### Spatial Audio Rendering  
For healthy listeners, the human auditory system is adept at decoding how a sound wave diffracts and interacts with the head, torso, and pinnae, resulting in both temporal and amplitude differences changes as well as spectral cues [24].  
In terms of localization interaural time and level differences (ITD and ILD) are the two major cues attributed to sound localization along the horizontal plane (see Figure 1). For low frequency sound sources (<1.5 kHz), the detection of ITD is the primary mechanism [25]. This frequency threshold is a result of the distance a sound wave must travel to reach the furthest ear, causing the phase angle to differ upon arrival. The corresponding angle being both the function of the wavelength and the source positioning. With frequencies below 1.5 kHz the wavelength is greater than then maximum difference in time, this phase difference will therefore provide accurate location cues [26]. For higher frequency targets, ILD detection takes over from temporal differences as the primary horizontal localization mechanism [25]. Shorter high frequency sound waves are more susceptible to the acoustic shadowing caused by the human head. It is this increased shadowing effect that produces a greater difference in sound levels between the two ears [27].  
Localization within the vertical plane is calculated from the spectral shaping of acoustic energy by torso and the unique and complex geometry of the pinna. Frequencies are distributed and consequently reflected causing minute but significant delays. It is these delays that will act as a comb filter effect on sound entering the inner part of the ear, representing a three-dimensional function of the elevation of the sound source [29; 30].  
The realistic reproduction of three-dimensional auditory environments through headphones, known as binaural-based spatial audio, is dependent upon the correct simulation of the interaural differences and spectral shaping cues caused by the torso, head and pinnae called Head Related Transfer Functions (HRTF) [31]. HRTF's are the functions of both frequency and position for both  
Figure 1: Binaural cues for horizontal localization. Plots display two time-domain representations of Head Related Transfer Functions (HRTF) recordings (45\({}^{\circ}\) azimuth & 0\({}^{\circ}\) elevation) extracted from the SADIE Database [28].  
azimuth and elevation, containing direction-dependent information on how a free field sound source reaches the ear [32; 33]. Binaural rendering can then be achieved through the convolution of a monoaural anechoic sound source and the HRTF of both the desired direction and the corresponding ear [32; 34].  
Today most VR systems rely on head-tracked headphone-based systems (see Figure 2). Head tracking is definitive in creating a plausible and realistic virtual audio scene. Current virtual reality head devices can provide stable multi-modal interaction through accelerometers which can detect force, 360 orientation and measure the device's position within a 3-D space. Once the rendering system has received the X, Y, and Z directional information, it performs interpolation between the closest HRTF's resulting perceived localization of a dynamic virtual sound source [35; 36]. Furthermore, by reproducing the audio over headphones it is possible to isolate the left and right audio channels and successfully reproduce the binaural localization cues. However, there are several auditory processing difficulties associated with autism spectrum disorders that may affect how a user may respond to auditory cues within a VR intervention environment.