[Internoise 2023 (invited)] Multilingual sound spot synthesis systems

Internoise 2023
21 Aug. 2023@Makuhari Messe
03.2 Spatil Capture & Reproduction
1-5-9 (invited) 14:20-14:40

Transcript

1. Multilingual sound spot synthesis systems 1 Takuma OKAMOTO National Institute of Information and Communications Technology, Japan ˏMakuhari Messe 03.2 Spatil Capture & Reproduction 1-5-9 (invited)
2. Multiple sound spot synthesis technology Technology introduction video Implementations of multiple sound spot synthesis systems Combined with real-time multilingual speech translation system Demo with implemented systems Conclusion Acknowledgements Outline 2
3. 3 Mode-matching-based sound fi eld control Localized sound zone control Sound fi eld recording and synthesis z = 0 [m] [dB] 1.5 2 2.5 y [m] -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 x [m] -30 -25 -20 -15 -10 -5 0 [dB] z = 0 [m] X axis [m] -1 0 1 Y axis [m] -1.5 -1 -0.5 0 0.5 1 1.5 -40 -30 -20 -10 0 Y axis [m] X axis [m] z = 0 [m] [dB] −2 −1 0 1 2 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 −40 −35 −30 −25 −20 −15 −10 −5 0 z = 0 [m] [dB] -1 0 1 2 3 4 y [m] -2 -1 0 1 2 x [m] -40 -35 -30 -25 -20 -15 -10 -5 0 ICASSP 2014 JASA 2017 ICASSP 2015 JIHMSP 2017 WASPAA 2015 JIHMSP 2017 IWAENC 2018 WASPAA 2019 ICASSP 2021 Quiet zone Listening zone rq rq rb r1 r2 ro ri ICASSP 2017 Reproduced sound field and reproduction error Sound field represented by angular spectrum coefficients Sound field recorded by linear receiver (Spatial Fourier transform) 2.5D HOA for circular secondary sources (J. Ahrens et al. 2008.) Analytical driving function of 2.5D synthesis Analytical approaches to sound field recording and reproduction Analytical conversion of sound field representation Analytical driving function of 2.5D synthesis for circular secondary sources Sound field recorded by linear microphone arrays can be reproduced by circular loudspeaker arrays 2.5D higher-order Ambisonics for a sound field described by angular spectrum coefficients Takuma OKAMOTO, National Institute of Information and Communication Technology, Japan 1. Introduction 2. Analytical conversion of sound field representation 3. Proposed formulation 4. Computer simulations Reproduction error Sound field Lmic = Lsp = 64 ch, x = 0.05 m, r0 = 2.0 m, xs = [1, 5, 0]T ˜ P( k, !) = ˜ P(kx, !) = Z 1 1 P(x, 0, !)ejkxxdx = Z 1 1 P(x, 0, !)ejk cos( k)xdx ˚ D2.5D,m(r0, !) = ( j)|m| 1 ⇡r0h(2) |m| (kr0) Z ⇡ 0 ˜ P( k, !) sin( k)e jm k d k ˚ D2.5D,m(r = 0, r0, !) = 1 2⇡r0 · ˇ Pm |m| (!) jkh(2) |m| (kr0)Y m |m| (⇡/2, 0)⇤ ˇ Pm |m| (rs, !) = jkh(2) |m| (krs)Y m |m| (✓s, s)⇤ ˇ Pm |m| ( k, !) = 4⇡( j)|m|Y m |m| (⇡/2, k)⇤ Plane wave : Point source : Z k p Higher order Ambisonics (HOA) Recording stage Reproduction stage Spectrum division method (SDM) Angular spectrum Spherical harmonics expansion Flexible sound field recording and reproduction J. Ahrens et al. 2012. WFS for SHE Proposed approach Integrated with from to k = 0 ⇡ (k/2⇡) ˜ P( k, !) sin( k) ICASSP 2016 (a) (c) (d) (b) ˇ Sm n Data-based synthesis Model-based synthesis ˜ Sm(kx) ˜ S(R, , kx) D(x0) R y0 x x x y y y z z z Appropriate rotation ˜ S(ysyn, 0, kx) ysyn WASPAA 2017 Appl. 