Introduction of our research (FY2020)

Transcript

1. Introduction of Our Research on Sound Field Analysis and Control

   in FY2020 Shoichi Koyama, Ph.D. The University of Tokyo

2. Analysis and control of acoustic field March 26, 2020 2

   Analysis Control Ø Visualization and reconstruction of acoustic field Ø Estimation of source locations and room-acoustic parameters Ø Spatial sound field recording Ø High-fidelity spatial audio reproduction Ø Directivity control and local reproduction Ø Spatial active noise control From theory to application of signal processing and inverse problems for acoustic fields Microphone Loudspeaker

3. Summary in sound field analysis March 26, 2020 3 •

   Sound field reconstruction based on harmonic analysis of infinite order [Ueno+ IEEE SPL 2018] • Optimization algorithm for sparse representation of acoustic field [Murata+ IEEE TSP 2018] • Sparse sound field decomposition in reverberant environment [Koyama+ IEEE JSTSP 2019] • Separation of internal and external sound fields [Takida+ EUSIPCO 2018] • Estimation of source parameters based on Reciprocity Gap Functional [Takida+ Elsevier SP 2019] Analysis inside region without sources Analysis inside region including sources

4. Summary in sound field control March 26, 2020 4 •

   Sound field control based on weighted mode-matching [Ueno+ IEEE/ACM TASLP 2019] • Sound field recording and reproduction in wave-number domain [Koyama+ IEEE(/ACM) TASLP 2013, 2014, JASA 2016] • Super-resolution in recording and reproduction [Koyama+ IEEE JSTSP 2015, JASA 2018] • Optimization of source and sensor placement for sound field control [Koyama+ IEEE/ACM TASLP 2020, IEEE ICASSP 2018] • Spatial active noise control based on kernel interpolation [Ito+ IEEE ICASSP 2019]

5. SOUND FIELD ANALYSIS March 26, 2020 5

6. Analysis inside region without sources March 26, 2020 6 Ø

   Sound field satisfies homogeneous Helmholtz eq. <latexit sha1_base64="U/XXJXKvIw2E1EilpsiBLtz7MGo=">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</latexit> <latexit sha1_base64="okEXIY/pPSAfenmSSDCRtw4HgOI=">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</latexit> Microphone Sound wave Unknown boundary condition outside <latexit sha1_base64="ff/e1A/38XpRts4D3M/3UmeqwhY=">AAADXnicdZJfaxNBEMC3Oa01WvvHF8GXwyD4FO6soC9CaF/6Uqxg0kIulLnNXLJm/xy7c5p4pJ/BV/1mvvlR3EtTNc1lYGH4zfyY3WXSXApHUfRrqxHcu7/9YOdh89Hj3Sd7+weHPWcKy7HLjTT2MgWHUmjskiCJl7lFUKnEi3RyUtUvvqB1wuhPNMtxoGCkRSY4kEe95IPCEVztt6J2tIhwPYmXSYst4/zqoHGcDA0vFGriEpzrx1FOgxIsCS5x3kwKhznwCYyw71MNCt2gXFx3Hr70ZBhmxvqjKVzQ/40SlHMzlfpOBTR2d2sVrKv1C8reDUqh84JQ85tBWSFDMmH19nAoLHKSM58At8LfNeRjsMDJ/9DKlFT5N2j8yo1SoIdlAnakYDovk2qqycvEqtCz6womUihBrsYQusbwcKPhinzdqOBGQ+hs3ahgveGne/wNV52/dIME0zrplv6TFEwQ/A6S/9BmwjtnMD0DsmLqF9G9j49uOwyN0fqti+/u2HrSe92Oo3b88U2rc7zcvx32nL1gr1jM3rIOO2XnrMs4+8y+sx/sZ+N3sB3sBns3rY2tpfOUrUTw7A+oOyHJ</latexit> Expansion into finite number of plane waves / spherical harmonics is typical approach

