# Interpolating the Directional Room Impulse Response for Dynamic Spatial Audio Reproduction
## 1 Introduction
While such extrapolation approaches can introduce inaccurate source localization and audible processing artifacts, such as spectral coloration [11], a number of interpolation-based approaches using HOA microphone array recordings are prone to mitigate these effects, such as the regularized least-squares interpolation approaches using spherical harmonic translation coefficients [12; 13; 14; 15]. More recent related work [16; 17] utilized frequency-dependent regularization to limit spectral variation and exclude any microphones closer to a sound source than to the target listening position in order to obtain accurate results for near-field sources. While promising, HOA representations require many more channels compared to FOA representations, which may not be desirable in low bandwidth applications. Hence, this paper focuses on FOA representations for improving the accuracy of interpolation and localization in limited bandwidth scenarios, which considers parametric approaches to interpolate known DRIR signals to reproduce the DRIR at a new position. The approach is inspired from earlier research that identifies, localizes, and isolates discrete sound sources in the time-frequency domain before treating them as virtual sound sources to achieve soundfield navigation [18; 19]. While the previous work separated anechoic FOA recordings of sound mixtures into multiple virtual sources, this paper centers on separating FOA DRIR recordings into virtual components representing the directional and reverberant components, focusing on the early specular reflections. The approach assumes the DRIR is recorded or represented as an FOA (B-format) encoding at a finite number of known positions within a virtual environment, for example covering a grid of locations across the room. Based on knowledge of the user position, the known DRIR signals at the two closest positions in the grid are decomposed into the FOA representations of the direct sound, specular reflection, and diffuse signals. The specular reflection FOA signals are analyzedin the time domain to estimate individual specular reflections and their corresponding directions of arrival (DOAs) and time of arrival (TOA); these components are then formed into FOA signals representing virtual image sources. At the new listening position, direct sound and early specular reflections are estimated using the corresponding DOA and TOA of these virtual sources and a known FOA signal. The motivation of using the DOA and TOA information of early specular reflections is that sounds arriving up to 50 ms are inclined to be perceived as mixed together instead of as individual echoes. Their timing and directions impact spatial perception significantly on the depth and broadening of sources, as well as the size of the space and the distance to surfaces [20]. In addition, including the DOA of the early reflections allows their direction to be adjusted as the listener turns their head during a VR session. Hence this information can enable increased immersive perception, as if users are in the real target environment. The approach is compared with two representative navigational methods based on FOA representations [4; 16] and working on guaranteeing the high accuracy in estimating the DOA and TOA of the direct sound and estimated early specular reflections. The remainder of this paper is organized as follows. Section 2 analyzes the signal model and decomposition of FOA recordings, before introducing an approach to extract the DOA information and interpolate DRIRs at positions where microphones are not available. Section 3 conducts experiments using both real-world and simulated DRIR recordings to validate the proposed algorithm, and Section 4 compares the experimental results with that of two previous representative approaches. Contributions and discussions are concluded in Section 5.