modal frequencies, decay rates, and shape factors, directly interpretable in physical terms. Sub-band fitting is employed to accommodate high modal densities and broadband content, with stabilisation diagrams used to isolate physically relevant poles. The method is applied to both synthetic and measured responses acquired in three large historical spaces. Results indicate close agreement with the target responses in both frequency and time domains, along with substantial reductions in computational cost. The modal representation further permits statistical post-analysis of decay behaviour and supports real-time synthesis on commodity hardware. The overall framework offers a scalable alternative to traditional numerical solvers for room acoustics modelling.