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sha1_base64="ZBaPq56in3VJal6g+UtGvaq7eXU=">AAACiXichVFNLwNBGH6sr6qv4iJxaRSpRJiVJhonSS+OqCJRaXbXaCe2u5vZaaMaf8AfcHAiEREXV64u/oCDnyCOlbg4eLvdRBC8k5l55pn3eeeZGdOzha8Ye2rT2js6u7ojPdHevv6BwdjQ8IbvVqTFc5Zru3LLNHxuC4fnlFA23/IkN8qmzTfN/Uxzf7PKpS9cZ13VPL5TNoqO2BOWoYgqxCbyih+oetKYjktuuXJXOMX4UTYpZ/KemJunsSSmC7EEm2VBxH8CPQQJhLHixi6Rxy5cWKigDA4HirANAz61behg8IjbQZ04SUgE+xxHiJK2QlmcMgxi92ks0mo7ZB1aN2v6gdqiU2zqkpRxTLJHdsUa7IFds2f2/mutelCj6aVGs9nScq8weDyafftXVaZZofSp+tOzwh7SgVdB3r2Aad7CaumrhyeN7OLaZH2KnbMX8n/Gntg93cCpvloXq3ztFFH6AP37c/8EG/OzOuHVVGIpFX5FBGMYR5LeewFLWMYKcnTuMW5wizutV9O1tLbYStXaQs0IvoSW+QA8FZZr</latexit> (c) 2.5D synthesis with D(r0) <latexit 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sha1_base64="4+PPGmsftDSr+89kP3iDJgP1RIA=">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</latexit> <latexit sha1_base64="4+PPGmsftDSr+89kP3iDJgP1RIA=">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</latexit> Estimation <latexit 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sha1_base64="XRMgqSyauROpNi/jKmh6GVf/8Ng=">AAACbXichVHLSgMxFD0d3/VVFUFQpFiqriRTBMWVIIJL21oVaykzY9TQeTGTFrT4A64FF6KgICJ+hht/wEU/QVy4UHDjwtvpgGhRb0hycnLPzUmiu6bwJWO1iNLS2tbe0dkV7e7p7euPDQyu+07ZM3jOcEzH29Q1n5vC5jkppMk3XY9rlm7yDb20VN/fqHDPF469Jg9cXrC0PVvsCkOTRG0t+1JYASzGEmyGBRFvBmoIEghj1YndYBs7cGCgDAscNiRhExp8anmoYHCJK6BKnEdIBPscR4iStkxZnDI0Yks07tEqH7I2res1/UBt0CkmdY+UcSTZI7tlr+yB3bEn9vFrrWpQo+7lgGa9oeVusf94JPv+r8qiWWL/S/WnZ4ldzAdeBXl3A6Z+C6OhrxyevmYXMsnqJLtiz+T/ktXYPd3ArrwZ12meOUOUPkD9+dzNYD01oxJOpxKLs+FXdGIUE5im957DIlawihyda+ME57iIvCjDypgy3khVIqFmCN9CmfoEnpCN5w==</latexit> <latexit sha1_base64="XRMgqSyauROpNi/jKmh6GVf/8Ng=">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</latexit> <latexit 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sha1_base64="RBbvDr1eV60H5EkJzP33VJ153rI=">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</latexit> Exterior Ambisonics
4. Interior sound fi eld reproduction 4QIFSJDBM
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6. Principle Sound pressure for audible area: 1, that for inaudible area: 0 -> Spatial rectangular window Fourier transform of rectangular window -> analytically derived as Sinc function Properties Considering wave equation Stable driving signals by omitting evanescent components 6 Mode-matching-based localized sound fi eld control y x z r0 rref Φ φs P(rref , φ, 0, ω) = 1 P(rref , φ, 0, ω) = 0 Bright zone Circular loudspeaker array Reference circle Dark Zone x Linear sound source lb xb Bright Dark shift Dark Window function y y = yb P(x, yb) = 0 T. Okamoto et al. J. Accost. Am. 2017 T. Okamoto WASPAA 2015
