Perceptual Quality Enhancement of Sound Field Synthesis Based on Combination of Pressure and Ampitude Matching

Presentation slides for IEEE WASPAA 2023

Transcript

1. Perceptual Quality Enhancement of Sound Field Synthesis Based on Combination of Pressure and Amplitude Matching Keisuke Kimura1, Shoichi Koyama2, and Hiroshi Saruwatari1 1The University of Tokyo, Japan 2National Institute of Informatics, Japan
2. Sound field synthesis Ø Spatial audio reproduction in a large listening area / personal audio in multiple listening regions Ø Methods based on the minimization of square error have practical advantages compared with methods based on analytical representation – E.g., (Weighted) pressure matching and mode matching October 19, 2023 2 Synthesizing desired pressure field with multiple loudspeakers Loudspeaker Target region: [Koyama+ 2023]
3. Sound field synthesis Ø Optimization problem to be solved October 19, 2023 3 Goal: 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 : Target region Secondary source 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. Pressure matching Ø Discretize target region into control points Ø Optimization problem for pressure matching becomes simple least-squares problem October 19, 2023 4 <latexit sha1_base64="V9SycBRbehDy9zsTAA8X3hDIM1c=">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</latexit> ⌦ <latexit sha1_base64="q0uECYVB1NlCDNpVOene+1Qk19c=">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</latexit> N ( L) <latexit sha1_base64="Sfob4tqImS+gkH7eBMlgYAHh4Uo=">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</latexit> minimize d2CL Gd udes 2 + ⌘kdk2 <latexit sha1_base64="i9WfaOjLrhWO59r+nVt9MC7/SLM=">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</latexit> d = GHG + ⌘I 1 GHudes Transfer function matrix Driving signal vector Desired pressure vector Regularization term Closed-form solution is obtained as J Simple implementation L Fine discretization of is necessary <latexit sha1_base64="V9SycBRbehDy9zsTAA8X3hDIM1c=">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</latexit> ⌦ : Target region Secondary source Control points [Nelson 1993]
5. Spatial aliasing artifacts in sound field synthesis Ø Owing to discrete placement of secondary sources, spatial aliasing artifacts are unavoidable – E.g., Synthesizing sound field by 12 loudspeakers at 800 Hz October 19, 2023 5 Desired Pressure Matching Pressure § Degradation of sound localization § Coloration of source signals
6. Idea for perceptual quality enhancement Ø Interaural level difference (ILD) is the dominant cue for horizontal sound localization above 1500 Hz, compared with interaural time difference (ITD) Ø Amplitude response should be accurately synthesized as much as possible, rather than phase response, to alleviate coloration effects October 19, 2023 6 Synthesizing amplitude (or magnitude) distribution leaving phase distribution arbitrary at high frequencies Applying amplitude matching for high frequencies Pressure Magnitude
7. Amplitude matching Ø Synthesizing desired amplitude at control points – By leaving phase arbitrary, number of parameters to be control can be reduced – First proposed for multizone sound field control for personal audio Ø Optimization problem of amplitude matching October 19, 2023 7 : Target region Secondary source [Koyama+ 2021, Abe+ 2023] Desired amplitude No closed-form solution, but majorization minimization (MM) algorithm or alternating direction method of multipliers (ADMM) can be applied Element-wise absolute value
