Wellenfeldsynthese: Grundlagen und Perspektiven

Transcription

1 Wellenfeldsynthese: Grundlagen und Perspektiven Sascha Spors, udolf abenstein, Stefan Petrausch, Herbert Buchner ETH Akustisches Kolloquium 22.Juni 2005 Telecommunications aboratory University of Erlangen-Nuremberg

2 Übersicht 1. Stereophonie 2. Wellenfeldsynthese Grundlagen 3. Wellenfeldsynthese Praktische Umsetzung 4. Wellenfeldanalyse 5. aumkompensation 6. Perpektiven, Zusammenfassung Page 1

3 Stereophonic eproduction Stereo ents sweet-spot Page 2

4 Stereophonic eproduction Stereo ents sweet-spot stereophonic reproduction is mainly based on psychoacoustic principles loudspeaker setup can only be configured to give optimum results for a very limited listening area sweet-spot often common listening environments cannot be realized as shown above Page 2

5 Stereophonic eproduction Stereo 5-hannel Surround PSfrag replacements ents sweet-spot S sweet-spot S stereophonic reproduction is mainly based on psychoacoustic principles loudspeaker setup can only be configured to give optimum results for a very limited listening area sweet-spot often common listening environments cannot be realized as shown above Page 2

6 Wave Field Produced by a Point Source PSfrag replacements S S sweet-spot 5-hannel Surround Page 3

7 Stereophonic eproduction of a Virtual Point Source PSfrag replacements S S sweet-spot 5-hannel Surround Page 4

8 Übersicht 1. Stereophonie 2. Wellenfeldsynthese Grundlagen 3. Wellenfeldsynthese Praktische Umsetzung 4. Wellenfeldanalyse 5. aumkompensation 6. Perpektiven, Zusammenfassung Page 5

9 Wave Field Synthesis (WFS) Milestones 1988 Paper: A.J.Berkhout, A holographic approach to acoustic control, J. Audio Engineering Society, Dec Paper: A.J.Berkhout, D.de Vries and P.Vogel, Acoustic control by wave field synthesis, J. Acoustical Society of America, May channel laboratory WFS system at the Technical University of Delft channel / 192 loudspeaker WFS prototype at the Technical University of Delft Page 6

10 Wave Field Synthesis (WFS) Milestones 1988 Paper: A.J.Berkhout, A holographic approach to acoustic control, J. Audio Engineering Society, Dec Paper: A.J.Berkhout, D.de Vries and P.Vogel, Acoustic control by wave field synthesis, J. Acoustical Society of America, May channel laboratory WFS system at the Technical University of Delft channel / 192 loudspeaker WFS prototype at the Technical University of Delft 2001 E IST Project AOUSO with focus on WFS 2003 first companies founded with focus on WFS (sonic emotion/iosono) first WFS/IOSONO cinema in Ilmenau/Germany (192 channels) 2004 first commercially avaiable WFS mixing console from AWO AG Page 6

11 WFS in a Nutshell Huygens (1690): Any point on a propagating wavefront can be taken as a point source for the production of spherical secondary waves. PSfrag replacements S S sweet-spot 5-hannel Surround primary source Page 7

12 WFS in a Nutshell Huygens (1690): Any point on a propagating wavefront can be taken as a point source for the production of spherical secondary waves. PSfrag replacements S S sweet-spot 5-hannel Surround virtual source Page 7

13 WFS in a Nutshell Huygens (1690): Any point on a propagating wavefront can be taken as a point source for the production of spherical secondary waves. PSfrag replacements S S sweet-spot 5-hannel Surround virtual source Page 7

14 eproduction of a Point Source with WFS PSfrag replacements S S sweet-spot 5-hannel Surround Page 8

15 eproduction of a Plane Wave with WFS PSfrag replacements S S sweet-spot 5-hannel Surround Page 9

