Design theory for binaural synthesis: Combining microphone array recordings and head-related transfer function datasets

Signal processing methods that accurately synthesize sound pressure at the ears are important in the development of spatial audio devices for personal use. This paper reviews the current methods and focuses on a promising class of these methods that rely on combining the spatial information available in microphone array recordings and datasets of head-related transfer functions (HRTFs). These two kinds of spatial information enable the consideration of dynamic and individual auditory localization cues during binaural synthesis. A general formulation for such a class of methods is presented in terms of a linear system of equations, whose associated matrix is composed of acoustic transfer functions that relate the positions of microphones and HRTFs. Based on this formulation, it is shown that most of the existing methods under consideration can be classified into two prominent approaches: 1) the HRTF modeling approach and 2) the microphone signal modeling approach. An important relation between these two approaches is evidenced in the general formulation: when one approach arises from the solution to an overdetermined system, the other corresponds to an underdetermined system, and vice versa. Illustrative examples of binaural synthesis from spherical arrays are provided by means of simulations. Underdetermined systems generally achieve better performance than overdetermined ones.