A Virtual Endfire Loudspeaker Array for the Generation of Sound Beams

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

Transcript

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
   

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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
   

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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
   

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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
   

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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
   

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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
   

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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
   

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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
   

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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
   

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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
    

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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
    

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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
    

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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
    

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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
    

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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
    

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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
    

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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
    

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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
    

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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
    

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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
    

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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
    

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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
    

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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
    

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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
    

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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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26. Thanks for your attention!
    www.spatialaudio.net
    

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