A binaural spatializer simulates the auditory experience of one or
more sound sources arbitrarily located around a listener
[9]. The basic idea is to reproduce the acoustical
signals at the two ears that would occur in a normal listening
situation. This is accomplished by convolving each source signal with
the pair of head-related transfer functions (HRTFs)
that correspond to the
direction of the source, and the resulting binaural signal is presented to
the listener over headphones. Usually, the HRTFs are equalized to
compensate for the headphone to ear frequency response
[26, 17]. A schematic diagram of a single
source system is shown in figure
9. The direction of the source ( 
azimuth, 
elevation) determines which pair of HRTFs to use, and the distance
(r) determines the gain. Figure 10 shows a multiple source
spatializer that adds a constant level of reverberation to enhance
distance perception.
The simplest implementation of a binaural spatializer uses the measured HRTFs directly as finite impulse response (FIR) filters. Because the head response persists for several milliseconds, HRTFs can be more than 100 samples long at typical audio sampling rates. The interaural delay can be included in the filter responses directly as leading zero coefficients, or can be factored out in an effort to shorten the filter lengths. It is also possible to use mimimum phase filters derived from the HRTFs [15], since these will in general be shorter than the original HRTFs. This is somewhat risky because the resulting interaural phase may be completely distorted. It would appear, however, that interaural amplitudes as a function of frequency encode more useful directional information than interaural phase [16].
There are several problems common to headphone spatializers: