Local Sound Field Synthesis by Virtual Secondary Sources

Local Sound Field Synthesis by Virtual Secondary Sources Sascha Spors and Jens Ahrens Deutsche Telekom Laboratories Quality and Usability Lab Technische Universität Berlin

AES 40th International Conference Tokyo 2010

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Introduction most Sound Field Synthesis (SFS) approaches aim at large listening area practical realization limits frequency range and/or size of listening area local high-resolution synthesis with limited number of loudspeakers → local Sound Field Synthesis previous work position dependent optimization of Wave Field Synthesis (WFS) [Corteel et al. 2008], [Melchior et al. 2008], ... translation of sweet-spot in higher-order Ambisonics (HOA) [Ahrens et al. 2009], [Wu et al. 2009], ... multipoint synthesis [Poletti et al. 2008], [Hannemann et al. 2008], [Kolundzija et al. 2009],...

Here: introduction of novel approach based on the concept of virtual loudspeakers illustration on the example of WFS S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 1 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Example – Influence of Secondary Source Density Synthesis of monochromatic plane wave with fpw = 1 kHz R = 1.50 m

1.5

1.5

1

1

0.5

0.5

0 −0.5

0 −0.5

−1

−1

−1.5

−1.5

−2 −2

−1

0 x −> [m]

R = 0.50 m

2

y −> [m]

y −> [m]

2

1

−2 −2

2

−1

0 x −> [m]

1

2

2.5D WFS, N = 56, αpw = 90o

S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 2 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Example – Influence of Secondary Source Density Synthesis of monochromatic plane wave with fpw = 2 kHz R = 1.50 m

1.5

1.5

1

1

0.5

0.5

0 −0.5

0 −0.5

−1

−1

−1.5

−1.5

−2 −2

−1

0 x −> [m]

R = 0.50 m

2

y −> [m]

y −> [m]

2

1

2

−2 −2

−1

0 x −> [m]

1

2

2.5D WFS, N = 56, αpw = 90o

S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 2 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Example – Influence of Secondary Source Density Synthesis of monochromatic plane wave with fpw = 3 kHz R = 1.50 m

1.5

1.5

1

1

0.5

0.5

0 −0.5

0 −0.5

−1

−1

−1.5

−1.5

−2 −2

−1

0 x −> [m]

R = 0.50 m

2

y −> [m]

y −> [m]

2

1

−2 −2

2

−1

0 x −> [m]

1

2

2.5D WFS, N = 56, αpw = 90o

S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 2 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Example – Influence of Secondary Source Density Synthesis of monochromatic plane wave with fpw = 4 kHz R = 1.50 m

1.5

1.5

1

1

0.5

0.5

0 −0.5

0 −0.5

−1

−1

−1.5

−1.5

−2 −2

−1

0 x −> [m]

R = 0.50 m

2

y −> [m]

y −> [m]

2

1

2

−2 −2

−1

0 x −> [m]

1

2

2.5D WFS, N = 56, αpw = 90o

S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 2 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Local SFS by Virtual Secondary Sources accuracy of SFS depends on spatial density of secondary sources number of secondary sources is restricted in practice use existing ones to create virtual ones with a higher spatial density drive virtual secondary sources like real ones placed at their positions virtual source

∂ Vl

S (x, ω)

Vl ∂V

V

⇒ use acoustic focusing techniques to create virtual secondary sources S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 3 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Application to Sound Field Synthesis Techniques straightforward application to approaches that can synthesize focused sources for instance WFS, HOA, Spectral Division Method (SDM), ... different SFS techniques can be combined

xfs

nfs

2

M

x0

1 2

...

