Covering the Spatial Hearing Frequency Range

Spatial hearing (Blauert, 1997) is accomplished by two ears sampling the acoustic field through small apertures (ear canals) having diameters smaller than the wavelength across almost the entire audio band. As a result, the directionality of a sound is inferred primarily from the relative intensity ($\Delta I$ ) and time-of-arrival ($\Delta T$ ) at the two ears. There is also directionality information impressed on the signal by pinnae filtering and shoulder reflections, etc., that are especially important for elevation perception.¹³For azimuth perception, $\Delta T$ is the dominant cue below about 800 Hz, and $\Delta I$ dominates above 1600 Hz or so.¹⁴In the octave between these limits, both $\Delta T$ and $\Delta I$ are used. Also, $\Delta T$ is picked up as phase delay for low frequencies, and group delay at high frequencies (ibid.). Perceptual accuracy is on the order of 1$\hbox{${}^{\circ}$}$ for azimuth in front of the listener. The lower limit of azimuth perception based on $\Delta T$ is approximately 80 Hz, below which phase differences become imperceptible. Thus, our spec is to synthesize correct $\Delta T$ s down to 80 Hz. Note, however, that since the acoustic wavelength at 80 Hz is over 4 meters long, we could get by with reduced spatial resolution in this frequency range, such as simple stereo. Multiresolution speaker arrays are discussed starting in §4 below.