Amplitude Matching for Multizone Sound Field Control

Presentation slides for IEEE ICASSP 2023

Transcript

1. Amplitude Matching for Multizone Sound Field Control Takumi Abe1, Shoichi Koyama2, Natsuki Ueno1, and Hiroshi Saruwatari1 1The University of Tokyo, Japan 2National Institute of Informatics, Japan Published in IEEE/ACM Transactions on Audio, Speech, and Language Processing, vol, 31, pp. 656-669, 2023. 2023 IEEE International Conference on Acoustics, Speech and Signal Processing
2. Mutizone sound field control May 1, 2023 2 Generating independent sound zones using multiple loudspeakers Sound zone Sound zone Essential technique for developing personal audio systems
3. Sound field control problem Ø Optimization problem to be solved May 1, 2023 3 Synthesizing desired sound field inside with secondary sources (loudspeakers) <latexit sha1_base64="SbdBLMPsjw6ciQkjzJuiJJhjGvk=">AAACF3icbVDLSsNAFJ3UV62vqksXBotQQUoiRV0W3bisYB/QlDCZ3LZDZyZhZiKUkKUf4Te41bU7cevSpX/i9LGwrQcuHM65l3vvCWJGlXacbyu3srq2vpHfLGxt7+zuFfcPmipKJIEGiVgk2wFWwKiAhqaaQTuWgHnAoBUMb8d+6xGkopF40KMYuhz3Be1RgrWR/OJx4qcex3ogeRqCyrKyF/BUZudexKGPz/xiyak4E9jLxJ2REpqh7hd/vDAiCQehCcNKdVwn1t0US00Jg6zgJQpiTIa4Dx1DBeaguunkkcw+NUpo9yJpSmh7ov6dSDFXasQD0zm+WS16Y/E/r5Po3nU3pSJONAgyXdRLmK0je5yKHVIJRLORIZhIam61yQBLTLTJbm5LwDOTibuYwDJpXlTcy0r1vlqq3czSyaMjdILKyEVXqIbuUB01EEFP6AW9ojfr2Xq3PqzPaWvOms0cojlYX7/bXqDc</latexit> udes(r, !) <latexit sha1_base64="OlngG7bMYm0AnUElZFcGXeuuUPg=">AAAB/HicbVA9SwNBEJ2LXzF+RS1tFoNgFe5E1DJoY2cE8wHJEfY2k2TN7t2xuyeEI/4GW63txNb/Yuk/cZNcYRIfDDzem2FmXhALro3rfju5ldW19Y38ZmFre2d3r7h/UNdRohjWWCQi1QyoRsFDrBluBDZjhVQGAhvB8GbiN55QaR6FD2YUoy9pP+Q9zqixUr19J7FPO8WSW3anIMvEy0gJMlQ7xZ92N2KJxNAwQbVueW5s/JQqw5nAcaGdaIwpG9I+tiwNqUTtp9Nrx+TEKl3Si5St0JCp+ncipVLrkQxsp6RmoBe9ifif10pM78pPeRgnBkM2W9RLBDERmbxOulwhM2JkCWWK21sJG1BFmbEBzW0J5Nhm4i0msEzqZ2Xvonx+f16qXGfp5OEIjuEUPLiECtxCFWrA4BFe4BXenGfn3flwPmetOSebOYQ5OF+/In2Vmg==</latexit> ⌦ <latexit sha1_base64="VJ5RMQ2GKmQZdUQJz96dZvLRnxA=">AAAB93icbVA9SwNBEN2LXzF+RS1tFoNgFe4kqGXQxsIiAfMByRH2NnPJkt29Y3dPOI78Alut7cTWn2PpP3GTXGESHww83pthZl4Qc6aN6347hY3Nre2d4m5pb//g8Kh8fNLWUaIotGjEI9UNiAbOJLQMMxy6sQIiAg6dYHI/8zvPoDSL5JNJY/AFGUkWMkqMlZqPg3LFrbpz4HXi5aSCcjQG5Z/+MKKJAGkoJ1r3PDc2fkaUYZTDtNRPNMSETsgIepZKIkD72fzQKb6wyhCHkbIlDZ6rfycyIrRORWA7BTFjverNxP+8XmLCWz9jMk4MSLpYFCYcmwjPvsZDpoAanlpCqGL2VkzHRBFqbDZLWwIxtZl4qwmsk/ZV1buu1pq1Sv0uT6eIztA5ukQeukF19IAaqIUoAvSCXtGbkzrvzofzuWgtOPnMKVqC8/ULSPOTbw==</latexit> L Difficult to solve owing to regional integration Synthesized sound field <latexit sha1_base64="jXBfTdmzlzCxe3eJ2RCk10ZxZxw=">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</latexit> dl <latexit sha1_base64="2143p1RAQMlzka1H5YkQBHUMHYo=">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</latexit> gl(r) • : Driving signal of th secondary sources • : Transfer function of th secondary source <latexit sha1_base64="bKgRyukOmCpfZztJEARaEMlc1nM=">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</latexit> l <latexit sha1_base64="bKgRyukOmCpfZztJEARaEMlc1nM=">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</latexit> l
4. Current methods for multizone sound field control Ø Pressure Matching (PM) – Discretizing target region into control points – Desired pressures are synthesized at the control points – Driving signals are obtained as simple least-squares solution Ø Acoustic Contrast Control (ACC) – Aimed at generating regions of high- and low-acoustic potential energy – Ratio of acoustic potential energy in one region to that in the other region is maximized – Solved as generalized eigenvalue problem May 1, 2023 4 J Simple implementation owing to the closed-form solution L Feasibility depends on the setting of desired phase distribution J Suitable for generating audible and inaudible regions L Power distribution inside the target region cannot be controlled L Flat amplitude response cannot be guaranteed