16 frag replacements Sound eproduction The theoretical basis of sound reproduction is given by the Kirchhoff-Helmholtz integral: ( P (x, ω) = G(x x 0, ω) V n S(x 0, ω) S(x 0, ω) ) S n G(x x 0, ω) ds 0 S sweet-spot hannel Surround virtual source n ϕ x x 0 V S(x, ω) x 0 x V O Page 10

17 Sound eproduction The theoretical basis of sound reproduction is given by the Kirchhoff-Helmholtz integral: P (x, ω) = V Elimination of dipole secondary sources ( G(x x 0, ω) n S(x 0, ω) S(x 0, ω) ) n G(x x 0, ω) P (x, ω) = 2 V a(x 0 ) n (S(x 0, ω)) G(x x 0, ω) ds 0 ds 0 Page 10

18 Sound eproduction The theoretical basis of sound reproduction is given by the Kirchhoff-Helmholtz integral: P (x, ω) = V Elimination of dipole secondary sources ( G(x x 0, ω) n S(x 0, ω) S(x 0, ω) ) n G(x x 0, ω) P (x, ω) = 2 V a(x 0 ) n (S(x 0, ω)) G(x x 0, ω) ds 0 ds 0 hoice of G(x x 0, ω) eproduction in a Plane (2D): G 2D (x x 0, ω) = j 4 H(2) 0 (k x x 0 ) Secondary line sources eproduction in a Volume (3D): G 3D (x x 0, ω) = 1 e jk x x 0 4π x x 0 Secondary point sources Page 10

19 ine versus Point Sources Secondary ine Sources G 2D (x x 0, ω) = j 4 H(2) 0 (k x x 0 ) Secondary Point Sources G 3D (x x 0, ω) = 1 e jk x x 0 4π x x 0 Far-field approximation of H ν (1),(2) (kr): H ν (1),(2) (kr) 2 πkr e±j(kr 1 2 νπ 1 4 π) Page 11

20 ine versus Point Sources Secondary ine Sources G 2D (x x 0, ω) = j 4 H(2) 0 (k x x 0 ) Secondary Point Sources G 3D (x x 0, ω) = 1 e jk x x 0 4π x x 0 Far-field approximation of H ν (1),(2) (kr): H ν (1),(2) (kr) 2 πkr e±j(kr 1 2 νπ 1 4 π) 1/ r amplitude decay 1/ k frequency response esulting characteristics for secondary sources: Page 11

21 ine versus Point Sources Secondary ine Sources G 2D (x x 0, ω) = j 4 H(2) 0 (k x x 0 ) Secondary Point Sources G 3D (x x 0, ω) = 1 e jk x x 0 4π x x 0 Far-field approximation of H ν (1),(2) (kr): H ν (1),(2) (kr) 2 πkr e±j(kr 1 2 νπ 1 4 π) esulting characteristics for secondary sources: 1/ r amplitude decay 1/ k frequency response 1/r amplitude decay flat frequency response Page 11

22 Wave Field Synthesis WFS aims at correctly reproducing the wave field in a plane using point sources: reproduction in a plane only is suitable for typical scenarios point sources can be approximated by closed loudspeakers Mismatch of secondary source types (line point source) Page 12

23 Wave Field Synthesis WFS aims at correctly reproducing the wave field in a plane using point sources: reproduction in a plane only is suitable for typical scenarios point sources can be approximated by closed loudspeakers Mismatch of secondary source types (line point source) onsequences of secondary source type mismatch: amplitude errors due to different amplitude decays over distance spectral errors due to different spectral characteristics Page 12

24 Wave Field Synthesis WFS aims at correctly reproducing the wave field in a plane using point sources: reproduction in a plane only is suitable for typical scenarios point sources can be approximated by closed loudspeakers Mismatch of secondary source types (line point source) onsequences of secondary source type mismatch: amplitude errors due to different amplitude decays over distance spectral errors due to different spectral characteristics orrection of reproduced amplitude and spectral characteristics required! Page 12

