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

The room impulse response (RIR) is crucial in designing acoustic applications owing to its vital role in characterizing sound propagation in a room. A typical sound propagation system is like a linear time-invariant system consisting of a loudspeaker and a microphone which serves as an input and output, respectively. Since sound propagation is affected by the microphone and loudspeaker positions, RIR measurement at multiple points is challenging for two main reasons. One, it requires iteration of the experiment after replacing or relocating the microphone. Second, it requires a huge microphone array with many microphones at all the measurement points. Moreover, an increase in the number of microphones enlarges the sound reflections from the microphones, thus further complicating the microphone calibration, leading to inaccurate RIR measurements.

To date, several interpolation and extrapolation methods for measuring RIRs from multiple points have been proposed. Based on the previous experimental data, extrapolation methods are more efficient than interpolation methods. This can be attributed to its simplicity and ease of placing the microphones. However, in the previous studies, the effectiveness of RIR extrapolation has only been demonstrated at frequencies below 1 kHz, as extrapolation at higher frequencies proved quite challenging. Thus, developing efficient and feasible strategies for RIR extrapolation at higher frequencies is highly desirable as it is a requirement for various applications. In addition, since sound localization is mainly affected by the early parts of RIRs, effective design and control of the early RIRs is of extreme importance in acoustic applications.

On this account, Izumi Tsunokuni, Kakeru Kurokawa, Haruka Matsuhashi, Dr. Yusuke Ikeda, Dr. Naotoshi Osaka from Tokyo Denki University proposed a spatial extrapolation method for RIRs of direct sound and early reflections in a local area with limited measurement points. In their approach, the RIRs around the microphones were represented using superpositions of the image source method and sparse equivalent sources located around the image sources and the loudspeaker. Through a measurement experiment conducted in an anechoic chamber, the authors used sound-reflection boards to estimate the RIPs around the microphones. Further, the extrapolation accuracies of RIPs were evaluated with two different microphone array configurations at higher frequencies up to 8.5 kHz. Their research work is currently published in the journal, Applied Acoustics.

Results showed that the proposed method could determine the reflection components of the direct sound and of each wall with improved accuracy. This method achieved about 10 dB signal-to-noise ratio in the vicinity of the microphones array. RIRs of both primary and secondary reflections was estimated over higher frequencies of 0.5 – 8.5 kHz over an entire evaluation area of 0.54 × 0.6 m2. This was achieved using only two microphone arrays having 13 and 16 microphones. The average estimation accuracy for the two microphone arrays in terms of the signal-to-noise ratio was approximately 5 – 6 dB higher than that for plane wave decomposition. It was worth noting that the extrapolation and estimation accuracies were higher near the microphone arrays but gradually decreased away from the microphones due to the increase in the frequency.

In summary, a spatial extrapolation method to efficiently obtain early room impulse responses in the local area with a relatively reduced number of microphones was reported in this study. The feasibility of the proposed method was successfully validated, and the results were superior to those of plane wave decomposition. The impact of higher frequency on extrapolation accuracy was confirmed. Based on the relationship between the reflecting objects and the individual reflection components, the research findings would help improve the sound image and tone caused by early reflections. In light of these findings, Professor Yusuke Ikeda noted that the proposed method could find various applications in architectural acoustics, such as sound visualization.


Tsunokuni, I., Kurokawa, K., Matsuhashi, H., Ikeda, Y., & Osaka, N. (2021). Spatial extrapolation of early room impulse responses in local area using sparse equivalent sources and image source methodApplied Acoustics, 179, 108027.

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