Head-related transfer function

In acoustics, a head-related transfer function (HRTF) is the output from a linear time invariant system[?], composed of the listener's head, pinna[?] and torso. The output from this system is different from the input due to the diffraction and reflection properties of the head, pinna, and torso.

Linear systems analysis defines the transfer function as the complex ratio between the output signal spectrum and the input signal spectrum as a function of frequency. Blauert (1974; cited in Blauert, 1981) initially defined the transfer function as the free-field transfer function (FFTF). Other terms include free-field to eardrum[?] transfer function and the pressure transformation from the free-field to the eardrum. Less specific descriptions include the pinna transfer function, the outer ear transfer function, the pinna response, directional transfer function (DTF) or what is commonly termed the head-related transfer function (HRTF). If the HRTF has been Fourier transformed to the time domain it will be referred to as the head-related impulse response (HRIR).

The transfer function (H(ω)) of any LTI system at an angular frequency (ω) is:

H(ω) = Output (ω) / Input (ω)

where the angular frequency ω is related to frequency f by ω = 2πf .