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Nearfield Spherical Microphone Arrays for speech enhancement and dereverberationPowerPoint Presentation

Nearfield Spherical Microphone Arrays for speech enhancement and dereverberation

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### Nearfield Spherical Microphone Arraysfor 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

- 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

- 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

- 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 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 Wave

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

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 Decomposition

- Amplitude density:
- Using the identity:
where Θ is the angle between Ω and Ωp,

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 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 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”

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 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

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

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 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 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

- Amplitude density:
- Impulse response at direction Ω0:where is the ordinary inverse Fourier transform.

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

Room IR Directional IR

{ 8 X 6 X 3 }

N = 4

r = 0.1 m

r0= 1.9 m “Dry”

“Rev.”

“Derev.”

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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