Convex-optimization-based post-processing for computing room impulse response by frequency-domain FEM

Abstract

Numerical simulation of impulse responses is an important task for room acoustic design and prediction. Since an impulse response is a concept in the time domain, time-domain simulation methods are popular for this task. At the same time, frequency-domain simulation methods are also used for simulating a room impulse response by computing frequency responses and applying the inverse discrete Fourier transform (IDFT). In this case, well-established frequency-domain solvers, including finite element method (FEM) and boundary element method (BEM), can be used. However, IDFT generates some artifacts that are undesirable for room acoustic evaluation. If such artifacts can be attenuated, then the frequency-domain methods become more attractive for simulating room impulse responses. In this paper, we propose a post-processing method to attenuate the artifacts from the impulse responses computed by the combination of frequency-domain simulation and IDFT. It is formulated as a convex optimization problem, and the alternating direction method of multipliers (ADMM) is applied to obtain the solution. Numerical experiments confirmed that the proposed method can effectively reduce the undesirable artifacts from the reconstructed impulse responses. An example implementation of the proposed method in MATLAB is provided at https://doi.org/g9h5.