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Spatial Fourier transform-based localized sound zone generation with loudspeaker array

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Invited lecture in the 178th Meeting of the Acoustical Society of America@San Diego
2nd Dec. 2019

Published in: Engineering
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Spatial Fourier transform-based localized sound zone generation with loudspeaker array

  1. 1. Spatial Fourier transform-based localized sound zone generation methods with loudspeaker arrays Takuma Okamoto National Institute of Information and Communications Technology (NICT), Japan 1 2nd Dec. 2019, 178th Meeting of the Acoustical Society of America@San Diego
  2. 2. Introduction: Generating localized sound zone with loudspeakers Previous methods and their problems Proposed spatial Fourier transform-based localized sound zone generation methods Acoustically bright and dark zones with linear and circular arrays Localized sound zones near loudspeakers with linear and circular arrays Challenges and prospects Conclusions Outline 2
  3. 3. Generating localized sound zones
 with loudspeakers Acoustically bright and dark zones Generating listening and quiet zones Multiple sound zones Superposition of bright and dark zones Localized sound zones near loudspeakers Listening zone is only near loudspeakers Used in reverberant environments Multizone sound field synthesis Multiple sound fields are synthesized in multiple zones Not only sound pressures but also wavefronts Introduction 3Ket point: How to realize “quiet zones”!! Bright zone (Listening 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> こんにちは Hello 你好 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> Brightzone (Listeningarea)<latexitsha1_base64="(null)">(null)</latexit><latexitsha1_base64="(null)">(null)</latexit><latexitsha1_base64="(null)">(null)</latexit><latexitsha1_base64="(null)">(null)</latexit> Darkzone (Quietarea)<latexitsha1_base64="(null)">(null)</latexit><latexitsha1_base64="(null)">(null)</latexit><latexitsha1_base64="(null)">(null)</latexit><latexitsha1_base64="(null)">(null)</latexit>
  4. 4. Discretized multiple point control: Kirkeby93, Choi02 Principle Numerical calculation of inverse of spatial (correlation) matrix Problems Quite unstable (ill-conditioned) Numerical solutions and NOT based on wave equation Spatial Fourier transform-based analytical sound field synthesis Higher-order Ambisonics (HOA): Ahrens08 Spherical / circular harmonic analysis-based method for spherical / circular arrays Spectral division method (SDM): Ahrens10 Angular spectrum-based method for planar / linear arrays Previous methods and their problems 4 P (!) = G(!)D(!) D(!) = G+ (!)P (!) 5 P (!) = G(!)D(!) ↓ D(!) = G+ (!)P (!) 例:BoSCシステム Pressure matching-based sound field control ... ... ... ... G(!) P (!)D(!) Loudspeakers<latexitsha1_base64="(null)">(null)</latexit><latexitsha1_base64="(null)">(null)</latexit><latexitsha1_base64="(null)">(null)</latexit><latexitsha1_base64="(null)">(null)</latexit> Controlpoints<latexitsha1_base64="(null)">(null)</latexit><latexitsha1_base64="(null)">(null)</latexit><latexitsha1_base64="(null)">(null)</latexit><latexitsha1_base64="(null)">(null)</latexit> Stable driving function without evanescent component Physically derived solutions based on wave equation
  5. 5. Generating localized sound zones
