Headphone transfer function ($H(f)$)

A headphone transfer function describes how an input electrical signal becomes acoustic pressure at a specified point near or within the listener's ear. For a linear small-signal description,where $p(f)$ is complex sound pressure amplitude and $V(f)$ the input electric potential difference. This transfer function includes both magnitude and phase. With these variables its units are pascals per volt, rather than a dimensionless gain.^[ref]

For example, at one frequency let $H=2Pa/V$ and apply a $10\mathrm{mV}$ sinusoidal input. The pressure amplitude is $0.020\mathrm{Pa}$ under the model. A compensating filter for a desired pressure $p_d$ would ideally supply $V=p_d/H$, but division by a small or uncertain response can demand a large, fragile correction.

The coupling to the ear is part of the system. Abhijit Kulkarni and H. Steven Colburn repeatedly positioned headphone cushions on a KEMAR acoustic mannequin and measured changes in response. Their measurements showed that repositioning could complicate compensation using a fixed inverse filter. A transfer function measured for one fitting need not remain identical after the device is moved.^[ref]

This differs from a head-related transfer function, which characterizes transformation from an external sound source to an ear location. Reproducing a desired spatial sound over headphones can require accounting for both transformations, rather than confusing the headphone's coloration with the directional effect being simulated.