# 3-D Sound and Spatial Audio

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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. - PowerPoint PPT Presentation

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• 3-D Sound and Spatial AudioMUS_TECH 348

• Physical ModelingProblem: 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 SpherePredictions 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 pressureka = 0.5, 1ka = 2, 3ka = 4, 5ka = 8, 10ka = 6,7

• Head as a SphereRayleigh diffraction transfer function predicts ripples in magnitude and group delay.

magnitudegroup delay

• Head as a SphereCreeping waves are created at shadow zone boundaries.

Anthony J. Rudgers, Acoustic Pulses Scattered by a Rigid Sphere Immersed in a Fluid (1968)Plane waveshadow zonecreeping waveSpeed is less than usual speed of sound, 97% for high frequenciesAmplitude decreases exponentiallyradius=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 q

ITD above 3000 Hz is independent of frequency2 (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 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-pw-2ppphase delay = -q(w) wunwrap phaseq(w)msecw

• Group Delay-pw-2ppgroup delay = -d q(w) d wunwrap phaseq(w)msecw

• 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?ffComb filterPinna 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.

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