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Binaural technology has various applications in virtual acoustics, architectural acoustics, tele-communications, and auditory science. One key element in binaural technology is the binaural room impulse response (BRIR), which represents a continuum of plane waves spatially filtered by head related transfer functions (HRTFs). Such BRIRs can be rendered from spherical microphone array recordings and free-field HRTFs, either in the space domain using plane-wave composition or in the spherical-harmonics domain using order-limited spherical harmonics representation of the sound field. While these approaches have been individually employed in a number of recent studies, it appears that the literature does not offer a comprehensive analysis or a theoretical framework relating the two representations with respect to binaural reproduction and perception. In this paper, we provide a mathematical analysis showing that when certain sampling conditions are maintained, the plane-wave and spherical-harmonics representations are equivalent. Further, we show that under these conditions, resulting binaural signals are independent of the employed spatial sampling schemes. The analysis is complemented by a listening experiment, in which both plane-wave and spherical-harmonics representations are perceptually evaluated for different spatial sampling schemes and spherical harmonic orders. |
