2.5 The head-related transfer function

Combining all of the above — the pinna’s spectral filtering, the canal’s resonance, the head-shadow attenuation, the contralateral path difference — yields the head-related transfer function (HRTF). It is a complex function of frequency, azimuth, elevation, and (to a lesser degree) distance. For each direction in space, the HRTF tells you what filter the body applies to a sound arriving from that direction before it reaches your eardrum.

HRTF measurements are routinely made on individual subjects using miniature microphones inserted near the eardrum, or on dummy heads (KEMAR, Neumann KU100) that approximate average human geometry. Public HRTF databases (CIPIC, KEMAR) provide measurements for hundreds of directions and are the foundation of binaural audio rendering for headphones.

The brain’s localization circuitry, built into the brainstem and processed further in the midbrain and cortex, is essentially an inverse problem: given the spectrum and timing arriving at each eardrum, infer the most likely sound source direction. This inversion uses ITD, ILD, and pinna-spectrum cues simultaneously. The result is the everyday sense that you can point at a sound source you cannot see.

The signal arriving at the eardrum, then, is not the signal the source produced — it has been head-and-pinna filtered for spatial information. The next stop in the pathway is the eardrum itself, the start of movement 4 (the middle ear) — which we have already seen. From there, the signal enters the cochlea, the subject of movement 5.

We have now described, end-to-end, the full path of “Hey Dr. Miles!” from the speaker’s mouth to the entrance of the cochlea. Everything from this point on is neural.