Our transaural filter is based on a simplified head model suggested by David Griesinger. The ipsilateral response is taken to be unity and the contralateral response is modeled as a delay, attenuation, and a lowpass filter:
where g < 1 is a broadband interaural gain, m is the interaural time delay (ITD) in samples, and is a one-pole, DC-normalized, lowpass filter that models the frequency dependent head shadowing. For a horizontal source at 30 degrees azimuth, typical contralateral parameters might be g = 0.85 (-1.5 dB broadband attenuation), m = 7 (ITD of 0.2 msec at 32 kHz) and a lowpass filter cutoff of 1000 Hz (the frequency where head shadowing becomes significant). These parameters were not in fact calculated but were established through a calibration procedure discussed below.
Using this simplified head model the transaural filter in shuffler form is given by:
This filter structure is efficiently implemented using only two delays and two lowpass filters.
The transaural filter is calibrated as follows. A standard stereo
listening setup was constructed with speakers at 
degrees with
respect to the listener. Several stereo test signals are sent through
the transaural filter and presented to the listener. The signals
include stereo uncorrelated pink noise, left only pink noise and right
only pink noise, and commercial binaural recordings made with dummy
head microphones. During playback, the listener can continuously
adjust the three transaural parameters (g, m, and the lowpass
cutoff frequency) using a MIDI controller. The calibration procedure
involves adjusting the parameters such that single sided noises are
located as close as possible to their corresponding ears and the
stereo noise is maximally enveloping [11]. The
interaural delay parameter has the most effect of steering the signal
and changing the timbre, provided the gain parameter is sufficiently
close to 1. The lowpass cutoff has the most subtle effect.
Interestingly, while it is possible to steer the single sided noise
close to the corresponding ear, this often has the effect of moving
the opposite sided noise closer to its corresponding
speaker. Consequently a compromise has to be reached. In general, the
final parameters one obtains via the calibration procedure agree with
the physics of the situation.
Listening to the binaural recordings through the transaural system is an enjoyable experience. The speakers vanish and are replaced by an immersive auditory scene. Sounds can be heard from all directions except directly behind the listener. The so-called ``sweet spot'' is readily apparent. When one moves outside of the sweet spot, the sensation of being surrounded by sound is lost, and is replaced by the the sensation of listening to a conventional stereo setup. Within the sweet spot, the transaural system is tolerant of head motion, particularly front-back translation, less so for left to right translation, and least tolerant of turning side to side. Turning to face either loudspeaker is sufficient to destroy the illusion.