 with loudspeakers Acoustically bright and dark zones Generating listening and quiet zones Multiple sound zones Superposition of bright and dark zones Localized sound zones near loudspeakers Listening zone is only near loudspeakers Used in reverberant environments Multizone sound field synthesis Multiple sound fields are synthesized in multiple zones Not only sound pressures but also wavefronts Introduction 5Ket point: How to realize “quiet zones”!! Bright zone (Listening 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> こんにちは Hello 你好 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> Brightzone (Listeningarea)<latexitsha1_base64="(null)">(null)</latexit><latexitsha1_base64="(null)">(null)</latexit><latexitsha1_base64="(null)">(null)</latexit><latexitsha1_base64="(null)">(null)</latexit> Darkzone (Quietarea)<latexitsha1_base64="(null)">(null)</latexit><latexitsha1_base64="(null)">(null)</latexit><latexitsha1_base64="(null)">(null)</latexit><latexitsha1_base64="(null)">(null)</latexit>
  6. 6. Analytically derived spatial filters in angular spectrum domain Spatial filters in angular spectrum domain Shift theorem introduced to shift rectangular window along with -axis Spatial filters for generating bright and dark zones x y y = yb Secondary source Bright DarkDark P(x, yb) = 1 P(x, yb) = 0 lb xb Shift ˜F(kx, !) = ˜P(kx, yref , !) ˜G(kx, yref , !) P(x, yref , !) = 1 P(x, yref , !) = 0 Modeled by Rectangular window P(x, yb) = ⇧ ✓ x lb ◆ = ⇢ 1, for |x|  lb/2 0, elsewhere ˜P(kx) = lb sinc ✓ kxlb 2⇡ ◆ Fx ˜F(kx, !) = lb sinc (kxlb/2⇡) exp(jkxxb) ˜G(kx, yb, !) ˜Pshift(kx) = ˜P(kx) exp(jkxxb) = lb sinc ✓ kxlb 2⇡ ◆ exp(jkxxb) x Arbitrary length : Arbitrary position : [xb, yb]T lb Proposed method with a linear array 6 ICASSP14
  7. 7. Demo with an actually implemented array 7 ICASSP14
  8. 8. 8
  9. 9. Comparison with 5 methods DS: Delay-and-sum bermforming CM: Contrast maximization: Choi02 LS: Pressure-matching: Kirkeby93 SFT: Proposed spatial Fourier transform rect: Rectangular window-based filter Hann: Hann window-based filter Results 9 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 Brighttodarkratio[dB] DS CM LS SFT (rect.) SFT (Hann) JASA17
  10. 10. Compaison between rectangular and Hann windows Fourier transform of rectangular window = sinc function Fourier transform of Hann window = superposition of sinc functions Comparison of calculated results on control line Fewer sidelobes in Hann window -> Fewer plane waves orthogonal to linear array -> Still higher accuracy except for control line Property of SFT-based methods Synthesized accuracy can be physically interpreted -40 -30 -20 -10 0 10 20 30 40 kx 0 5 10 15 20 25 30 35 40 45 |˜F(kx,k)| SFT (rect.) SFT (Hann) Z 1 1 Prect (x, lb) ejkxx dx = Z lb/2 lb/2 ejkxx dx = lb sin (kxlb/2) (kxlb/2) = lb sinc ✓ kxlb 2⇡ ◆ <latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit> Z 1 1 PHann (x, lb) ejkxx dx = Z lb/2 lb/2 cos (⇡x/lb) ejkxx dx = Z lb/2 lb/2 ej⇡x/lb + e j⇡x/lb 2 ejkxx dx = lb 2 sinc ✓ 1 2 + kxlb 2⇡ ◆ + lb 2 sinc ✓ 1 2 kxlb 2⇡ ◆ <latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit> Result analysis JASA17 10
  11. 11. Spatial filters in 2D cylindrical harmonic spectrum domain Proposed method with a circular array 11 WASPAA15 z = 0 [m] [dB]-1 0 1 X axis [m] -1.5 -1 -0.5 0 0.5 1 1.5 Yaxis[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 Yaxis[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 Yaxis[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 Yaxis[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 Yaxis[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 Yaxis[m] -40 -30 -20 -10 0 LSBeamformingSFT f=3000Hz Open Baffled 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) y x z r0 rref Φ φs P(rref , φ, 0, ω) = 1 P(rref , φ, 0, ω) = 0 Dark zone Bright zone Circular sound source Reference circle
  12. 12. Generating localized sound zones