7. Analysis inside region without sources Ø Spherical wavefunction expansion Ø

   Estimation of expansion coeff at arbitrary point March 26, 2020 7 [Ueno+ IEEE SPL 2018] <latexit sha1_base64="TnKjsQx5LCjG+RPMUHDUz7skgmU=">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</latexit> Spherical wavefunction Expansion coeff at center <latexit 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sha1_base64="8B+ZNBL5UQkvn4J1WUEojaP77iI=">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</latexit> Estimates of expansion coeff at <latexit sha1_base64="8B+ZNBL5UQkvn4J1WUEojaP77iI=">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</latexit> Matrix product of infinite orders can be analytically derived, and dependency on expansion center is eliminated Observations <latexit 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sha1_base64="PC9pAlu3s2zNT+S7GE8ISzdeo94=">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</latexit> Matrix of translation operators <latexit 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8. Relation to kernel ridge regression Ø Corresponds to kernel ridge

   regression using spherical Bessel function as kernel function March 26, 2020 8 [Ueno+ IEEE SPL 2018, IWAENC 2018] <latexit sha1_base64="Nwb3n7CEyAyxNvvm5JH9L1bryVs=">AAADz3icdZLPb9MwFICdBtjo+NHBkYtFhdQKrUoG0rhUqsYFDpU6iW6T6i56cZ3WNHYi22EtWSau/ImIfwan7YCuraXIz9/z55c4L0xjro3n/XIq7oOHj/b2H1cPnjx99rx2+OJcJ5mirE+TOFGXIWgWc8n6hpuYXaaKgQhjdhFOP5b5i29MaZ7IL2aesqGAseQRp2AsCmoZmYDJs6JBQpGroonbmOhMBLlo+8VVF5OYRaaBF2nS07zAby2z548Al+xz0bzKj/xisdB2Unw8Mc1A4K+BhxtTcrM8+Gg5BYLcBMfNoFb3Wt5i4M3AXwV1tBq94LBySkYJzQSThsag9cD3UjPMQRlOY1ZUSaZZCnQKYzawoQTB9DBf3E+B31gywlGi7CMNXtD/jRyE1nMR2p0CzETfz5VwW26QmejDMOcyzQyTdFkoymJsElxeNh5xxaiJ5zYAqrh9V0wnoIAa+0vWqoTCfoNk1zQRAuQoJ6DGAmZFTsqqSZoTJbBltyUkMRfc6C0Gl1sMC3caOks3jRLuNLiMNo0SbjdsdYu/s3XnL90hwWybdEf/SQKmDGzTG3uhVUI7XZh1wSg+s52v2/67ux2JmTBlu86/32Obwflxy/da/tn7eud01X/76BV6jRrIRyeogz6hHuojin47jlN1Dtwz99q9dX8st1aclfMSrQ335x+c9kl3</latexit> Gram matrix consisting of spherical Bessel functions Observations Position of th mic <latexit sha1_base64="0uStd8PEwCtmctIFyVxU/PU2PFc=">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</latexit> Kernel ridge regression with constraint that interpolation function satisfies Helmholtz eq. <latexit sha1_base64="E0VINkcXCNAwA1Jtzy3Bn53aBRg=">AAAELXicjZNNb9MwGMedhpcR3jo4crGoQONAlQDSxmFSNS5cKhWJbpPqKnIcpzWN7ch2RksWvhIfBnFAQlz5Gjh9GWubSliK9Nf/+f/0OPbjKEuZNr7/02m4N27eur13x7t77/6Dh839R6da5orQPpGpVOcR1jRlgvYNMyk9zxTFPErpWTR5V9XPLqjSTIqPZpbRIccjwRJGsLFW2PyOIl6gnmYlPIYeiuiIiSLi2Cg2Lb1PoX8wgeiyCqkyDF6uBLp8AZ9DRGJptBW7ct0qh5CHLpZBFK/EwrG1Dbb7nz2613t4iIr4atths+W3/fmC2yJYihZYrl643zhBsSQ5p8KQFGs9CPzMDAusDCMpLT2Ua5phMsEjOrBSYE71sJiffgmfWSeGiVT2EwbO3etEgbnWMx7ZpN3gWG/WKrOuNshNcjQsmMhyQwVZNEryFBoJq6uEMVOUmHRmBSaK2b1CMsYKE2MvfK1LxO0/CPqZSM6xPSmE1YjjaVmgqqvMCqQ4tN7XykQp48zoGoKJGsKaOwmdZ9tEZe4kmEi2icqsJ2x3a3+h68yVuwPC0zpo5f6DOJ5QbJ+UsQfqIdLp4ml3PmL2Xenj4PUqIc2YKjt1weaMbYvTV+3Abwcf3rQ6J8v52wNPwFNwAAJwCDrgPeiBPiDOWyd0xg5zv7k/3F/u70W04SyZx2BtuX/+AlX4a+A=</latexit>

