Head-related transfer function

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Head-related transfer function
A head-related transfer function (HRTF) is a response that characterizes how an ear receives a sound from a point in space; a pair of HRTFs for two ears can be used to synthesize a binaural sound that seems to come from a particular point in space. Some consumer home entertainment products designed to reproduce surround sound from stereo (two-speaker) headphonesuse HRTFs. Some forms of HRTF- processing have also been included in computer software to simulate surround sound playback from loudspeakers.
Humans have just two ears, but can locate sounds in three dimensions – in range (distance), in direction above and below, in front and to the rear, as well as to either side. This is possible because the brain, inner ear and the external ears (pinna) worktogether to make inferences about location. This ability to localize sound sources may have developed in humans as an evolutionary necessity, since the eyes can only see a fraction of the world around a viewer, and vision is hampered in darkness, while the ability to localize a sound source works in all directions, to varying accuracy,[1] and even in the dark.
Humans estimate the location of asource by taking cues derived from one ear (monaural cues), and by comparing cues received at both ears (difference cues or binaural cues). Among the difference cues are time differences of arrival and intensity differences. The monaural cues come from the interaction between the sound source and the human anatomy, in which the original source sound is modified before it enters the ear canal forprocessing by the auditory system. These modifications encode the source location, and may be captured via an impulse response which relates the source location and the ear location. This impulse response is termed the head-related impulse response (HRIR). Convolution of an arbitrary source sound with the HRIR converts the sound to that which would have been heard by the listener if it had been playedat the source location, with the listener's ear at the receiver location. HRIRs have been used to produce virtual surround sound.[2][3]
The HRTF is the Fourier transform of HRIR. The HRTF is also sometimes known as the anatomical transfer function (ATF).
HRTFs for left and right ear (expressed above as HRIRs) describe the filtering of a sound source (x(t)) before it is perceived at the left andright ears as xL(t) and xR(t), respectively.
The HRTF can also be described as the modifications to a sound from a direction in free air to the sound as it arrives at the eardrum. These modifications include the shape of the listener's outer ear, the shape of the listener's head and body, the acoustical characteristics of the space in which the sound is played, and so on. All these characteristicswill influence how (or whether) a listener can accurately tell what direction a sound is coming from.
How HRTF works
The associated mechanism varies between individuals, as their head and ear shapes differ.
HRTF describes how a given sound wave input (parameterized as frequency and source location) is filtered by the diffraction and reflection properties of the head, pinna, and torso, beforethe sound reaches the transduction machinery of the eardrum and inner ear (see auditory system). Biologically, the source-location-specific prefiltering effects of these external structures aid in the neural determination of source location, particularly the determination of the source's elevation.[4]
Technical derivation
Linear systems analysis defines the transfer function as the complex ratiobetween 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...
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