 with loudspeakers Acoustically bright and dark zones Generating listening and quiet zones Multiple sound zones Superposition of bright and dark zones Localized sound zones near loudspeakers Listening zone is only near loudspeakers Used in reverberant environments Multizone sound field synthesis Multiple sound fields are synthesized in multiple zones Not only sound pressures but also wavefronts Introduction 12Ket point: How to realize “quiet zones”!! Bright zone (Listening 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> こんにちは Hello 你好 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> Brightzone (Listeningarea)<latexitsha1_base64="(null)">(null)</latexit><latexitsha1_base64="(null)">(null)</latexit><latexitsha1_base64="(null)">(null)</latexit><latexitsha1_base64="(null)">(null)</latexit> Darkzone (Quietarea)<latexitsha1_base64="(null)">(null)</latexit><latexitsha1_base64="(null)">(null)</latexit><latexitsha1_base64="(null)">(null)</latexit><latexitsha1_base64="(null)">(null)</latexit> NOT realized by beamforming and parametric arrays
  13. 13. Proposed localized sound zone generation based on residual sound field between two types of sound sources A circular and linear array combination ICASSP15, JIHMSP17b A linear array and an additional loudspeaker JIHMSP17a A circular array and an additional loudspeaker IWAENC18 Problems Undesired sound pressures propagate vertical directions: JIHMSP17a, IWAENC18 Complicated arrangement of loudspeakers are required: ICASSP15, JIHMSP17b Proposed methods and their problems 13 Quiet zone<latexit 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Y axis [m] Xaxis[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 1076 T. Okamoto 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 (a) x-y plane (f = 500 Hz) x = 0 [m] [dB]-1 0 1 2 3 4 y [m] -2 -1 0 1 2 z[m] -40 -35 -30 -25 -20 -15 -10 -5 0 (b) y-z plane (f = 500 Hz) Figure 6. Results of sound pressure level produced using linear array of 64 loudspeakers with x =0.05 Produced sound pressure level at x = [0, 0.1, 0]T i circles are loudspeakers. [d0 0.5 1 1.5 2 2.5 3 Distance [m] 0.5 1 1.5 2 2.5 3 3.5 4 Temporalfrequency[kHz] Figure 7. Results of distance amplitude properties 1072 T. Okamoto (a) Producing monopole source! using a point source A(1) y = yrefy Point source x y = yd (b) Producing virtual monopole source! using the linear sound source A(2) y = yrefy Virtual point source x Linear sound source y = yd (c) Proposed method! Producing (a) and (b) simultaneously y = yrefy Point source x Linear sound source y = ydDA(1) = S(!) PA(1)(x, yref , 0, !) PA(2)(x, yref , 0, !) DA(2) DA(2) DA(1) = S(!) PA(x, yref , 0, !) = 0 Figure 2. Arrangements of sound sources and scheme of proposed method. DA(1) and DA(2) are respective driving functions of point source A(1) given as equation (7) and linear sound source A(2) given as equation (11). PA(1) and PA(2) are sound pressures produced by sound sources A(1) and A(2) defined in equations (9) and (12). PA is total produced sound pressure in proposed method given in equation (13). in the spectral division method (SDM) [28]. From equations (3) and (5), the produced sound pressure is then represented: ˜P(kx, y, 0, !) = ˜P(kx, yref, 0, !) H (2) 0 (k⇢yref) H (2) 0 (k⇢y) . (6) In the SDM using a linear sound source (2.5-dimensional SDM), equation (6) shows that the produced sound pressure is correct only at reference receiver line y = yref because
  14. 14. 3D localized sound zone generation with multiple circular arrays and an additional loudspeaker Principle Sound field produced by a center loudspeaker is cancelled by using multiple circular arrays Property Sound field produced by only has 0th order spherical harmonic spectrum Alternative proposed method 14 (b) Exterior sound field synthesis + (c) Proposed method D D D0 D0 − ˇB0 0 = − jk √ 4π for r > rQ rQ ˇB0 0 = jk √ 4π for r > 0 (a) Monopole sound field Residual sound field for r < rQ WASPAA19 RODUCED BY POINT TAL PLANE lative to Cartesian coordi- und field for regions exte- n(kr)Y m n (✓, ), (1) onic spectra of the exterior Hankel function of the first ber [22]; ! ! P|m| n (cos ✓) } ejm (2) | is the associated Legen- assumption, the transfer = [r, ✓0, 0]T to a point ld Green’s function [22]: m (✓ , )⇤ Y m (✓, ), (3) n + |m| even because P |m| n (0) = 0 when n + |m| is odd [27–30]. Therefore, to