9. Results of simulation experiments March 26, 2020 9 Proposed Proposed

   Kernel ridge regression using Gaussian kernel Error Ø Estimation of plane wave field at 200Hz

10. Application to spatial ANC Ø Active Noise Control: ANC –

    Noise cancellation using adaptive filter and loudspeaker Ø Noise control at discrete positions in conventional method March 26, 2020 10 ANC inside continuous region: spatial ANC Loudspeaker Error mic Noise source Control region Reference mic [Ito+ IEEE ICASSP 2019]

11. Application to spatial ANC Ø ANC based on weighted normalized

    least mean square (NLMS) as adaptive filter March 26, 2020 11 Noise source Reference mic Secondary path Error mic Weighted NLMS Adaptive filter <latexit sha1_base64="6jxgo/ZFQN4grGNTy6hJW6mkfw8=">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</latexit> <latexit sha1_base64="gZ4y0s+Ju4HTfczPeU9lR8uUGGM=">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</latexit> <latexit sha1_base64="p08G7F0QTz8++Zfa7RXJ2cJdAGo=">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</latexit> <latexit sha1_base64="cd2ZPdzJsne9Qg0zaED0AnVkuHg=">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</latexit> <latexit sha1_base64="RCYKXy3tAXaKbjqf0uxQlC+5rBg=">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</latexit> Driving signals <latexit sha1_base64="fUoTzLAXQTCGuzUzainTxTdFqRg=">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</latexit> Cost function: Filter update: Power of error mic including weighting coeff <latexit sha1_base64="eK62SxlrjP6i2nyGxlFlB6zwMj0=">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</latexit> <latexit sha1_base64="zanf4fTgx+iNYFFPFxKmlWRqETc=">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</latexit>

12. Application to spatial ANC Ø Cost function is formulated as

    regional noise power which is estimated by using kernel interpolation method for acoustic field March 26, 2020 12 <latexit sha1_base64="8sG3MC3lrsBMuNZaKxR7z4Tos08=">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</latexit> <latexit sha1_base64="Xjw/jwTwxeAj54v/lgakjUqgUCg=">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</latexit> Gram matrix for sound field interpolation Kernel function for sound field interpolation Regional noise power Weighted NLMS can be applied Ø Not only on discrete points, but regional noise control. Ø Computational cost for filter update is equivalent to conventional method [Ito+ IEEE ICASSP 2019]

13. Results of simulation experiment Ø Reduction of noise from three

    sources March 26, 2020 13 Proposed Conventional (multipoint control) Power dist. Regional noise reduction is achieved by proposed method [Ito+ IEEE ICASSP 2019]

14. Analysis inside region including sources March 26, 2020 14 Ø

    Sound field satisfies inhomogeneous Helmholtz eq. Source Microphone Reflected wave <latexit sha1_base64="VXB56x8cV3M2DCu+b66chBSNCqQ=">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</latexit> Unknown boundary condition outside <latexit sha1_base64="okEXIY/pPSAfenmSSDCRtw4HgOI=">AAADanicdZLdahNREIBPs/7U+NO0XklvFqNQQcKuCnojhHrjTaGCaQvZEGZPZpNDzs9yzmxNXOKTeKvv5Dv4EJ5NUzXNZmBh+OZ8zOwwaS6Foyj6tdMIbt2+c3f3XvP+g4eP9lr7B2fOFJZjjxtp7EUKDqXQ2CNBEi9yi6BSiefp9ENVP79E64TRn2me40DBWItMcCCPhq1WcZQooEmalXbxcvoiHLbaUSdaRriZxKukzVZxOtxvHCcjwwuFmrgE5/pxlNOgBEuCS1w0k8JhDnwKY+z7VINCNyiXoy/C556MwsxY/2kKl/R/owTl3Fyl/mU1prtZq2BdrV9Q9m5QCp0XhJpfNcoKGZIJqz2EI2GRk5z7BLgVftaQT8ACJ7+ttS6p8v+g8Qs3SoEelQnYsYLZolwuzuRlYlXo2bcKJlIoQa7GELrG8HCr4Yp806jgVkPobNOoYL3hu3v8Fdedv3SLBLM66Zr+kxRMEfw9kl9oM+HdE5idAFkx80fp3sevr18YmqD1VxffvLHN5OxVJ4468ac37e7x6v522SF7yo5YzN6yLvvITlmPcXbJvrMf7Gfjd3AQPAkOr542dlbOY7YWwbM/H9wlzg==</latexit> Source distribution <latexit sha1_base64="ff/e1A/38XpRts4D3M/3UmeqwhY=">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</latexit> This ill-posed inverse problem requires some constraint on source distribution for reconstruction

