Compact representation of reflections from soft surfaces

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Compact representation of reflections from
soft surfaces

• Bård Støfringsdal, COWI AS

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Background, 1
For auralization, sound fields can usually be
represented accurately and very efficiently by a
set of image sources (IS). An IS
representation is easy to adapt to various sound
rendering techniques binaural, WFS, HOA, VBAP,
etc. It can also easily be used for dynamic
situations. An IS representation is inaccurate
when the source and receiver are bothclose to
reflecting surface Mechel02. This is most
common for the groundreflection outdoors, at low
frequencies.
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Background, 2
We can compute the field accurately with
alternative methods, e.g. FEM/BEM, or analytic
solutions, but how to combine it with an IS
representation? Solution find a small set
of virtual sources which represent the exact
field as well as possible.
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Outdoor sound propagationCalculating the
reflected wave field, 1
hr

• Homogenous, locally reacting ground
• Boundary described by its normal specific
  impedance

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Calculating the reflected wave field, 2

• Plane-wave reflection coefficient
• Boundary loss factor F, depending on the so
  called numerical distance ?

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Source signals

• Flow resistivity s 11 kNsm-4 (very soft snow
  or moss-like)
• Boundary loss, arrival time of surface wave
• Frequency dependence
• Dipole effect

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Sound field representation
Receiver
R1
Source
R2
Image source

• Local reproduction
• Dynamic positioning
• Vertical hearing sensitivity

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Plane wave decomposition

• Virtual loudspeakers
• Regularization
• Blind sound field decomposition method

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Other virtual source approaches
r1
r2
vs1
vs2

• Use knowledge of real and image sources
• Regularization?

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Virtual source representation direct solution

• Fine at high frequencies, but only for low s

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Virtual source representation regularized
inversion, 1

• 2 m microphone spacing

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Virtual source representation regularized
inversion, 2

• Does not preserve dipole effect

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Virtual source representation direct
inversion, 1

• 2 m microphone spacing

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Tine domain source signals

• Significantly increased dipole effect

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Frequency domain source signals

• Strong level increase

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Stability for reproduction

• HOA encoding/decoding (2D, r-z-plane)
• 31. order, 64 loudspeakers, 2 m loudspeaker
  radius

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Sensitivity to microphone spacing, 1

• 0.2 m microphone spacing

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Sensitivtity to microphone spacing, 2

• 2 m microphone spacing

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Sensitivity to microphone spacing, 3

• 20 m microphone spacing

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Sensitivity to microphone spacing, 4

• 40 m microphone spacing

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Validity domain, 1

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Validity domain, 2

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Validity domain, 3

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Further simplifications
t
Receiver
R1
vs1
R2
vs2

• 2D reproduction
• Simple source encoding

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Tilt to listener plane, 1
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Tilt to listener plane, 2
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Tilt to listener plane, 3
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Only one virtual source position

• Added time delay/phase compensation