7. Using a linear array of 64 loudspeakers Outperforms conventional methods 7 Experimental results using linear array DS CM LS SFT (rect.) SFT (Hann) z = 0 [m] [dB] 1.5 2 2.5 y [m] -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 x [m] -30 -25 -20 -15 -10 -5 0 z = 0 [m] [dB] 1.5 2 2.5 y [m] -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 x [m] -30 -25 -20 -15 -10 -5 0 z = 0 [m] [dB] 1.5 2 2.5 y [m] -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 x [m] -30 -25 -20 -15 -10 -5 0 z = 0 [m] [dB] 1.5 2 2.5 y [m] -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 x [m] -30 -25 -20 -15 -10 -5 0 z = 0 [m] [dB] 1.5 2 2.5 y [m] -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 x [m] -30 -25 -20 -15 -10 -5 0 0 1 2 3 4 5 Temporal frequency [kHz] 0 5 10 15 20 25 30 35 40 Bright to dark ratio [dB] DS CM LS SFT (rect.) SFT (Hann) T. Okamoto et al. J. Accost. Am. 2017
8. Using a circular array of 32 loudspeakers Outperforms conventional methods 8 0 1 2 3 4 5 Temporal Frequency [kHz] 0 5 10 15 20 25 BDR [dB] Spatial Nyquist Frequency LS method (open) LS method (baffled) Beamforming (open) Beamforming (baffled) Proposed (open) Proposed (baffled) z = 0 [m] [dB] -1 0 1 X axis [m] -1.5 -1 -0.5 0 0.5 1 1.5 Y axis [m] -40 -30 -20 -10 0 z = 0 [m] [dB] -1 0 1 X axis [m] -1.5 -1 -0.5 0 0.5 1 1.5 Y axis [m] -40 -30 -20 -10 0 z = 0 [m] [dB] -1 0 1 X axis [m] -1.5 -1 -0.5 0 0.5 1 1.5 Y axis [m] -40 -30 -20 -10 0 Pressure matching (LS) Beamforming Proposed Results for 3000 Hz Simulation results using circular array T. Okamoto WASPAA 2015
9. Multiple sound spot synthesis system with a linear array of 64 loudspeakers Previous implemented system 9 ͜Μʹͪ͸ )FMMP 㟬޷ Japanese area <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> English area <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> Chinese area <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> Dark zone (Quiet area) <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> Իͷฉ͑͜ͳ͍
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10. Technology introduction video using neural text-to-speech https://youtu.be/In8AfVcoTC4 10 Technology introduction video
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13. Demo system presentations Results with NICT collaborators 2022.6: Prototyping a small circular array 2022.10: Technology introduction HP and video release Conferences 2022.9: ASJ@Hokkaido University of Science -> Demo in oral session 2023.3: SPEASIP invited talk@Okinawa -> Demo in oral session 2023.3: ASJ@Online -> Demo in online session 2023.6: ICASSP 2023@Rhodes, Greece -> Show & Tell Demo session Demonstrations 2022.10: Keihanna R&D Fair@ATR & Kyoto Smartcity Expo@KICK 2023.12: Demonstration experiment@Miraikan From 2023.4: Permanent demo system@NICT Central, Tokyo 2023.4: The G7 Digital and Tech Ministers’ Meeting@Takasaki 2023.6: Combined with real-time multilingual speech translation@NICT Openhouse 13