synthesize a complete 3D exterior sound field using loudspeakers on the horizontal plane, both monopole and vertical dipole components are required. These vertical dipole components include the vertical derivatives of P |m| n (0) and can control the odd spectra. To approximately implement the vertical dipole compo- nents using actual monopole loudspeakers, monopole pairs are in- troduced [27, 28]. Therefore, the conventional approach requires double the number of loudspeakers. In the proposed approach, the sound field produced by a point source located at the origin only including the 0-th order spherical harmonic spectrum component (Fig. 1(a)), is cancelled using multi- ple co-centered circular loudspeaker arrays on the horizontal plane (Fig. 1(b)). As a result, the proposed method can be simply real- ized using a practical planar omni-directional array with half the number of loudspeakers required for the conventional method using monopole pairs [27,28]. 3. PROPOSED 3D LOCALIZED SOUND ZONE GENERATION From (3), the sound field produced by a monopole loudspeaker with driving function D0 located at the origin (Fig. 1(a)) is given as: S0(r, ✓, ) = D0G(r, r0 = 0) = D0 0X n=0 nX m= n jk p 4⇡ hn(kr)Y m n (✓, ) = D0 ejkr 4⇡r , (5)
  15. 15. Sound pressure Level: 500 Hz Sound pressure level on -axis Results of alternative proposed method 15(d) 20 log10 |S0+1(x, y = 0, z)|0)| (b) S0+1(x, y = 0, z) (d) 20 log10 |S0+1(x, y = 0, z)|(c) 20 log10 |S0+1(x, y, z = 0)| (a) S1(x, y = 0, z) (b) S0+1(x, y = 0, z) 再生音圧レベル:500 Hz z軸上の音圧レベル:∼ 800 Hz (a) Point source (b) Method with monopole pairs (c) Proposed method Simulation results (b) 20 log10 |S0+1(x, y = 0, z)|(a) S0+1(x, y = 0, z) 従来法(モノポール対) 提案法(無指向性) 提案法の有効性を確認 (d) 20 log10 |S0+1(x, y = 0, z)|(c) 20 log10 |S0+1(x, y, z = 0)| (a) S1(x, y = 0, z) (b) S0+1(x, y = 0, z) (d) 20 log10 |S0+1(x, y =(c) 20 log10 |S0+1(x, y, z = 0)| (a) S1(x, y = 0, z) (b) S0+1(x, y = 0, z) Previous problems can be successfully solved 音圧レベル:500 Hz の音圧レベル:∼ 800 Hz (a) Point source (b) Method with monopole pairs (c) Proposed method Simulation results 10 (b) 20 log10 |S0+1(x, y = 0, z)|S0+1(x, y = 0, z) 従来法(モノポール対) 提案法(無指向性) 提案法の有効性を確認 (d) 20 log10 |S0+1(x, y = 0, z)|(c) 20 log10 |S0+1(x, y, z = 0)| (a) S1(x, y = 0, z) (b) S0+1(x, y = 0, z) (d) 20 log10 |S0+1(x, y = 0, z)|(c) 20 log10 |S0+1(x, y, z = 0)| (a) S1(x, y = 0, z) (b) S0+1(x, y = 0, z) 従来法(モノポール対):(5 + 7 + 9) x 2 + 1 = 43チャネル Δz = 0.05 m 点音源位置:[0, 0, ­0.1]T 提案法(無指向性):5 + 7 + 9 + 1 = 22チャネル (a) Method with monopole pairs ∆z (b) Proposed method12+1=22 loudspeakers WASPAA19 opole pairs, and the proposed method. y Beven 0 and Bodd 0 components and the entional method, Deven+odd , was also mum order N in (12) was set at 100. ts for both the conventional and pro- n Fig. 2. ds S1(x, y, z) and S0+1(x, y, z), and 0 log10 |S0+1(x, y, z)|, produced us- h with monopole pairs and using the nar omni-directional array at a fre- shown in Figs. 3 and 4, respectively. he sound pressure levels on the z-axis Hz  f  800 Hz produced using a
  16. 16. Applied to flexible array configuration Spatial Fourier transform: Arrangements of arrays MUST be planar / linear or circular / spherical Arrangements and applications are limited -> Investigating other arrangements and their formulations 3D localized sound zone near loudspeakers Implementing a system with actual loudspeakers Investigating distance attenuation control Challenges and prospects 16
  17. 17. Spatial Fourier transform-based localized sound zone generation Multiple sound zones with linear and circular arrays Localized sound zone near loudspeakers with circular and linear arrays Challenges and prospects Acknowledgements These studies were partly supported by JSPS KAKENHI grand numbers JP25871208, JP15K21674, and JP18K11387 JP25871208: Apl. 2013 to Mar. 2015 ICASSP14, ICASSP15 JP15K21674: Apl. 2015 to Mar. 2018 WASPAA15, ICASSP16, JASA17, ICASSP17, JIHMSP17a, WASPAA17, JIHMSP17b JP18K11387: Apl. 2018 to Mar. 2021 Appl. Sci18, IWAENC18, ICASSP19, WASPAA19 Conclusions 17
