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Compact representation of reflections from soft surfaces

Compact representation of reflections from soft surfaces. Bård Støfringsdal, COWI AS. Background, 1. • For auralization, sound fields can usually be represented accurately and very efficiently by a set of image sources (IS).

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Compact representation of reflections from soft surfaces

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  1. Compact representation of reflections from soft surfaces Bård Støfringsdal, COWI AS

  2. 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.

  3. 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.

  4. Receiver R1 Source  hs R2 Outdoor sound propagation:Calculating the reflected wave field, 1 hr • Homogenous, locally reacting ground • Boundary described by its normal specific impedance

  5. Calculating the reflected wave field, 2 • Plane-wave reflection coefficient • Boundary loss factor F, depending on the so called numerical distance ρ

  6. Source signals • Flow resistivity σ = 11 kNsm-4 (very soft; snow or moss-like) • Boundary loss, arrival time of surface wave • Frequency dependence • Dipole effect

  7. Sound field representation Receiver R1 Source R2 Image source • Local reproduction • Dynamic positioning • Vertical hearing sensitivity

  8. Plane wave decomposition • Virtual loudspeakers • Regularization • Blind sound field decomposition method

  9. Other virtual source approaches r1 r2 vs1 vs2 • Use knowledge of real and image sources • Regularization?

  10. Virtual source representation – direct solution • Fine at high frequencies, but only for low σ

  11. Virtual source representation – regularized inversion, 1 • 2 m microphone spacing

  12. Virtual source representation – regularized inversion, 2 • Does not preserve dipole effect

  13. Virtual source representation – direct inversion, 1 • 2 m microphone spacing

  14. Tine domain source signals • Significantly increased dipole effect

  15. Frequency domain source signals • Strong level increase

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

  17. Sensitivity to microphone spacing, 1 • 0.2 m microphone spacing

  18. Sensitivtity to microphone spacing, 2 • 2 m microphone spacing

  19. Sensitivity to microphone spacing, 3 • 20 m microphone spacing

  20. Sensitivity to microphone spacing, 4 • 40 m microphone spacing

  21. Validity domain, 1

  22. Validity domain, 2

  23. Validity domain, 3

  24. Further simplifications τ Receiver R1 vs1 R2 vs2 • 2D reproduction • Simple source encoding

  25. Tilt to listener plane, 1

  26. Tilt to listener plane, 2

  27. Tilt to listener plane, 3

  28. Only one virtual source position • Added time delay/phase compensation

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