25 Wave Field Synthesis Stationary Phase Approximation orrection of secondary source mismatch for the reproduction of a plane wave (pw) using the stationary phase approximation: P (x, ω) 2 1 jk V 2π x x0 a(x 0 ) n S pw(x 0, ω) e jk x x0 4π x x 0 dv 0 Page 13

26 Wave Field Synthesis Stationary Phase Approximation orrection of secondary source mismatch for the reproduction of a plane wave (pw) using the stationary phase approximation: P (x, ω) 2 1 jk V 2π x x0 a(x 0 ) n S pw(x 0, ω) e jk x x0 4π x x 0 dv 0 spectral correction amplitude correction secondary sources Page 13

27 Wave Field Synthesis Stationary Phase Approximation orrection of secondary source mismatch for the reproduction of a plane wave (pw) using the stationary phase approximation: P (x, ω) 2 1 jk V 2π x x0 a(x 0 ) n S pw(x 0, ω) e jk x x0 4π x x 0 dv 0 spectral correction amplitude correction secondary sources spectral correction is independent of geometry amplitude correction is dependent on receiver position amplitude correction only possible for one reference position (line) similar results can be derived for the reproduction of point sources Page 13

28 S sweet-spot 5-hannel Surround Wave Field Synthesis Spatial Sampling V virtual source n x 0 x S(x, ω) V x x 0 ϕ O Page 14

29 S sweet-spot 5-hannel Surround Wave Field Synthesis Spatial Sampling V virtual source n x 0 x S(x, ω) V x x 0 ϕ O spatial sampling of secondary source distribution may result in spatial aliasing anti-aliasing conditions can be formulated in terms of bandwidth of the virtual source aliasing frequency of typical WFS systems: f al Hz for a loudspeaker distance of x = cm Page 14

30 S sweet-spot 5-hannel Surround Wave Field Synthesis Spatial Sampling V virtual source n x 0 x S(x, ω) V x x 0 ϕ O spatial sampling of secondary source distribution may result in spatial aliasing anti-aliasing conditions can be formulated in terms of bandwidth of the virtual source aliasing frequency of typical WFS systems: f al Hz for a loudspeaker distance of x = cm spatial aliasing contributions do not seem to be too audible Page 14

31 s WFS System H Wave Field Synthesis Signal Processing Time loudspeaker discretization of the underlying principles, yields that the loudspeaker driving signals driving signals can be obtained by a multichannel convolution: d s[k] h[k] d[k] Page 15

32 s WFS System H Wave Field Synthesis Signal Processing Time loudspeaker discretization of the underlying principles, yields that the loudspeaker driving signals driving signals can be obtained by a multichannel convolution: d s[k] h[k] d[k] The required impulse responses h[k] can be derived in two ways: Data-based endering record acoustic scene by wave field analysis techniques extrapolation of recorded data yields h[k] Model-based endering suitable source models allow closedform solutions for h[k] common models are point sources and plane waves Page 15

33 Advantages of Wave Field Synthesis No sweet-spot, correct spatial impression for all listener positions within the loudspeaker array virtual sources are localized instead of the loudspeakers Page 16

34 Advantages of Wave Field Synthesis No sweet-spot, correct spatial impression for all listener positions within the loudspeaker array virtual sources are localized instead of the loudspeakers real acoustic scenes can be recorded and auralized by WFS virtual acoustic scenes can be created: virtual rooms on the basis of room models spatial models for virtual sources: point sources, plane waves,... virtual sources can be placed at arbitrary positions, also within the listening area focused sources Page 16

35 Advantages of Wave Field Synthesis No sweet-spot, correct spatial impression for all listener positions within the loudspeaker array virtual sources are localized instead of the loudspeakers real acoustic scenes can be recorded and auralized by WFS virtual acoustic scenes can be created: virtual rooms on the basis of room models spatial models for virtual sources: point sources, plane waves,... virtual sources can be placed at arbitrary positions, also within the listening area focused sources WFS is backward compatible to existing reproduction standards Page 16