15. Sparse sound field decomposition Ø Summation of particular and homogeneous

    solutions Ø Discretizing region leads to linear equation March 26, 2020 15 <latexit sha1_base64="reMY8i1ewjRGRTHn33uoP6JqdRU=">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</latexit> Grid point [Koyama+ ICASSP 2014] Free-field Green’s func : Dictionary matrix : Observations : Direct source component : reverberant component

16. Sparse sound field decomposition Ø Assume that source distribution is

    spatially sparse and reconstruct sound field from observations Ø Group sparsity in time-frequency domain can also be taken into consideration March 26, 2020 16 <latexit sha1_base64="3unqeYcLzapR+kwzDMNoEVC+dbw=">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</latexit> <latexit sha1_base64="KdqboG5ErTF8Tsp8xTcQLhLEdoY=">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</latexit> Sparsity-inducing penalty term Non-zero grid point <latexit sha1_base64="CMp0bdMsbHJXrQaEDWLvT3oAJJo=">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</latexit> <latexit sha1_base64="f0AM1dFjbF0IvWOeeDQ4Zux15bE=">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</latexit> <latexit sha1_base64="HW0NkVNdxtG8JSmuoj2JEWTs8bY=">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</latexit> <latexit sha1_base64="0uStd8PEwCtmctIFyVxU/PU2PFc=">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</latexit> [Koyama+ ICASSP 2014] <latexit sha1_base64="TcKdDousfow9G7Auxdzcf+KrT68=">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</latexit>

17. Sparse optimization using mixed-norm penalty Ø Acoustic signals are generally

    sparse in time-frequency domain Ø Sparse optimization using mixed-norm penalty March 26, 2020 17 <latexit sha1_base64="jt8UZmLAo4CM+kOHoDXBXXv/2js=">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</latexit> <latexit sha1_base64="XMTa05C+9ds+LrBKIVtxIUVcJmU=">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</latexit> <latexit sha1_base64="jNNevYceU70kmgc9X62mIHeNJOc=">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</latexit> <latexit sha1_base64="UO/CtIGxHZlCwhDll94dyV4o5hI=">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</latexit> Optimization algorithm based on Majorization minimization method [Murata+ IEEE TSP 2018] Acoustic signal in time- frequency domain

18. Super-resolution in recording and reproduction Ø Experimental results using real

    data – Reproduction of speech signal from loudspeaker March 26, 2020 18 Spatial aliasing artifacts originating from microphone intervals can be alleviated Proposed Method based on plane- wave decomposition [Koyama+ JASA 2018]

19. SOUND FIELD CONTROL March 26, 2020 19

20. Sound field control using distributed array Ø Synthesize desired sound

    field inside using distributed loudspeakers March 26, 2020 20 <latexit sha1_base64="ff/e1A/38XpRts4D3M/3UmeqwhY=">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</latexit> Desired sound field Synthesized sound field Driving signal of th loudspeaker multiplied by transfer function Difficult to directly optimize because integration w.r.t. is included <latexit sha1_base64="ff/e1A/38XpRts4D3M/3UmeqwhY=">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</latexit>

