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Nearfield Spherical Microphone Arrays for speech enhancement and dereverberation

Nearfield Spherical Microphone Arrays for speech enhancement and dereverberation. Etan Fisher Supervisor: Dr. Boaz Rafaely. Microphone Arrays. Spatial sound acquisition Sound enhancement Applications: reverberation parameter estimation dereverberation video conferencing. Spheres.

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Nearfield Spherical Microphone Arrays for speech enhancement and dereverberation

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  1. Nearfield Spherical Microphone Arraysfor speech enhancement and dereverberation Etan Fisher Supervisor: Dr. Boaz Rafaely

  2. Microphone Arrays • Spatial sound acquisition • Sound enhancement • Applications: • reverberation parameter estimation • dereverberation • video conferencing

  3. Spheres • The sphere as a symmetrical, natural entity. • Spherical symmetry • Facilitates direct sound field analysis: • Spherical Fourier transform • Spherical harmonics Photo by Aaron Logan

  4. Nearfield Spherical Microphone Array • Generally, the farfield, plane wave assumption is made (Rafaely, Meyer & Elko). • In the nearfield, the spherical wave-front must be accounted for. • Examples: • Close-talk microphone • Nearfield music recording • Multiple speaker / video conferencing

  5. Sound Pressure - Spherical Wave • Sound pressure on sphere r due to point source rp (spherical wave): • Spherical harmonics: From the solution to the wave equation (spherical coordinates):

  6. Sound Pressure - Spherical Wave • Sound pressure on sphere r due to point source rp : • Spherical harmonics: • The spherical harmonicsare orthogonal and complete. From the solution to the wave equation (spherical coordinates):

  7. Sound Pressure - Spherical Wave • Sound pressure on sphere r due to point source rp: • is the spherical Hankel function. • is the modal frequency function (Bessel):

  8. Spherical Spectrum Functions

  9. Spherical Spectrum Functions

  10. Point Source Decomposition • Sound pressure on sphere r due to point source rp: • Spherical Fourier transform: • Spatial filter – cancel spherical wave-front, yielding unit amplitude at rp=r0.

  11. Point Source Decomposition • Amplitude density: • Using the identity: where Θ is the angle between Ω and Ωp,

  12. Nearfield Criteria N Order of array k Wave number rA Array radius rs Source distance

  13. Radial Attenuation N = 4; rA (array) = 0.1m; k = kmax kmax = N/rA = 40 kmax = 2πfmax /343 fmax = 2184 Hz r0 – Desired source location rp – Interference location

  14. Radial Attenuation N = 4; rA (array) = 0.1m; k = kmax/4 kmax = N/rA = 40 kmax = 2πfmax /343 fmax = 2184 Hz r0 – Desired source location rp – Interference location

  15. Radial Attenuation N = 4; rA (array) = 0.1m; k = kmax/10 kmax = N/rA = 40 kmax = 2πfmax /343 fmax = 2184 Hz r0 – Desired source location rp – Interference location

  16. Radial Attenuation –“Close Talk” N = 2; rA (array) = 0.05 m; k = kmax kmax = N/rA = 40 kmax = 2πfmax /343 fmax = 2184 Hz r0 – Desired source location rp – Interference location

  17. Radial Attenuation –“Close Talk” N = 2; rA (array) = 0.05 m; k = kmax /4 kmax = N/rA = 40 kmax = 2πfmax /343 fmax = 2184 Hz r0 – Desired source location rp – Interference location

  18. Radial Attenuation – Large Array N = 12; rA (array) = 0.3 m; k = kmax /4 kmax = N/rA = 40 kmax = 2πfmax /343 fmax = 2184 Hz r0 – Desired source location rp – Interference location

  19. Normalized Beampattern N = 4; rA (array) = 0.1m; k = kmax kmax = N/rA = 40 kmax = 2πfmax /343 fmax = 2184 Hz The natural radial attenuation has been cancelled by multiplying the array output by the distance.

  20. Normalized Beampattern N = 4; rA (array) = 0.1m; k = kmax /4 kmax = N/rA = 40 kmax = 2πfmax /343 fmax = 2184 Hz The natural radial attenuation has been cancelled by multiplying the array output by the distance.

  21. Normalized Beampattern N = 4; rA (array) = 0.1m; k = kmax /10 kmax = N/rA = 40 kmax = 2πfmax /343 fmax = 2184 Hz The natural radial attenuation has been cancelled by multiplying the array output by the distance.

  22. Directional Impulse Response • Amplitude density: • Impulse response at direction Ω0:where is the ordinary inverse Fourier transform.

  23. Speech Dereverberation Room IR Directional IR {4 X 3 X 2} N = 4 r = 0.1 m r0= 0.2 m “Dry” “Rev.” “Derev.”

  24. Music Dereverberation Room IR Directional IR { 8 X 6 X 3 } N = 4 r = 0.1 m r0= 1.9 m “Dry” “Rev.” “Derev.”

  25. Conclusions • Sphericalwave pressure on asphericalmicrophone array insphericalcoordinates. • Point source decomposition achieves radial attenuation as well as angular attenuation. • Directional impulse response (IR) vs. room IR. • Speech and music dereverberation. • Further work: • Develop optimal beamformer • Experimental study of array

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