Spatial extrapolation of early room impulse responses in local area using sparse equivalent sources and image source method

Abstract The room impulse response (RIR) is important in most acoustic applications, such as the design of concert halls and sound field control, because it characterizes the sound propagation. The measurement of RIRs at multiple points is challenging, as it requires a huge microphone array or repeating the experiment by microphone replacement. Several RIR interpolation and extrapolation methods of RIRs have been developed for obtaining RIRs from multiple measurement points efficiently. Extrapolation methods offer more efficient RIR measurement compared to interpolation. However, previous studies focused on extrapolation at frequencies below 1 kHz, and the extrapolation at higher frequencies was difficult. In this study, we propose an extrapolation method for RIRs of direct sound and early reflections in a local area using a small number of measurement points. The proposed method represents the RIRs around the microphones using superpositions of sparse equivalent sources located around the loudspeaker and image sources. We conducted a measurement experiment in an anechoic chamber to estimate RIRs around microphones using sound-reflecting boards. From the experimental results with 2.5 dimensional conditions, the proposed method achieved about above 10 dB of signal to noise ratio (SNR) near the microphone array from 0.5–8.5 kHz. For the extrapolation accuracy over the entire evaluation area (0.6 × 0.54 m2), the proposed method improved the SNR by about 5–6 dB compared to results using the plane wave decomposition.