21. Pressure matching Ø Synthesize desired sound field inside using distributed

    loudspeakers March 26, 2020 21 Desired pressure distribution Transfer function matrix Loudspeaker driving signals － Discretize target region and obtain driving signals so that pressure on control points corresponds to desired one <latexit sha1_base64="ff/e1A/38XpRts4D3M/3UmeqwhY=">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</latexit> Difficult to densely measure transfer functions inside region <latexit sha1_base64="ff/e1A/38XpRts4D3M/3UmeqwhY=">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</latexit>

22. Pressure matching Ø Synthesize desired sound field inside using distributed

    loudspeakers March 26, 2020 22 － Control points only on boundary of ? <latexit sha1_base64="ff/e1A/38XpRts4D3M/3UmeqwhY=">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</latexit> Significant degradation at several frequencies (Forbidden frequency problem) Can be alleviated by placing several control points inside target region, but to determine positions and number of these points is very difficult. <latexit sha1_base64="ff/e1A/38XpRts4D3M/3UmeqwhY=">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</latexit>

23. Weighted mode-matching Ø Control based on spherical wavefunction expansion of

    sound field March 26, 2020 23 [Ueno+ IEEE/ACM TASLP 2019] － Optimization problem including regional integral results in minimization problem w.r.t. expansion coefficients Expansion coeff of desired field Weighting matrix determined by regional integral Expansion coeff of transfer func

24. Weighted mode-matching Ø Control based on spherical wavefunction expansion of

    sound field March 26, 2020 24 [Ueno+ IEEE/ACM TASLP 2019] ü Truncation of expansion order can be avoided by weighting matrix ü Regional priority of control can be taken into consideration － Optimization problem including regional integral results in minimization problem w.r.t. expansion coefficients

25. Weighted mode-matching Ø Results of simulation experiment March 26, 2020

    25 -2 0 2 x (m) -2 0 2 y (m) -1 -0.5 0 0.5 1 Amplitude (real part) Synthesis of plane wave Generating quiet zone Suppression of external radiation Also applicable to multizone reproduction and external radiation suppression [Ueno+ IEEE/ACM TASLP 2019]

26. Optimization of source and sensor placement Ø Optimizing placement of

    loudspeakers and control points in pressure matching March 26, 2020 26 Dense sampling is Inherently necessary

27. Optimization of source and sensor placement Ø Optimizing placement of

    loudspeakers and control points in pressure matching March 26, 2020 27 Select optimal placement from candidates w.r.t. control accuracy and filter stability

28. Optimization of source and sensor placement Ø Optimizing placement of

    loudspeakers and control points in pressure matching March 26, 2020 28 － Optimal placement method based on Empirical Interpolation Method [Koyama+ IEEE ICASSP 2018] Sound field control problem is regarded as function interpolation problem: approximate desired sound field by using transfer functions as interpolation functions, control points as sampling points. Applied Empirical Interpolation Method proposed in numerical analysis of PDEs.

29. Optimization of source and sensor placement Ø Results of simulation

    experiments at 800Hz March 26, 2020 29 -2 0 2 x [m] -2 0 2 4 y [m] -2 0 2 x [m] -2 0 2 4 y [m] -0.5 0 0.5 x [m] -0.5 0 0.5 y [m] -1 0 1 -0.5 0 0.5 x [m] -0.5 0 0.5 y [m] -1 0 1 Proposed Regular Placement Pressure [Koyama+ IEEE ICASSP 2018] -0.5 0 0.5 x [m] -0.5 0 0.5 y [m] -40 -30 -20 -10 0 10 -0.5 0 0.5 x [m] -0.5 0 0.5 y [m] -40 -30 -20 -10 0 10 Error

30. Conclusion Ø Sound field analysis and control – Analysis: Harmonic

    analysis of infinite orders and its application to spatial ANC, Reconstruction based on sparse decomposition – Control: Weighted mode-matching, Optimization of source and sensor placement for sound field control Ø Recent topics – Optimization of sensor placement for field estimation, Interpolation of region-to-region acoustic transfer function, Binaural reproduction from measurements of distributed microphones, Spatial ANC Ø Keywords – Kernel method, Gaussian process, Reproducing kernel Hilbert space, Sparse modeling, Adaptive filter, Convex optimization, Physical acoustics, Partial differential equation March 26, 2020 30