36 eproduction of a Focused Source with WFS PSfrag replacements S S sweet-spot 5-hannel Surround Page 17

37 Improvement of Surround eproduction with WFS ag replacements hannel Surround S sweet-spot S Page 18

38 Improvement of Surround eproduction with WFS ag replacements S S sweet-spot hannel Surround S S Page 18

39 Improvement of Surround eproduction with WFS ag replacements S S sweet-spot hannel Surround S S Page 18

40 Übersicht 1. Stereophonie 2. Wellenfeldsynthese Grundlagen 3. Wellenfeldsynthese Praktische Umsetzung 4. Wellenfeldanalyse 5. aumkompensation 6. Perpektiven, Zusammenfassung Page 19

41 ents S S spot ound Sounds Trajectories Schematic Blockdiagramm of a WFS System Source Model WFS Soundcard D/A-onverter Amplifier oom Model P/DSP Speakers Page 20

42 TU Delft First WFS Demonstration System (1994) replacements S S sweet-spot nel Surround Page 21

43 MS WFS Systems ag replacements S S sweet-spot hannel Surround Page 22

44 MS WFS Systems ag replacements S S sweet-spot hannel Surround Page 22

45 MS WFS Systems ag replacements S S sweet-spot hannel Surround Page 22

46 WFS/IOSONO inema in Ilmenau replacements S S sweet-spot nel Surround Fraunhofer Institut für Digitale Medientechnologie, Ilmenau Page 23

47 Hardware: TU Delft DSP System (1994) ents S S spot und Page 24

48 MS Hardware: 16-channel PowerAmps ag replacements S S sweet-spot hannel Surround Page 25

49 MS Hardware: WFS endering Ps ag replacements S S sweet-spot hannel Surround Page 26

50 MS Model-Based endering Software: WFSAPP rag replacements S S sweet-spot hannel Surround Page 27

51 spot und WFS Application Scenario (E Project AOUSO) rtual primary sources virtual sources source recording weet spot recording room source position impulse responses WFS listening room virtual recording room Page 28

52 Übersicht 1. Stereophonie 2. Wellenfeldsynthese Grundlagen 3. Wellenfeldsynthese Praktische Umsetzung 4. Wellenfeldanalyse 5. aumkompensation 6. Perpektiven, Zusammenfassung Page 29

53 Wave Field epresentation Wave Field Analysis basic idea: expansion of the wave field into orthogonal components optimal transformation is dependent on the boundary conditions free-field solutions of the wave equation provide a reasonable basis: plane waves and circular harmonics Page 30

54 Wave Field epresentation Wave Field Analysis basic idea: expansion of the wave field into orthogonal components optimal transformation is dependent on the boundary conditions free-field solutions of the wave equation provide a reasonable basis: plane waves and circular harmonics Wave Field Measurement dense sampling of the entire listening area with microphones is not feasible the Kirchhoff-Helmholtz integral states that it is sufficient to measure on a curve surrounding the listening area spatial aliasing occurs due to the spatial sampling in practical implementations Page 30

55 Wave Field epresentation Wave Field Analysis basic idea: expansion of the wave field into orthogonal components optimal transformation is dependent on the boundary conditions free-field solutions of the wave equation provide a reasonable basis: plane waves and circular harmonics Wave Field Measurement dense sampling of the entire listening area with microphones is not feasible the Kirchhoff-Helmholtz integral states that it is sufficient to measure on a curve surrounding the listening area spatial aliasing occurs due to the spatial sampling in practical implementations ombination of both principles yields efficient implementations for wave field analysis using microphone arrays Page 30

