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A Virtual Endfire Loudspeaker Array for the Generation of Sound Beams

A Virtual Endfire Loudspeaker Array for the Generation of Sound Beams

Presentation given at the AIA-DAGA Conference on Acoustics, March 2013, Meran, Italy.

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Sascha Spors

March 19, 2013
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  1. A Virtual Endfire Loudspeaker Array for the Generation of Sound

    Beams Sascha Spors 1 and Hagen Wierstorf 2 1Universität Rostock, Institute of Communications Engineering 2Technische Universität Berlin, Assessment of IP-based Applications
  2. Motivation • applications: personal sound, binaural synthesis, room acoustics, ...

    • Acoustic Contrast Control [Choi et al. 2002], [Park et al. 2008] • modal synthesis techniques [Menzies 2012], [Wu et al. 2009], [Helwani et al. 2011] • beamforming with endfire arrays [Boone et al. 2009, Mabande et al. 2007] Spors, Wierstorf | Virtual Endfire Array | Motivation 1
  3. Endfire Loudspeaker Arrays Endfire Loudspeaker Array x y 1 2

    N . . . ∆x Delay-and-Sum Beamforming • equalizes propagation delays for listener • limited directivity for low frequencies • robust w.r.t loudspeaker mismatch and noise Superdirective Beamforming [Boone et al. 2009, Mabande et al. 2007] • adopted from micophone array processing • improved directivity at low frequencies by differential mechanisms • limited robustness for high directivity Spors, Wierstorf | Virtual Endfire Array | Endfire Loudspeaker Array 2
  4. Synthesized Sound Field Monofrequent Signal f = 1000 Hz Synthesized

    Sound Field x (m) y (m) −2 −1 0 1 2 0 1 2 3 4 5 −1 −0.5 0 0.5 1 Level (dB) x (m) y (m) −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −2 −1 0 1 2 0 1 2 3 4 5 Amplitude (dB) −40 −30 −20 −10 0 • Minimum Variance Distortionless Response (MVDR) Design [Bitzer et al. 2001] • Loudspeaker distance ∆x = 10 cm ⇒ frequency limit fh = 1715 Hz • Number of Loudspeakers N = 8 ⇒ max. directivity index DImax = 18 dB Spors, Wierstorf | Virtual Endfire Array | Endfire Loudspeaker Array 3
  5. Synthesized Sound Field Monofrequent Signal f = 500 Hz Synthesized

    Sound Field x (m) y (m) −2 −1 0 1 2 0 1 2 3 4 5 −1 −0.5 0 0.5 1 Level (dB) x (m) y (m) −20 −20 −20 −20 −20 −20 −20 −20 −2 −1 0 1 2 0 1 2 3 4 5 Amplitude (dB) −40 −30 −20 −10 0 • Minimum Variance Distortionless Response (MVDR) Design [Bitzer et al. 2001] • Loudspeaker distance ∆x = 10 cm ⇒ frequency limit fh = 1715 Hz • Number of Loudspeakers N = 8 ⇒ max. directivity index DImax = 18 dB Spors, Wierstorf | Virtual Endfire Array | Endfire Loudspeaker Array 3
  6. Synthesized Sound Field Monofrequent Signal f = 2000 Hz Synthesized

    Sound Field x (m) y (m) −2 −1 0 1 2 0 1 2 3 4 5 −1 −0.5 0 0.5 1 Level (dB) x (m) y (m) −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −2 −1 0 1 2 0 1 2 3 4 5 Amplitude (dB) −40 −30 −20 −10 0 • Minimum Variance Distortionless Response (MVDR) Design [Bitzer et al. 2001] • Loudspeaker distance ∆x = 10 cm ⇒ frequency limit fh = 1715 Hz • Number of Loudspeakers N = 8 ⇒ max. directivity index DImax = 18 dB Spors, Wierstorf | Virtual Endfire Array | Endfire Loudspeaker Array 3
  7. Spatio-Temporal Impulse Response Superdirective x (m) y (m) −2 −1

    0 1 2 0 1 2 3 4 Amplitude (dB) −40 −30 −20 −10 0 Delay-and-Sum x (m) y (m) −2 −1 0 1 2 0 1 2 3 4 Amplitude (dB) −40 −30 −20 −10 0 • Minimum Variance Distortionless Response (MVDR) Design [Bitzer et al. 2001] • Loudspeaker distance ∆x = 10 cm ⇒ frequency limit fh = 1715 Hz • Number of Loudspeakers N = 8 Spors, Wierstorf | Virtual Endfire Array | Endfire Loudspeaker Array 4
  8. Virtual Endfire Loudspeaker Array Drawbacks of superdirective beamforming with endfire

    loudspeaker arrays • directivity for high frequencies requires small loudspeaker spacing • limited robustness against loudspeaker mismatch • very limited steering of beam possible Virtual endfire array x y 1 2 N . . . • similar to beam generation in parametric arrays • flexible placement of virtual sources • steering of beam by tilting of virtual endfire array Spors, Wierstorf | Virtual Endfire Array | Endfire Loudspeaker Array 5
  9. Focused Sources in Wave Field Synthesis x (m) y (m)

