Title: Nearfield Spherical Microphone Arrays for speech enhancement and dereverberation
1Nearfield Spherical Microphone Arraysfor speech
enhancement and dereverberation
- Etan Fisher
- Supervisor
- Dr. Boaz Rafaely
2Microphone Arrays
- Spatial sound acquisition
- Sound enhancement
- Applications
- reverberation parameter estimation
- dereverberation
- video conferencing
3Spheres
- The sphere as a symmetrical, natural entity.
- Facilitates direct sound field analysis
- Spherical Fourier transform
- Spherical harmonics
Photo by Aaron Logan
4Nearfield 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
5Sound 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
6Sound 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.
7Sound Pressure - Spherical Wave
- Sound pressure on sphere r due to point source
rp - is the spherical Hankel function.
- is the modal frequency function (Bessel)
8Spherical Spectrum Functions
9Spherical Spectrum Functions
10Point 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.
11Point Source Decomposition
- Amplitude density
- Using the identity
- where T is the angle between O and Op,
12Nearfield Criteria
-
- N Order of array
- k Wave number
rA Array radius rs Source distanc
e
13Radial 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
14Radial 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
15Radial 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
16Radial 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
17Radial 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
18Radial 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
19Normalized 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.
20Normalized 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.
21Normalized 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.
22Directional Impulse Response
- Amplitude density
- Impulse response at direction O0where
is the ordinary inverse Fourier transform.
23Speech Dereverberation
- Room IR Directional IR
- 4 X 3 X 2
- N 4
- r 0.1 m
- r0 0.2 m
- Dry
- Rev.
- Derev.
24Music Dereverberation
- Room IR Directional IR
- 8 X 6 X 3
- N 4
- r 0.1 m
- r0 1.9 m Dry
- Rev.
- Derev.
25Conclusions
- 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