1

nfs

driving functions focused sources

xfs

...

s (t )

driving function virtual source

virtual source parameters

N

n0

S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 4 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Basic Concept for Linear Arrays Application of Huygens-Fresnel principle to sound synthesis in a half-space V )

V

primary source

continuous linear distribution ∂ V of monopole sources (secondary sources) strength (driving function) of secondary sources is given by Rayleigh integral in practice spatial discrete distribution of loudspeakers as secondary sources secondary point sources for 2D reproduction ⇒ 2.5D WFS S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 5 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Basic Concept for Linear Arrays Application of Huygens-Fresnel principle to sound synthesis in a half-space V

V

∂V primary source

continuous linear distribution ∂ V of monopole sources (secondary sources) strength (driving function) of secondary sources is given by Rayleigh integral in practice spatial discrete distribution of loudspeakers as secondary sources secondary point sources for 2D reproduction ⇒ 2.5D WFS S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 5 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Basic Concept for Linear Arrays Application of Huygens-Fresnel principle to sound synthesis in a half-space V

V

∂V virtual source

continuous linear distribution ∂ V of monopole sources (secondary sources) strength (driving function) of secondary sources is given by Rayleigh integral in practice spatial discrete distribution of loudspeakers as secondary sources secondary point sources for 2D reproduction ⇒ 2.5D WFS S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 5 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Basic Concept for Linear Arrays Application of Huygens-Fresnel principle to sound synthesis in a half-space V )

V

∆x

virtual source

continuous linear distribution ∂ V of monopole sources (secondary sources) strength (driving function) of secondary sources is given by Rayleigh integral in practice spatial discrete distribution of loudspeakers as secondary sources secondary point sources for 2D reproduction ⇒ 2.5D WFS S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 5 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Extension to Curved Arrays and Properties Extension to curved arrays approximation of Kirchhoff-Helmholtz integral limitation to convex secondary source distributions sensible selection of active secondary sources

Properties of WFS minor deviations due to involved approximations typically model-based rendering virtual source models: plane waves, point and complex sources sources inside listening area → focused sources very efficient implementation by pre-filter, weight and delay structure

S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 6 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Example – Curved Arrays Synthesis of monochromatic plane wave with fpw = 1 kHz Rectangular Array 2

1.5

1.5

1

1

0.5

0.5

y −> [m]

y −> [m]

Circular Array 2

0 −0.5

0 −0.5

−1

−1

−1.5

−1.5

−2 −2

−1

0 x −> [m]

1

2

−2 −2

2.5D WFS, N = 56, αpw = −45o

−1

0 x −> [m]

1

2 ∆x = 0.15 m

S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 7 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Example – Curved Arrays Synthesis of monochromatic plane wave with fpw = 4 kHz Rectangular Array 2

1.5

1.5

1

1

0.5

0.5

y −> [m]

y −> [m]

Circular Array 2

0 −0.5

0 −0.5

−1

−1

−1.5

−1.5

−2 −2

−1

0 x −> [m]

1

−2 −2

2

−1

0 x −> [m]

1

2.5D WFS, N = 56, αpw = −45o

2 ∆x = 0.15 m

S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 7 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Example – Curved Arrays Synthesis of monochromatic point source with fps = 1 kHz Rectangular Array 2

1.5

1.5

1

1

0.5

0.5

y −> [m]

y −> [m]

Circular Array 2

0 −0.5

0 −0.5

−1

−1

−1.5

−1.5

−2 −2

−1

0 x −> [m]

1

2

−2 −2

2.5D WFS, N = 56, xps = [0 3]T m

−1

0 x −> [m]

1

2 ∆x = 0.15 m

S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 7 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Example – Curved Arrays Synthesis of monochromatic point source with fps = 4 kHz Rectangular Array 2

1.5

1.5

1

1

0.5

0.5

y −> [m]

y −> [m]

Circular Array 2

0 −0.5

0 −0.5

−1

−1

−1.5

−1.5

−2 −2

−1

0 x −> [m]

1

−2 −2

2

−1

0 x −> [m]