  18. 18. Deep neural network-based text-to-speech synthesis T. Okamoto, T. Toda, Y. Shiga, and H.Kawai,“Tacotron-based acoustic model using phoneme alignment for practical neural text-to-speech systems,” in Proc. ASRU, Dec. 2019. (to appear) ASRU 2019: IEEE Automatic speech recognition and understanding workshop, 14–18, December, 2019, Sentosa, Singapore Announcement 18
  19. 19. Sound field control with least square-based Pressure-matching Kirkeby93: O. Kirkeby and P.Nelson, “Reproduction of plane wave sound fields,” J. Acoust. Soc. Am., vol. 94, no. 5, pp. 2992–3000, Nov. 1993. Acoustic contrast control Choi02: J.-W. Choi and Y.-H. Kim, “Generation of an acoustically bright zone with an illuminated region using multiple sources,” J. Acoust. Soc. Am., vol. 111, no. 4, pp. 1695– 1700, Apr. 2002. Spectral division method Ahrens08: J. Ahrens and S. Spors, “An analytical approach to sound field reproduction using circular and spherical loudspeaker distributions,” Acta Acust. Acust., vol. 94, no. 6, pp. 988–999, Nov. 2008. Spectral division method Ahrens10: J. Ahrens and S. Spors, “Sound field reproduction using planar and linear arrays of loudspeakers,” IEEE Trans. Audio, Speech, Lang. Process., vol. 18, no. 8, pp. 2038– 2050, Nov. 2010. Related works 19
  20. 20. ICASSP14: T. Okamoto, “Generation of multiple sound zones by spatial filtering in wavenumber domain using a linear array of loudspeakers,” in Proc. ICASSP, May 2014, pp. 4733–4737. ICASSP15: T. Okamoto, “Near-field sound propagation based on a circular and linear array combination,” in Proc. ICASSP, Apr. 2015, pp. 624–628. WASPAA15: T. Okamoto, “Analytical methods of generating multiple sound zones for open and baffled circular loudspeaker arrays,” in Proc. WASPAA, Oct. 2015. JASA17: T. Okamoto and A. Sakaguchi, “Experimental validation of spatial Fourier transform- based multiple sound zone generation with a linear loudspeaker array,” J. Acoust. Soc. Am., vol. 141, no. 3, pp. 1769–1780, Mar. 2017. JIHMSP17a: T. Okamoto, “Localized sound zone generation based on external radiation canceller,” J. Inf. Hiding Multimed. Signal Pro- cess., vol. 8, no. 6, pp. 1335–1351, Nov. 2017. Publications: Localized sound zone (1) 20
  21. 21. JIHMSP17b: T. Okamoto, “Horizontal local sound field propagation based on sound source dimension mismatch,” J. Inf. Hiding Multimed. Signal Process., vol. 8, no. 5, pp. 1069–1081, Sept. 2017. IWAENC18: T. Okamoto, “2.5D localized sound zone generation with a circular array of fixed- directivity loudspeakers,” in Proc. IWAENC, Sept. 2018, pp. 321–325. WASPAA19: T. Okamoto, “3D localized sound zone generation with a planar omni-directional loudspeaker array,” in Proc. WASPAA, Oct. 2019, pp. 370–374. Publications: Localized sound zone (2) 21
  22. 22. ICASSP16: T. Okamoto, “2.5D higher-order Ambisonics for a sound field described by angular spectrum coefficients,” in Proc. ICASSP, Mar. 2016, pp. 326–330. ICASSP17: T. Okamoto, “Analytical approach to 2.5D sound field control using a circular double-layer array of fixed-directivity loudspeakers,” in Proc. ICASSP, Mar. 2017, pp. 91–95. WASPAA17: T. Okamoto, “Angular spectrum decomposition-based 2.5D higher-order spherical harmonic sound field synthesis with a linear loudspeaker array,” in Proc. WASPAA, Oct. 2017, pp. 180–184. Appl. Sci.18: T.Okamoto,“Mode-matching-based sound field recording and synthesis with circular double-layer arrays,” Appl. Sci., vol. 8, no. 7, 1048, July 2018. ICASSP19: T. Okamoto, “Horizontal 3D sound field recording and 2.5D synthesis with omni- directional circular arrays,” in Proc. ICASSP, May 2019, pp. 960–964. Publications: Sound field synthesis 22

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