Delay Lines and Effects
65
localization blur
Head-Related Transfer
Function
HRIR
1 kHz
- 0.38 ms
- 0.26 ms
frequency
Time Difference
1 kHz
frequency
0 dB
- 10 dB
Intensity Difference
(a)
(b)
Figure 9: Frequency-dependent interaural time (a) and intensity (b) difference
for azimuth 30
o
.
times the head radius increase the intensity difference in low frequency. The ITD
also increases for very close sources but its changes do not provide significant
information about source range.
Several researchers have measured the filtering properties of the system pinna
- head - torso by means of manikins or human subjects. A popular collection
of measurements was taken by Gardner and Martin using a KEMAR dummy
head, and made freely available [36, 38, 2]. Measurements of this kind are usually
taken in an anechoic chamber, where a loudspeaker plays a test signal which
invests the head from the desired direction. The directions should be taken
in such a way that two neighbor directions never exceed the localization blur,
which ranges from about ±3
in azimuth for frontal sources, to about ±20
in
elevation for sources above and slightly behind the listener [13]. The result of
the measurements is a set of Head-Related Transfer Functions (HRIR) that can
be directly used as coefficients of a pair of FIR filters. Since the decay time of
the HRIR is always less than a few milliseconds, 256 to 512 taps are sufficient
at a sampling rate of 44.1kHz.
A cookbook of HRIRs and direct convolution seems to be a viable solution
for providing directionality to sound sources using current technology. A funda-
mental limitation comes from the fact that HRIRs vary widely between different
subjects, in such an extent that front-back reversals are fairly common when
listening through someone else's HRIRs. Using individualized HRIRs dramati-
cally improves the quality of localization. Moreover, since we unconsciously use
small head movements to resolve possible directional ambiguities, head-motion
tracking is also desirable.
There are some reasons that make a model of the external hearing system
more desirable than a raw catalog of HRIRs. First of all, a model might be
implemented more efficiently, thus allowing more sources to be spatialized in real
time. Second, if the model is well understood, it might be described with a few
parameters having a direct relationship with physical or geometric quantities.
This latter possibility can save memory and allow easy calibration.
Modeling the structural properties of the system pinna - head - torso gives
us the possibility to apply continuous variation to the positions of sound sources
and to the morphology of the listener. Much of the physical/geometric proper-
ties can be understood by careful analysis of the HRIRs, plotted as surfaces,
functions of the variables time and azimuth, or time and elevation. This is the
approach taken by Brown and Duda [19] who came up with a model which can