2.5D WFS, N = 56, xps = [0 3]T m

1

2 ∆x = 0.15 m

S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 7 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Focused Sources typical realization in WFS by modeling acoustic sink at focus point results in converging wave field towards focus point, diverging after source must be located between listeners and loudspeakers for correct auralization sensible selection of active secondary sources (listener dependent)

x0 xfs

n0

nfs

V

S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 8 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Focused Sources typical realization in WFS by modeling acoustic sink at focus point results in converging wave field towards focus point, diverging after source must be located between listeners and loudspeakers for correct auralization sensible selection of active secondary sources (listener dependent) Properties of focused sources [Spors et al. 2008] high accuracy in proximity of focus point (high aliasing frequency) amplitude decay in proximity of focus point similar to line source audible pre-echos and localization errors may be apparent

S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 8 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Example – Properties of Focused Sources Synthesis of monochromatic focused source with fpw = 1 kHz 2 1.5

y −> [m]

1 0.5 0 −0.5 −1 −1.5 −2 −2

−1

0 x −> [m]

1

2

xfs = [0 0.2]T m, nfs = [0 − 1]T , N = 56, R = 1.50 m

S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 9 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Example – Properties of Focused Sources Synthesis of monochromatic focused source with fpw = 2 kHz 2 1.5

y −> [m]

1 0.5 0 −0.5 −1 −1.5 −2 −2

−1

0 x −> [m]

1

2

xfs = [0 0.2]T m, nfs = [0 − 1]T , N = 56, R = 1.50 m

S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 9 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Example – Properties of Focused Sources Synthesis of monochromatic focused source with fpw = 3 kHz 2 1.5

y −> [m]

1 0.5 0 −0.5 −1 −1.5 −2 −2

−1

0 x −> [m]

1

2

xfs = [0 0.2]T m, nfs = [0 − 1]T , N = 56, R = 1.50 m

S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 9 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Example – Properties of Focused Sources Synthesis of monochromatic focused source with fpw = 4 kHz 2 1.5

y −> [m]

1 0.5 0 −0.5 −1 −1.5 −2 −2

−1

0 x −> [m]

1

2

xfs = [0 0.2]T m, nfs = [0 − 1]T , N = 56, R = 1.50 m

S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 9 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Example – Properties of Focused Sources Synthesis of monochromatic focused source with fpw = 4 kHz 2 1.5

y −> [m]

1 0.5 0 −0.5 −1 −1.5 −2 −2

−1

0 x −> [m]

1

2

xfs = [−0.2 0]T m, nfs = [1 0]T , N = 56, R = 1.50 m

S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 9 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Derivation of Local Synthesis Operator limited listening area and propagation direction of focused sources has to be considered carefully secondary source selection by normal vector of virtual secondary source superposition of individual listening areas determines local listening area

virtual source xfs

S (x, ω)

nfs

Vl

S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 10 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Derivation of Local Synthesis Operator limited listening area and propagation direction of focused sources has to be considered carefully secondary source selection by normal vector of virtual secondary source superposition of individual listening areas determines local listening area

virtual source S (x, ω)

Vl nfs xfs

S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 10 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Derivation of Local Synthesis Operator limited listening area and propagation direction of focused sources has to be considered carefully secondary source selection by normal vector of virtual secondary source superposition of individual listening areas determines local listening area

virtual source Vl

S (x, ω)

S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 10 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Combination of Driving Functions

wM

w01 w02

+

δ(t − τ01 ) δ(t − τ02 )

+

...