8. Proposed method for perceptual quality enhancement Ø Combination of pressure and amplitude matching – is determined so that for low frequencies and for high frequencies – For example, can be defined as sigmoid function October 19, 2023 8 <latexit sha1_base64="7PBZJNy5EyF+eucvkOfjzch+WsM=">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</latexit> minimize d2CL J(d) := (1 )kGd udesk2 2 + k|Gd| |udes|k2 2 + kdk2 2 <latexit sha1_base64="A4dv1PYDkl/3NJ52frUgh4Qg2ME=">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</latexit> <latexit sha1_base64="v6ZpLa9I3hnLLs2O89d3S1l6XjM=">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</latexit> = 1 <latexit sha1_base64="nFwv8TaL4YCj47fcATfYtfC3o0Y=">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</latexit> = 0 <latexit sha1_base64="A4dv1PYDkl/3NJ52frUgh4Qg2ME=">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</latexit> <latexit sha1_base64="ROtRu2ks9BH5ktUl1T0BgfcB3qQ=">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</latexit> (!) = 1 1 + e 2⇡ (! !T) Transition frequency Can still be solved by MM algorithm or ADMM Pressure matching Amplitude matching
9. Numerical experiments Ø Setting – 3D free field – Target region : Cuboid of 1.0 m x 1.0 m x 0.04 m – 32 loudspeakers on borders of squares of 2.0 m x 2.0 m at z=±0.1 m – 1152 control points regularly placed over every 0.04 m – Desired sound field: point source at (2.0 m, 0.0 m, 0.0 m) – Proposed method and pressure matching (PM) are compared October 19, 2023 9 <latexit sha1_base64="aJVm6ibCtbqRlu7KgruECMVr7Qw=">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</latexit> ⌦ <latexit sha1_base64="aJVm6ibCtbqRlu7KgruECMVr7Qw=">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</latexit> ⌦
10. Numerical experiments Ø Evaluation of ILD – Binaural signals in the synthesized sound field were calculated by using transfer functions from loudspeakers to a listener obtained by Mesh2HRTF [Ziegelwanger+ 2015] – Evaluation measure was normalized error of ILD: – Distribution of NE October 19, 2023 10 <latexit sha1_base64="EndMQejlYdBkvqIegxmgN2TX4IM=">AAAD5niclVLdatRAFJ40amv8a+ulN4OL0Eq7JFLa3hSKVqjgTwW3LWyWZTJ7sjs0MwkzE3Gdzit4pXjb5/BWX8K3cbLdSLe7FXsg8OU73/mZc05SZEzpMPztzfk3bt6aX7gd3Ll77/6DxaXlQ5WXkkKL5lkujxOiIGMCWprpDI4LCYQnGRwlJy8q/9FHkIrl4oMeFtDhpC9YyijRjuoueesxJ3oguXn70q7ECTfSdk3N7Vu7indwEKeSUBOrkjtfMWATCotP679Xr/cuRKuhsDNzrk3lWF2fnULLEv47xym21+7xegVsd7ERNsOR4WkQjUEDje3ADfgs7uW05CA0zYhS7SgsdMcQqRnNwAZxqaAg9IT0oe2gIBxUx4wWa/ETx/Rwmkv3CY1H7MUIQ7hSQ544ZdWmuuyryFm+dqnT7Y5hoig1CHpeKC0zrHNcXQnuMQlUZ0MHCJXM9YrpgLgj0O6WJqokfOINZjQulSobBPEeuCdLeOOodwVIonP51MRE9jn5ZN0I+vFahf4lZKIWOnSV0CVhnH0Ga/6iK6VM1NIauZ1Glzc4DQ6fNaPN5sb7jcbu8/F2F9Aj9BitoAhtoV20jw5QC1Hvq/fD++n98gf+F/+b//1cOueNYx6iCfPP/gCusFhL</latexit> NE(r H ) = P H |ILD syn (r H , H ) ILD true (r H , H )| P H |ILD true (r H , H )| Position and direction of listener s head PM Proposed
11. Numerical experiments Ø Evaluation of amplitude response – At origin October 19, 2023 11
12. Listening experiments Ø Evaluation by MUSHRA – Desired sound field: point source at (2.0 m, 0.5 m, 0.0 m) – Reverberation time (T60 ): 0.19 s – 14 male subjects in 20-30s – Listening at center of target region – Test signals: • Reference: Source signal from reference loudspeaker • C1/Hidden anchor: lowpass-filtered source signal up to 3.5 kHz • C2/PM: Synthesized sound by PM • C3/Proposed: Synthesized sound by Proposed • C4/Hidden reference: Same as reference October 19, 2023 12
13. Listening experiments Ø Results of two source signals (Vocals/Instrumental) October 19, 2023 13 Vocals Instrumental C1/Hidden anchor C2/PM C3/Proposed C4/Hidden reference Synthesized sound by Proposed is perceptually close to reference sound compared to PM
14. Conclusion Ø Perceptual quality enhancement of sound field synthesis – Spatial aliasing artifacts are unavoidable in sound field synthesis – Synthesizing amplitude distribution leaving phase distribution arbitrary at high frequencies • ILD is the dominant cue for horizontal sound localization at high frequencies • Amplitude response should be accurately synthesized to alleviate coloration effects – Proposed method: combination of pressure and amplitude matching – Numerical experiments indicated that ILD and amplitude response were accurately synthesized by Proposed compared to PM – Listening experiments indicated that synthesized sound by Proposed was perceptually close to reference sound compared to PM October 19, 2023 14