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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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Nearfield spherical microphone arrays for speech enhancement and dereverberation l.jpg

Nearfield Spherical Microphone Arraysfor speech enhancement and dereverberation

Etan Fisher

Supervisor:

Dr. Boaz Rafaely


Microphone arrays l.jpg

Microphone Arrays

  • Spatial sound acquisition

  • Sound enhancement

  • Applications:

    • reverberation parameter estimation

    • dereverberation

    • video conferencing


Spheres l.jpg

Spheres

  • The sphere as a symmetrical, natural entity.

  • Spherical symmetry

  • Facilitates direct sound field analysis:

    • Spherical Fourier transform

    • Spherical harmonics

Photo by Aaron Logan


Nearfield spherical microphone array l.jpg

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


Sound pressure spherical wave l.jpg

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):


Sound pressure spherical wave6 l.jpg

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):


Sound pressure spherical wave7 l.jpg

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):


Spherical spectrum functions l.jpg

Spherical Spectrum Functions


Spherical spectrum functions9 l.jpg

Spherical Spectrum Functions


Point source decomposition l.jpg

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.


Point source decomposition11 l.jpg

Point Source Decomposition

  • Amplitude density:

  • Using the identity:

    where Θ is the angle between Ω and Ωp,


Nearfield criteria l.jpg

Nearfield Criteria

NOrder of array

kWave number

rA

Array

radius

rs

Source

distance


Radial attenuation l.jpg

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


Radial attenuation14 l.jpg

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


Radial attenuation15 l.jpg

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


Radial attenuation close talk l.jpg

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


Radial attenuation close talk17 l.jpg

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


Radial attenuation large array l.jpg

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


Normalized beampattern l.jpg

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.


Normalized beampattern20 l.jpg

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.


Normalized beampattern21 l.jpg

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.


Directional impulse response l.jpg

Directional Impulse Response

  • Amplitude density:

  • Impulse response at direction Ω0:where is the ordinary inverse Fourier transform.


Speech dereverberation l.jpg

Speech Dereverberation

Room IR Directional IR

{4 X 3 X 2}

N = 4

r = 0.1 m

r0= 0.2 m

“Dry”

“Rev.”

“Derev.”


Music dereverberation l.jpg

Music Dereverberation

Room IR Directional IR

{ 8 X 6 X 3 }

N = 4

r = 0.1 m

r0= 1.9 m “Dry”

“Rev.”

“Derev.”


Conclusions l.jpg

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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