Download B-3DPhysicalAcoustics3

MUS_TECH 348
3-D Sound and Spatial Audio
Physical Modeling
Problem: Can we model the physical acoustics of
the directional hearing system and thereby
understand the relationship between the physical
system and the HRTF?
Consider the head as a Sphere
Predictions of sound intensity and phase can
be verified with acoustic measurements.
Francis Wiener “Sound Diffraction by Rigid Sphere and Circular Cylinders (1947)
Measurement are expressed relative to 1/3 < ka < 10, where a is
the radius of the sphere and k is the wave number.
Consider the head as a Sphere
Francis Wiener “Sound Diffraction by Rigid Sphere and Circular Cylinders (1947)
Comparison of predictions and measurements.
Sound
pressure
Head as a Sphere
One verified prediction is that there will be a ‘bright spot’ in
the back of the sphere.
ka = 0.5, 1
ka = 2, 3
ka = 4, 5
Sound pressure
ka = 6,7
ka = 8, 10
Head as a Sphere
Rayleigh diffraction transfer function predicts
ripples in magnitude and group delay.
magnitude
group delay
Head as a Sphere
“Creeping waves” are created at shadow zone
boundaries.
Anthony J. Rudgers, Acoustic Pulses Scattered by a Rigid Sphere Immersed in
a Fluid (1968)
creeping wave
Plane wave
radius=a
shadow zone
•Speed is less than usual speed of sound, 97% for high
frequencies
•Amplitude decreases exponentially
Changes with
distance
Richard Duda and William Martens, Rangedependence of the HRTF for a Spherical Head
(1997)
The plane wave assumption breaks
down when sources are close to
sphere.
ILD = interaural level difference predicted on basis
of sphere with ears set back 10-degrees
p is normalized distance relative to sphere radius
Correlation with Dummy Head
George Kuhn, Model for the interaural time differences in the
azimuthal plane (1977) and Towards a Model for Sound Localization
(1982)
Compare predictions with measures done with dummy head.
•ITD below 500 Hz is independent of frequency
3 (head radius/ speed of sound) sin q
•ITD above 3000 Hz is independent of frequency
2 (head radius/ speed of sound) sin q
•Minimum ITD appear around 1,500 Hz
•Between the low and high frequency regions there is a
considerable difference between phase delay and group delay
High frequency delays are 2/3 of low frequency delays.
George Kuhn, Model for the interaural time differences in the
azimuthal plane (1977)
Phase Delay
p
unwrap
w phase
q(w)
-p
-2p
q(w)
phase delay = - w
msec
w
Group Delay
p
unwrap
w phase
q(w)
-p
-2p
d q(w)
group delay = - d w
msec
w
Phase Delay
and Group
Delay
Measures phase delay and group
delay differ. The more difficult
question is in what way does the
auditory system responds to
delay.
Asymmetries of
head and pinna
John Middlebrooks, Directional
sensitivity of sound-pressure in the
human ear canal (1989)
Small features of the head such as
the nose and pinna are clearly in
play above 4 kHz
Sound pressure
Asymmetries
of head and
pinna
John Middlebrooks, Directional
dependence of interaural
envelope delays (1990)
Envelope delay is more
appropriate for sound above 4
kHz due to what we know
about how the auditory system
detects delays.
Modeling the Pinna Filter
Notches in the HRTF are the result of delayed
energy. Can we model the source?
Comb filter
+
delay
f
Pinna filter
+
filter
delay
f
Modeling the Torso
Algazi, Duda and Thompson, “The use of Head- and-Torso Models
for Improved Spatial Sound Synthesis (2002)
This is an example of using a model to create better directional hearing cues.
Modeling the Torso
Algazi, Duda and Thompson, “The use of Head- and-Torso Models
for Improved Spatial Sound Synthesis (2002)
Simulated time response.
Frontal plane
(response below
5 kHz)
Modeling the Torso
Algazi, Duda and Thompson, “The use of Head- and-Torso Models
for Improved Spatial Sound Synthesis (2002)
Model can be implemented
computationally.
Alternative Approaches
Yuvi Kahana, et. Al, Numerical Modelling of the Transfer Functions of a
Dummy-Head and of the External Ear (1999)
Sound pressure at
2 KHz with sound
source at 45degrees in
azimuth and 45degrees in
elevation.
Alternative Approaches
Yuvi Kahana, et. Al, Numerical Modelling of the
Transfer Functions of a Dummy-Head and of the
External Ear (1999)
Three snapshots of time domain simulation
with wave up to 6.4 kHz.
We still lack a comprehensive
model of the physical acoustics of
the directional hearing system.