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Nearfield Spherical Microphone Arrays for speech enhancement and dereverberation

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Generally, the farfield, plane wave assumption is made (Rafaely, Meyer & Elko) ... is the modal frequency function (Bessel): Spherical Spectrum Functions ... – PowerPoint PPT presentation

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Title: Nearfield Spherical Microphone Arrays for speech enhancement and dereverberation


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
From the solution to the wave equation (spherical
coordinates)
  • Sound pressure on sphere r due to point source
    rp (spherical wave)
  • Spherical harmonics

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

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 rpr0.

11
Point Source Decomposition
  • Amplitude density
  • Using the identity
  • where T is the angle between O and Op,

12
Nearfield Criteria
  • N Order of array
  • k Wave number

rA Array radius rs Source distanc
e
13
Radial Attenuation
  • N 4 rA (array) 0.1m k kmax
  • kmax N/rA 40
  • kmax 2pfmax /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 2pfmax /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 2pfmax /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 2pfmax /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 2pfmax /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 2pfmax /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 2pfmax /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 2pfmax /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 2pfmax /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 O0where
    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
  • Spherical wave pressure on a spherical microphone
    array in spherical coordinates.
  • 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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