56 Wave Field Decomposition... into Plane Waves: P (α, r, ω) = k (2π) 2 2π 0 P (θ, ω) e jkr cos(θ α) dθ Page 31

57 Wave Field Decomposition... into Plane Waves: P (α, r, ω) = k (2π) 2 2π 0 P (θ, ω) e jkr cos(θ α) dθ lacements S S weet-spot l Surround y > [m] f = 1kHz, θ = 45 o x > [m] PSfrag replacements S S sweet-spot 5-hannel Surround y > [m] f = 1kHz, θ = 90 o x > [m] Page 31

58 ... into ircular Harmonics: Wave Field Decomposition P (α, r, ω) = ν= ( P (1) (ν, ω) H (1) ν (kr) + P (2) (ν, ω) H ν (2) ) (kr) e jνα Page 31

59 ... into ircular Harmonics: Wave Field Decomposition P (α, r, ω) = ν= ( P (1) (ν, ω) H (1) ν (kr) + P (2) (ν, ω) H ν (2) ) (kr) e jνα lacements S S eet-spot l Surround PSfrag replacements angular basis functions ν = ν = ν = ν = 3 5-hannel 0 Surround S 240 S 210 sweet-spot {H ν (1) (kr)} I{H ν (1) (kr)} radial basis functions ν = 0 ν = 1 ν = 2 ν = kr kr Page 31

60 TU Delft: Wave Field Analysis of oncertgebouw g replacements S S sweet-spot annel Surround Page 32

61 Übersicht 1. Stereophonie 2. Wellenfeldsynthese Grundlagen 3. Wellenfeldsynthese Praktische Umsetzung 4. Wellenfeldanalyse 5. aumkompensation 6. Perpektiven, Zusammenfassung Page 33

62 Influence of the istening oom ents S S -spot round imary urce room area Page 34

63 Influence of the istening oom ents S S -spot round primary source room area Page 34

64 Influence of the istening oom ents S S -spot round primary source room area Page 34

65 Influence of the istening oom ents S S -spot round listening area listening room virtual source Page 34

66 Influence of the istening oom ents S S -spot round listening area listening room virtual source Goal: ompensation of listening room reflections Page 34

67 Influence of the istening oom ents S S -spot round listening area listening room virtual source Proposed solution: Active compensation of listening room reflections Page 34

68 eproduction of a Plane Wave everberant istening oom PSfrag replacements S S sweet-spot 5-hannel Surround Page 35

69 M F M Traditional Approaches to oom ompensation 1 1 l a e s h M 1 d M M listening area + Page 36

70 M F M Traditional Approaches to oom ompensation 1 1 l a e s h M 1 d M M M w M listening area + Basic idea: Pre-filtering of the loudspeaker driving signals with suitable compensation filters Page 36

71 Traditional Approaches to oom ompensation 1 1 s h M 1 d M M w M M M F M + e listening area 1 a l + Basic idea: Pre-filtering of the loudspeaker driving signals with suitable compensation filters Page 36

72 Traditional Approaches Applied to WFS 1 s h M 1 d M M w 1 M M M d F M e listening area + 1 a l + Page 37

73 Traditional Approaches Applied to WFS 1 s h M 1 d M M w 1 M M M d F M e listening area + 1 a l + Page 37

74 Traditional Approaches Applied to WFS 1 s h M 1 d M M w 1 M M M d F M e listening area + 1 a l + oom compensation can be understood as inverse multiple-input multiple-output (MIMO) system modeling. Page 37

75 Traditional Approaches Applied to WFS 1 s h M 1 d M M w 1 M M M d F M e listening area + 1 a l + Straightforward implementation of active room compensation with WFS/WFA is not feasible due to the large number of (correlated) channels. Page 37

76 Proposed Approach c 1 c N T 1 w T 2 s q w N N M F ẽ listening area ã + N l T 3 l Proposed approach: Introduce spatio-temporal transformations T 1, T 2, T 3 and Page 38