δ(t − τ2 )

δ(t − τM )

w0N

preequalization

δ(t − τ0N )

wM 1 wM 2

+

δ(t − τM 1 ) δ(t − τM 2 )

...

s (t )

preequalization

...

w2 preequalization

δ(t − τ1 )

...

w1

wMN

S.Spors and J.Ahrens Local Sound Field Synthesis

δ(t − τMN )

8.10.2010 11 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Combination of Driving Functions combination of driving function for virtual source with focused sources exemplarily shown for a plane wave (details in paper) D (x0,n , ω) = Sˆpw (ω)

M ω ω
am,n wm ,n e −j c τm ,n c m =1

Inverse Fourier transformation F

d (x0,n , t ) = s (t ) ∗ h (t ) ∗

M


am,n wm ,n δ(t − τm ,n )

m =1

modified pre-equalization in comparison with traditional WFS efficient implementation by pre-equalization of virtual source and multiple delays/weights applied to pre-filtered signal (per loudspeaker) S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 11 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Example – Linear Loudspeaker Array Synthesis of monochromatic plane wave with fpw = 4 kHz 3 2.5

y −> [m]

2 1.5 1 0.5 0 −1.5

−1

−0.5

0 0.5 x −> [m]

1

1.5

N = 20, ∆x = 0.15 m, Nfs = 20, Rfs = 0.20 m, αpw = 90o

S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 12 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Example – Linear Loudspeaker Array Local synthesis of monochromatic plane wave with fpw = 4 kHz 3 2.5

y −> [m]

2 1.5 1 0.5 0 −1.5

−1

−0.5

0 0.5 x −> [m]

1

1.5

N = 20, ∆x = 0.15 m, Nfs = 20, Rfs = 0.20 m, αpw = 90o

S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 12 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Example – Linear Loudspeaker Array Local synthesis of monochromatic plane wave with fpw = 4 kHz 1.4 1.3

y −> [m]

1.2 1.1 1 0.9 0.8 0.7 0.6 −0.4

−0.2

0 x −> [m]

0.2

0.4

N = 20, ∆x = 0.15 m, Nfs = 20, Rfs = 0.20 m, αpw = 90o

S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 12 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Example – Circular Loudspeaker Array Synthesis of monochromatic plane wave with fpw = 4 kHz 2 1.5

y −> [m]

1 0.5 0 −0.5 −1 −1.5 −2 −2

−1

0 x −> [m]

1

2

N = 56, R = 1.50 m, Nfs = 56, Rfs = 0.20 m, αpw = 90o

S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 13 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Example – Circular Loudspeaker Array Local synthesis of monochromatic plane wave with fpw = 4 kHz 2 1.5

y −> [m]

1 0.5 0 −0.5 −1 −1.5 −2 −2

−1

0 x −> [m]

1

2

N = 56, R = 1.50 m, Nfs = 56, Rfs = 0.20 m, αpw = 90o

S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 13 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Example – Circular Loudspeaker Array Local synthesis of monochromatic plane wave with fpw = 4 kHz −0.1 −0.2

y −> [m]

−0.3 −0.4 −0.5 −0.6 −0.7 −0.8 −0.9 −0.4

−0.2

0 x −> [m]

0.2

0.4

N = 56, R = 1.50 m, Nfs = 56, Rfs = 0.20 m, αpw = 90o

S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 13 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Some Practical Aspects... sensible placement of virtual secondary sources necessary number of virtual secondary sources should not exceed number of available loudspeakers modified pre-equalization in comparison with WFS 6dB/Octave high-pass below spatial aliasing frequency 3dB/Octave high-pass above spatial aliasing frequency

moving listeners (local listening areas) can be handled by known techniques pre-echos of focused sources may become critical for large secondary source distributions investigation of countermeasures → [Wierstorf et al. 2010]

S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 14 / 15

Introduction Basic Concept Wave Field Synthesis Local Wave Field Synthesis Conclusions

Summary and Conclusions We have presented a versatile framework for local Sound Field Synthesis which is based upon the concept of virtual secondary sources virtual secondary sources can be realized by acoustic focusing techniques applicable to most of the known SFS approaches improved synthesis accuracy in a local listening area local WFS flexibility with respect to array layout and source models efficient implementation

interesting applications: in-car entertainment, gaming, home cinema, ... Further work links to established methods (e.g. multipoint synthesis) evaluation (listening experiments) S.Spors and J.Ahrens Local Sound Field Synthesis

8.10.2010 15 / 15