3-D Sound and Spatial Audio

MUS_TECH 348

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 SphereFrancis Wiener “Sound Diffraction by Rigid Sphere and Circular Cylinders (1947)

Comparison of predictions and measurements.

Sound pressure

Head as a SphereOne verified prediction is that there will be a ‘bright spot’ in

the back of the sphere.

Sound pressure

ka = 0.5, 1 ka = 2, 3 ka = 4, 5

ka = 8, 10ka = 6,7

Head as a SphereRayleigh 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)

Plane wave shadow zone

creeping wave

•Speed is less than usual speed of sound, 97% for high frequencies

•Amplitude decreases exponentially

radius=a

Changes with distance

Richard Duda and William Martens, Range-dependence 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 HeadGeorge Kuhn, Model for the interaural time differences in the azimuthal plane (1977) and Towards a Model for Sound Localization (1982)

•ITD below 500 Hz is independent of frequency 3 (head radius/ speed of sound) sin

•ITD above 3000 Hz is independent of frequency2 (head radius/ speed of sound) sin

•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

Compare predictions with measures done with dummy head.

George Kuhn, Model for the interaural time differences in the azimuthal plane (1977)

High frequency delays are 2/3 of low frequency delays.

Phase Delay

phase delay = - ()

unwrap phase()

msec

Group Delay

group delay = - d()d

unwrap phase()

msec

Phase Delay and Group

DelayMeasures 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)

Sound pressure

Small features of the head such as the nose and pinna are clearly in play above 4 kHz

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 FilterNotches in the HRTF are the result of delayed energy. Can we model the source?

delay

+

delay

+

filter

f

f

Comb filter

Pinna filter

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)

Frontal plane (response below5 kHz)

Simulated time response.

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 45-degrees in azimuth and 45-degrees 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.