14. Linear array with small drivers for circular array About 1.7 m 14 Linear array of 64 loudspeakers
15. 10 to 18 December 2022 Circular array of 16 loudspeakers@Geo-Cosmos Linear array of 64 loudspeakers@Nobel Q 15 Demonstration experiment@Miraikan
16. 16 Circular array system@Geo-Cosmos
17. 17 Linear array system@Nobel Q
18. Weekdays: 9:30-17:00 18 Permanent demo system@NICT Central, Tokyo
19. 19 DemoˏG7 Gunma, Apr. 2023
20. T. Okamoto, K. Ueno, T. Okabe, K. Tani, Y. Yoshikata, M. Sudo, M. Kuwahara, and K. Hikita, 
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 ICASSP 2023 Show & Tell Demo Session, June 2023. 20 ICASSP 2023 Show & Tell Demo
21. 21 DemoˏICASSP 2023, Rhodes, Greece
22. Improving sound quality and output power 22 Development of new loudspeaker array 134.4 mm Previous - Too small - Low sound quality - Low output power Improved - Still portable - High sound quality - High output power 184 mm
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26. Multiple sound spot synthesis with an improved array of 16 loudspeakers Four-language (English, Japanese, Chinese, and Korean) for four-spot synthesis Two types of music sounds for two spot synthesis 26 Today’s demo@Makuhari Messe
27. 27 Implementation is really all we need Conclusion
28. Demos for multiple sound spot synthesis 2023.10.6-7: Keihanna R&D Fair 2023@Keihanna plaza 2023.10.8-12: Internet Governance Forum 2023@Kyoto International Conference Center 2023.10.17-20: CEATEC 2023@Makuhari Messe 2023:10.22-25: WASPAA 2023 Demonstrations@Mohonk Mountain House, New Paltz, NY, USA T. Okamoto, K. Ueno, T. Okabe, K. Tani, Y. Yoshikata, M. Sudo, M. Kuwahara, and K. Hikita, “Improving portable multiple sound spot synthesis system with a ba ff l ed circular array of 16 loudspeakers” Voice conversion 2023.8.22 13:30-15:30: Interspeech 2023ˏDublin, Ireland T. Okamoto, T. Toda and H. Kawai, “E2E-S2S-VC: End-to-end sequence-to-sequence voice conversion”
 -> I must move to Haneda airport quickly after the session for presenting my poster at Dublin tomorrow 28 Next presentations
29. Funding This research was partly supported by JSPS KAKENHI Grant Numbers JP18K11387 and JP23K11177, and JST A-STEP Tryout Grant Number JPMJTM22D8 External collaboration The development of the prototypes of the compact circular array of 16 loudspeakers and linear array of 64 loudspeakers was supported by JST Program Manager (PM) Development and Promotion Program (PI: Keita Hikita), and were developed in collaboration with Kitanihon Onkyo Co. Ltd The demonstration test of multiple sound spot synthesis systems using the compact circular array and linear array was conducted at Miraikan in Tokyo, Japan Internal collaboration we would like to thank Keita Hikita, Miyuki Sudo, and Manae Kuwahara for their support of NICT Innovation Design Initiative (IDI), Project of Co-Creation Design (PoCC) for the social deployment of multiple sound spot synthesis technology 29 Acknowledgements