    −2 −1 0 1 2 0 1 2 3 Amplitude (dB) −40 −30 −20 −10 0 (2.5D WFS, ∆x = 10 cm, L = 4 m) • virtual acoustic sink at focus point • main propagation direction can be chosen by loudspeaker selection [Spors et al. 2007] Spors, Wierstorf | Virtual Endfire Array | Focused Sources 6
  10. Focused Sources in Wave Field Synthesis x (m) y (m)

    −2 −1 0 1 2 0 1 2 3 Amplitude (dB) −40 −30 −20 −10 0 (2.5D WFS, ∆x = 10 cm, L = 4 m) • virtual acoustic sink at focus point • main propagation direction can be chosen by loudspeaker selection [Spors et al. 2007] Spors, Wierstorf | Virtual Endfire Array | Focused Sources 6
  11. Focused Sources in Wave Field Synthesis x (m) y (m)

    −2 −1 0 1 2 0 1 2 3 Amplitude (dB) −40 −30 −20 −10 0 (2.5D WFS, ∆x = 10 cm, L = 4 m) • virtual acoustic sink at focus point • main propagation direction can be chosen by loudspeaker selection [Spors et al. 2007] Spors, Wierstorf | Virtual Endfire Array | Focused Sources 6
  12. Properties of Focused Sources in WFS Monofrequent Signal f =

    1000 Hz Synthesized Sound Field x (m) y (m) −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 0 0.5 1 1.5 2 2.5 3 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 Level for x = 0 0 0.5 1 1.5 2 2.5 3 −5 0 5 10 15 20 25 y (m) level (dB) focused source 1/r 1/sqrt(r) (2.5D WFS, ∆x = 10 cm, L = 10 m) Properties of focused sources [Spors et al. 2008] • high accuracy in proximity of focus point (high aliasing frequency) • amplitude decay in between point/line source • audible pre-echos and localization errors may be apparent Spors, Wierstorf | Virtual Endfire Array | Focused Sources 7
  13. Properties of Focused Sources in WFS Monofrequent Signal f =

    3000 Hz Synthesized Sound Field x (m) y (m) −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 0 0.5 1 1.5 2 2.5 3 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 Level for x = 0 0 0.5 1 1.5 2 2.5 3 −5 0 5 10 15 20 25 y (m) level (dB) focused source 1/r 1/sqrt(r) (2.5D WFS, ∆x = 10 cm, L = 10 m) Properties of focused sources [Spors et al. 2008] • high accuracy in proximity of focus point (high aliasing frequency) • amplitude decay in between point/line source • audible pre-echos and localization errors may be apparent Spors, Wierstorf | Virtual Endfire Array | Focused Sources 7
  14. Properties of Focused Sources in WFS Monofrequent Signal f =

    5000 Hz Synthesized Sound Field x (m) y (m) −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 0 0.5 1 1.5 2 2.5 3 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 Level for x = 0 0 0.5 1 1.5 2 2.5 3 −5 0 5 10 15 20 25 y (m) level (dB) focused source 1/r 1/sqrt(r) (2.5D WFS, ∆x = 10 cm, L = 10 m) Properties of focused sources [Spors et al. 2008] • high accuracy in proximity of focus point (high aliasing frequency) • amplitude decay in between point/line source • audible pre-echos and localization errors may be apparent Spors, Wierstorf | Virtual Endfire Array | Focused Sources 7
  15. Implementation s(t) Superdirective Beamformer Acoustic Focusing beamsteering 1 1 2

    2 . . . . . . N M • superdirective (MVDR) design for static virtual monopoles • generation of focused sources by Wave Field Synthesis • level normalized for focused sources • beamsteering by tilting of virtual endfire array Spors, Wierstorf | Virtual Endfire Array | Focused Sources 8
  16. Comparison to Endfire Loudspeaker Array Monofrequent Signal f = 1000

    Hz Endfire Array x (m) y (m) −2 −1 0 1 2 0 1 2 3 4 5 −1 −0.5 0 0.5 1 Virtual Endfire Array x (m) y (m) −2 −1 0 1 2 0 1 2 3 4 5 −1 −0.5 0 0.5 1 • (virtual) endfire array loudspeaker distance ∆x = 10 cm • number of (virtual) endfire loudspeakers N = 8 • WFS loudspeaker distance 10 cm, length 10 m Spors, Wierstorf | Virtual Endfire Array | Results 9
  17. Comparison to Endfire Loudspeaker Array Monofrequent Signal f = 1000

    Hz Endfire Array x (m) y (m) −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −2 −1 0 1 2 0 1 2 3 4 5 Amplitude (dB) −40 −30 −20 −10 0 Virtual Endfire Array x (m) y (m) −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −2 −1 0 1 2 0 1 2 3 4 5 Amplitude (dB) −40 −30 −20 −10 0 • (virtual) endfire array loudspeaker distance ∆x = 10 cm • number of (virtual) endfire loudspeakers N = 8 • WFS loudspeaker distance 10 cm, length 10 m Spors, Wierstorf | Virtual Endfire Array | Results 9
  18. Distance/Number of Virtual Endfire Sources Endfire array loudspeaker distance ∆x