5. Proposed method: Amplitude matching (AM) Ø Setting control points over Ø Optimization problem for PM Ø Optimization problem for AM May 1, 2023 5 Synthesizing desired amplitude (or magnitude) distribution inside the target region, leaving the phase distribution arbitrary <latexit sha1_base64="OlngG7bMYm0AnUElZFcGXeuuUPg=">AAAB/HicbVA9SwNBEJ2LXzF+RS1tFoNgFe5E1DJoY2cE8wHJEfY2k2TN7t2xuyeEI/4GW63txNb/Yuk/cZNcYRIfDDzem2FmXhALro3rfju5ldW19Y38ZmFre2d3r7h/UNdRohjWWCQi1QyoRsFDrBluBDZjhVQGAhvB8GbiN55QaR6FD2YUoy9pP+Q9zqixUr19J7FPO8WSW3anIMvEy0gJMlQ7xZ92N2KJxNAwQbVueW5s/JQqw5nAcaGdaIwpG9I+tiwNqUTtp9Nrx+TEKl3Si5St0JCp+ncipVLrkQxsp6RmoBe9ifif10pM78pPeRgnBkM2W9RLBDERmbxOulwhM2JkCWWK21sJG1BFmbEBzW0J5Nhm4i0msEzqZ2Xvonx+f16qXGfp5OEIjuEUPLiECtxCFWrA4BFe4BXenGfn3flwPmetOSebOYQ5OF+/In2Vmg==</latexit> ⌦ Control points <latexit sha1_base64="lBJueI+9nR6+v444Orp/qYScf/A=">AAACrHicfZHbSgMxEIbT9VzPeunNYhFEpOyKp0tRL7wRW2hVaBeZTWdraJJdkqxYl30Cb/XhfBuzPYjngcDHP/8kM5kw4Uwbz3srOROTU9Mzs3Pl+YXFpeWV1bVrHaeKYpPGPFa3IWjkTGLTMMPxNlEIIuR4E/bOivzNAyrNYtkw/QQDAV3JIkbBWKl+ebdS8areINyf4I+gQkZRu1stvbY7MU0FSkM5aN3yvcQEGSjDKMe83E41JkB70MWWRQkCdZANOs3dLat03ChW9kjjDtTPFRkIrfsitE4B5l5/zxXib7lWaqLjIGMySQ1KOnwoSrlrYrcY2+0whdTwvgWgitleXXoPCqixn1P+8kwodov7lY50bjPnaMdUeGmlqwQVmFjtZG1QXQGPuR27294t6D8jk2Ojpb+M9hIm2BPm2Qf9aWVybB1T2S7S/762n3C9V/UPqwf1/crJ6Wils2SDbJJt4pMjckIuSI00CSVInskLeXWqTsNpOcHQ6pRGNevkSzjRO8Na14c=</latexit> M <latexit sha1_base64="P09u6SpT/CzYrw09JLkb6DzPdBY=">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</latexit> minimize d2CL kGd udesk2 + kdk2 <latexit sha1_base64="xHTP+Y0VPGUaop882+RHZBjsR0M=">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</latexit> minimize d2CL k|Gd| |udes|k2 + kdk2 Driving signals Transfer function matrix Desired pressures Element-wise absolute value
6. Proposed method: Amplitude matching (AM) Ø Algorithm – Optimization problem for AM does not have closed-form solution – Proposed algorithm based on alternating direction method of multipliers (ADMM) – Computationally efficient compared with gradient methods Ø Differential-norm penalty for time-domain filter design – Driving signals may have phase discontinuities between frequency bins – To induce smoothness between frequency bins and avoid unnecessarily large time- domain filter length, differential-norm penalty is introduced May 1, 2023 6 Differential-norm penalty Index of frequency bin
7. Experimental results (1400 Hz) 7 PM ACC AM Pressure Magnitude Ø Target: Magnitude 1 in upper region and 0 in lower region
8. Demo May 1, 2023 8 https://youtu.be/oYw7kmpZcY4 Full version:
9. Conclusion Ø Amplitude matching for multizone sound field control – Synthesizing desired amplitude distribution over target region, leaving phase distribution arbitrary – ADMM-based algorithm for AM is formulated – Differential-norm penalty for inducing continuities of phase between frequency bins – Desired amplitude distribution is accurately and efficiently synthesized, compared with PM and ACC Ø Code is available: – https://github.com/sh01k/AmplitudeMatching May 1, 2023 9 Paper📝 Code🧑💻 Demo🎥