30. Thank you for your !! Takuma OKAMOTOˏNICT e-mail: HP: https://www.okamotocamera.com Twitter: @okamotocamerea 30
31. 2.5D Mode-matching-based method Sound pressure for audible area: 1, that for inaudible area: 0
 ɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹT. Okamoto, WASPAA 2015 For actual implemented circular array Measuring transfer function Driving signal: Filter: 31 Deriving driving signals of loudspeakers y x z r0 rref Φ φs P(rref , φ, 0, ω) = 1 P(rref , φ, 0, ω) = 0 Bright zone Circular loudspeaker array Reference circle Dark Zone <latexit sha1_base64="WeZsnZwk5UGw+Dx58344ySFZpfU=">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</latexit> cn,l(rref ) = 1 2⇡ Z 2⇡ 0 Hl(rref , )e jn d ' 1 M M X m=1 Hl(rref , m)e jn m <latexit sha1_base64="w77DHJ0cpBVEi7ri+sh27w+FFVo=">AAACsnichVHPTxQxFH6MKDiKrHgx8bJxgUBCNh2yQcKJ4IWLCb8WiDubSafbZRva6aTTXcHJ/AP8Ax48aWKM8eifwMV/wMNe5WQ8YuLFg29nJzFCgDeZ9ntf3/f6tQ1jKRJLSH/EuTV6+87Y+F333v2JB5Olh1O7ie4axutMS232Q5pwKSJet8JKvh8bTlUo+V54+HywvtfjJhE62rHHMW8qehCJtmDUIhWUXvgRf8W0UjRqpX4osobXTH0V6iPMtGwpajvl6Yo3nWVueT1IZTZnAixA2qjU8HaWLbh+3BFBqrL5oFQhVZJH+TLwClCBIjZ06SP40AINDLqggEMEFrEECgl+DfCAQIxcE1LkDCKRr3PIwEVtF6s4VlBkD3E8wKxRsBHmg55Jrma4i8TfoLIMM+Qb+UTOyVfymfwgf67sleY9Bl6OcQ6HWh4HkyePt3/fqFI4W+j8U13r2UIblnOvAr3HOTM4BRvqe6/fnG+vbM2ks+Q9+Yn+35E+OcUTRL1f7MMm33oLLj6Ad/G6L4Pdxaq3VK1t1iqra8VTjMMTeApzeN/PYBXWYQPquO8X6MN3OHNqzkuHOmxY6owUmkfwXzjyL+OzqKU=</latexit> Hl(rref , m) <latexit sha1_base64="ENxoC8BAov895nidMWiG1Mvap1E=">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</latexit> ˆ d = C(r ref )HC(r ref ) + I 1 C(r ref )Ha(r ref ) <latexit sha1_base64="pudrKLQmB8dnxmsYuHL5YGr2ceg=">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</latexit> C(rref ) = 2 6 4 c N,1(rref ) · · · c N,L(rref ) . . . ... . . . cN,1(rref ) . . . cN,L(rref ) 3 7 5 <latexit sha1_base64="u25XTEhOVbL/8OuvkFUjAmPUrGs=">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</latexit> an,rect( , S) = sinc ✓ n 2⇡ ◆ e jn s <latexit sha1_base64="DB31CbEgzeBbvhJ6gGtkWpP5wRY=">AAADQHichVHNahRBEK4Z/+L6k1UvgpfBJbLBZOkJIYogRL143GTdJJCOQ0/bu9Nmpmcy07sQh34BX8CDJwUR8S304gt4CL6A4kEkgiAerPlRiSGxhp6q+qq+6q+7/SSUmSZkx7KPHD12/MTEycap02fOTjbPnV/J4lHKRZ/HYZyu+SwToVSir6UOxVqSChb5oVj1N+8U9dWxSDMZq3t6OxEbERsqOZCcaYS85gfm5WqGRkwHaZQHTClj2rQbyBmaBNLLf1d6xkw3HOcmDcVA0z9wJhU3Jdamg5Tx3DX5nHGuOlWmikmI0EQamsphoKeL2uHk2YPJlaOmaqjrRtzPZx+qvXozY4zXbJEOKc3ZH7h10ILaunHzJVB4ADFwGEEEAhRojENgkOG3Di4QSBDbgByxFCNZ1gUYaCB3hF0COxiim/gfYrZeowrzYmZWsjnuEuJKkenAFHlPXpFd8o68Jp/IzwNn5eWMQss2er/iisSbfHyx9/2/rAi9huAv61DNGgZwvdQqUXtSIsUpeMUfP3qy27uxPJVfIc/JZ9T/jOyQt3gCNf7GXyyJ5afQwAdw/73u/cHKXMdd6MwvzbcWb9dPMQGX4DK08b6vwSLchS70gVu3rKGVWFv2G/uj/cX+WrXaVs25AHvM/vELczrhjQ==</latexit> an,hann( , S) = ⇢ sinc ✓ 1 2 + n 2⇡ ◆ + sinc ✓ 1 2 n 2⇡ ◆ 2 e jn s Rectangular window Hann window
32. 32 Results (a) 750 Hz (b) 1.5 kHz (c) 3 kHz (d) 4.5 kHz (e) 6 kHz (f) 7.5 kHz