77 c 1 1 Proposed Approach 1 c N s T q w 1 N N M F + ẽ 1 listening area ã l + N Proposed approach: Introduce spatio-temporal transformations T 1, T 2, T 3 and perform adaptation in transformed signal domain. Page 38

78 l Proposed Approach 1 1 c 1 c Ñ s T q w 1 _t N N M F + ẽ 1 listening area ã l + N Desired: Diagonalization of room response through transformations T 2 and T 3 decoupling of MIMO system into several SISO systems. Page 38

79 l Proposed Approach 1 1 c 1 c Ñ s T q w 1 _t N N M F + ẽ 1 listening area ã l + N In practice: Use data-independent transformations that perform energy compaction and decorrelation of. Page 38

80 l Proposed Approach 1 1 c 1 c Ñ s T q w 1 _t N N M F + ẽ 1 listening area ã l + N How to derive suitable choices for the transformations T 1, T 2 and T 3? Page 38

81 oom ompensation: Experimental Setup Parameters Used for the Experiments: Geometry of Set-up: listening room size m ( 105 m 3 ), T ms 48 channel circular WFSPSfrag systemreplacements (virtual) circular microphone array with 48 discrete microphone positions S S sweet-spot 5-hannel Surround Page 39

82 oom ompensation: Experimental Setup Parameters Used for the Experiments: Geometry of Set-up: listening room size m ( 105 m 3 ), T ms 48 channel circular WFS system (virtual) circular microphone array with 48 discrete microphonepsfrag positions replacements mic = 0.75 m, S = 1.5 m frequency range: Hz desired wave field: moving point source S angle α = , distance = 5 m S sweet-spot basis functions for T 1, T5-hannel 2 and T 3 : Surround circular harmonics microphone array = 0.75 m = 1.5 m virtual source position Page 39

83 esults Decoupling of oom esponse room response (energy) ments S S t-spot rround Microphone oudspeaker 8 Page 40

84 esults Decoupling of oom esponse room response (energy) wave domain room response (energy) ments S S t-spot rround Microphone oudspeaker 1 2 PSfrag replacements S 7 S sweet-spot 8 5-hannel Surround k θin > k > θout Page 40

85 esults Decoupling of oom esponse room response (energy) wave domain room response (energy) ments S S t-spot rround Microphone oudspeaker 1 2 PSfrag replacements S 7 S sweet-spot 8 5-hannel Surround k θin > k > θout compensation filters were used to calculate the results (down from 2304) Page 40

86 esults Adaptation cements S S et-spot urround Mean squared error > [db] virtual source angle > [ o ] time > [s] Page 41

87 esults Tracking 30 o 0 o 0 db 5 30 o o o eplacements S S sweet-spot el Surround result target measured 90 o 120 o o 0 db 150 o 180 o 120 o 90 o Page 42

88 Active Players in Wave Field Synthesis Universities Technical University of Delft University Erlangen-Nuremberg Universitat Politecnica de Valencia Technical University Berlin and several more... esearch Institutions Fraunhofer Institute for Digital Media Technology Institut für undfunktechnik (IT) Institut de echerche et de oordination Acoustique/Musique (IAM) ompanies sonic emotion ag IOSONO GmbH SchlenkerTec GmbH Page 43

89 Summary & Perspectives Summary WFS allows physically correct auralization of wave fields WFS provides new possibilities for auralization, e.g. free placement of virtual sources focused sources realistic auralization of recorded/virtual acoustic scenes non-audibility of spatial aliasing relies on psychoacoustic principles Page 44

90 Summary & Perspectives Summary WFS allows physically correct auralization of wave fields WFS provides new possibilities for auralization, e.g. free placement of virtual sources focused sources realistic auralization of recorded/virtual acoustic scenes non-audibility of spatial aliasing relies on psychoacoustic principles Perspectives for WFS several demonstration/prototype systems have proven the realizability of WFS WFS based auralization systems are already commercial available! Applications for WFS: inema, Exhibitions, Virtual eality,... Page 44