= Headphone transfer function
{title2=$H(f)$}
A \b[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,
$$
H(f)=\frac{p(f)}{V(f)},
$$
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.<Variability in the characterization of the headphone transfer-function by Abhijit Kulkarni and H. Steven Colburn>[Section I: electrical input, pressure at an ear-canal point and headphone transfer.]{ref}
For example, at one frequency let $H=2\,\mathrm{Pa/V}$ 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.<Variability in the characterization of the headphone transfer-function by Abhijit Kulkarni and H. Steven Colburn>[Abstract and introduction: placement-dependent supra-aural measurements and inverse compensation.]{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.
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