Editing Head-related transfer function (section)

==Sound localization==
Humans have just two [[ear]]s, but can locate sounds in three dimensions – in range (distance), in direction above and below (elevation), in front and to the rear, as well as to either side (azimuth). This is possible because the brain, inner ear, and the external ears ([[Pinna (anatomy)|pinna]]) work together to make inferences about location. This ability to [[Sound localization|localize sound sources]] may have developed in humans and ancestors 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,<ref>
{{cite book
 | title = Perimetry of the localization of sound
 | author = Daniel Starch
 | publisher = State University of Iowa
 | year = 1908
 | page = 35 ff
 | url = https://books.google.com/books?id=ClRVAAAAMAAJ&pg=PA35
 | author-link = Daniel Starch
 }}</ref> 
regardless of the surrounding light.

Humans estimate the location of a source 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 for processing 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 played at the source location, with the listener's ear at the receiver location. HRIRs have been used to produce virtual surround sound.<ref>Begault, D.R. (1994) 3D sound for virtual reality and multimedia. AP Professional.</ref><ref>So, R.H.Y., Leung, N.M., Braasch, J. and Leung, K.L. (2006) A low cost, Non-individualized surround sound system based upon head-related transfer functions. An Ergonomics study and prototype development. Applied Ergonomics, 37, pp.&nbsp;695–707.</ref> {{Example needed|date=December 2018}}

The HRTF is the [[Fourier transform]] of HRIR.

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 and right ears as ''x''<sub>L</sub>(''t'') and ''x''<sub>R</sub>(''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 acoustic characteristics of the space in which the sound is played, and so on. All these characteristics will influence how (or whether) a listener can accurately tell what direction a sound is coming from.

In the AES69-2015 standard,<ref>{{Cite web|url=http://www.aes.org/publications/standards/search.cfm?docID=99|title=AES Standard AES69-2015: AES standard for file exchange - Spatial acoustic data file format|website=www.aes.org|access-date=2016-12-30}}</ref> the [[Audio Engineering Society]] (AES) has defined the SOFA file format for storing spatially oriented acoustic data like head-related transfer functions (HRTFs). SOFA software libraries and files are collected at the Sofa Conventions website.<ref>{{Cite web|url=https://www.sofaconventions.org/|title=Sofa Conventions Website|publisher=Acoustics Research Institute, a research institute of the Austrian Academy of Sciences.}}</ref>