    = 10 cm, N = 8 Synthesized Sound Field x (m) y (m) −2 −1 0 1 2 0 1 2 3 4 5 −1 −0.5 0 0.5 1 Level (dB) x (m) y (m) −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −2 −1 0 1 2 0 1 2 3 4 5 Amplitude (dB) −40 −30 −20 −10 0 • monofrequent signal f = 1000 Hz • WFS loudspeaker distance 10 cm, length 10 m Spors, Wierstorf | Virtual Endfire Array | Results 10
  19. Distance/Number of Virtual Endfire Sources Endfire array loudspeaker distance ∆x

    = 5 cm, N = 16 Synthesized Sound Field x (m) y (m) −2 −1 0 1 2 0 1 2 3 4 5 −1 −0.5 0 0.5 1 Level (dB) x (m) y (m) −20 −20 −20 −20 −20 −20 −20 −20 −2 −1 0 1 2 0 1 2 3 4 5 Amplitude (dB) −40 −30 −20 −10 0 • monofrequent signal f = 1000 Hz • WFS loudspeaker distance 10 cm, length 10 m Spors, Wierstorf | Virtual Endfire Array | Results 10
  20. Distance/Number of Virtual Endfire Sources Endfire array loudspeaker distance ∆x

    = 2.5 cm, N = 32 Synthesized Sound Field x (m) y (m) −2 −1 0 1 2 0 1 2 3 4 5 −1 −0.5 0 0.5 1 Level (dB) x (m) y (m) −20 −20 −20 −20 −20 −20 −20 −20 −2 −1 0 1 2 0 1 2 3 4 5 Amplitude (dB) −40 −30 −20 −10 0 • monofrequent signal f = 1000 Hz • WFS loudspeaker distance 10 cm, length 10 m Spors, Wierstorf | Virtual Endfire Array | Results 10
  21. Influence of Frequency/Spatial Sampling Monofrequent Signal f = 1000 Hz

    Synthesized Sound Field x (m) y (m) −2 −1 0 1 2 0 1 2 3 4 5 −1 −0.5 0 0.5 1 Level (dB) x (m) y (m) −20 −20 −20 −20 −20 −20 −20 −20 −2 −1 0 1 2 0 1 2 3 4 5 Amplitude (dB) −40 −30 −20 −10 0 • (virtual) endfire array loudspeaker distance ∆x = 2.5 cm • number of (virtual) endfire loudspeakers N = 32 • WFS loudspeaker distance 10 cm, length 10 m Spors, Wierstorf | Virtual Endfire Array | Results 11
  22. Influence of Frequency/Spatial Sampling Monofrequent Signal f = 2000 Hz

    Synthesized Sound Field x (m) y (m) −2 −1 0 1 2 0 1 2 3 4 5 −1 −0.5 0 0.5 1 Level (dB) x (m) y (m) −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −2 −1 0 1 2 0 1 2 3 4 5 Amplitude (dB) −40 −30 −20 −10 0 • (virtual) endfire array loudspeaker distance ∆x = 2.5 cm • number of (virtual) endfire loudspeakers N = 32 • WFS loudspeaker distance 10 cm, length 10 m Spors, Wierstorf | Virtual Endfire Array | Results 11
  23. Influence of Frequency/Spatial Sampling Monofrequent Signal f = 4000 Hz

    Synthesized Sound Field x (m) y (m) −2 −1 0 1 2 0 1 2 3 4 5 −1 −0.5 0 0.5 1 Level (dB) x (m) y (m) −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −2 −1 0 1 2 0 1 2 3 4 5 Amplitude (dB) −40 −30 −20 −10 0 • (virtual) endfire array loudspeaker distance ∆x = 2.5 cm • number of (virtual) endfire loudspeakers N = 32 • WFS loudspeaker distance 10 cm, length 10 m Spors, Wierstorf | Virtual Endfire Array | Results 11
  24. Beamsteering by Placement of Virtual Sources Steering angle θ =

    60o Synthesized Sound Field x (m) y (m) −2 −1 0 1 2 0 1 2 3 4 5 −1 −0.5 0 0.5 1 Level (dB) x (m) y (m) −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −20 −2 −1 0 1 2 0 1 2 3 4 5 Amplitude (dB) −40 −30 −20 −10 0 • (virtual) endfire array loudspeaker distance ∆x = 2.5 cm, N = 32 • monofrequent Signal f = 2000 Hz • WFS loudspeaker distance 10 cm, length 10 m Spors, Wierstorf | Virtual Endfire Array | Results 12
  25. Conclusions Generation of acoustic beams by two stage approach 1.

    synthesis of focused sources 2. superdirective beamforming using virtual endfire array • combination of delay-and-sum focusing with superdirective beamforming • achieved gain comparable to other techniques • not limited to linear arrays • reproducible research → Sound Field Synthesis (SFS) Toolbox Outlook • investigation of robustness (loudspeaker mismatch) • incorporate properties of focused sources into beamformer design Spors, Wierstorf | Virtual Endfire Array | Results 13
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