koyama aes conference sfc 2016
TRANSCRIPT
Source-Location-Informed Sound Field Recording and Reproduction:
A Generalization to Arrays of Arbitrary Geometry
Shoichi Koyama The University of Tokyo / Université Paris Diderot (Institut Langevin)
July 19, 2016
Super-resolution in Recording and Reproduction
Improve reproduction accuracy when less microphones than loudspeakers
# of microphones > # of loudspeakers– Higher reproduction accuracy within local region of target area
# of microphones < # of loudspeakers– Higher reproduction accuracy of sources in local region of recording area
[Koyama+ ICASSP 2014], [Koyama+ IEEE JSTSP 2015]
[Ahrens+ AES Conv. 2010]
Microphone array Loudspeaker array
Sound Field Recording and Reproduction
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Recording area Target area
Obtain driving signals of secondary sources (= loudspeakers)arranged on to reconstruct desired sound field inside
Inherently, sound pressure and its gradient on is required to obtain , but sound pressure is usually only known
Fast and stable signal conversion for sound field recording and reproduction with ordinary acoustic sensors and transducers is required
Primary sources
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Wave field reconstruction (WFR) filtering methodTarget area
Receivedsignals
Driving signals
Plane wave Plane wave
Each plane wave determines entire sound field
Spatial aliasing artifacts due to plane wave decomposition Significant error at high freq. even when microphone < loudspeaker
Recording area[Koyama+ IEEE TASLP 2013]
Signalconversion
Secondary source planeReceiving plane
Primary sources
Source-Location-Informed Recording and Reproduction
Signal conversion method that takes into account a priori knowledge of primary source locations
This prior information can be obtained by using various types of sensors or by manual input
By exploiting this prior information, reproduction accuracy above the spatial Nyquist freq can be improved
Apply the method proposed in [Koyama+ IEEE JSTSP 2015] to several array geometries
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Target areaRecording area
Signalconversion
Secondary source planeReceiving plane
Primary sources
Approximate location is obtained by sensors
Statement of Problem
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Target areaRecording area
Primary sources
Secondary source distribution:
Microphone array on baffle
Control pointsConstraint on driving signals
Linear combination of spatial basis functions
Transfer functionDesired pressures
Optimize and by using prior information on
source locations
Statement of Problem
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Target areaRecording area
Primary sources
Secondary source distribution:
Control points
Two requirement must be satisfied to apply the method proposed in [Koyama+ IEEE JSTSP 2015]
1. The relationship between and can be obtained
2. The amplitude distribution of the driving signals of the secondary sources can be predicted from prior information on the source location
Microphone array on baffle
Modified Transfer Function For the first requirement, we consider modified transfer function
that relates with
For planar / linear array case, because can be equivalent to
When microphones are mounted on baffle, We here show an example of a cylindrical array
– Spherical array case is presented in [Koyama+ WASPAA 2015]
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Modified Transfer Function Synthesized sound field in cylindrical
harmonic domain
Desired sound field in cylindrical harmonic domain
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Modified transfer function for cylindrical arrays of microphones and loudspeakers
MAP Estimation of Driving Signals
Likelihood function: complex Gaussian distribution
Prior distribution: Amplitude distribution of ( ) predicted from approximate primary source location is incorporated
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Maximum a posteriori (MAP) estimation
Bayes’ rule
Likelihood function Prior distribution
MAP Estimation of Driving Signals Objective function:
Assume that spatial basis functions are M orthogonal functions, which satisfies the following relation of singular value decomposition
Optimal spatial basis functions and their coefficients
Driving signals obtained by MAP estimation
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( : regularization parameter)
Prior Based on Primary Source Locations Amplitude distribution can be obtained by assuming point
source at prior source location with sound field synthesis techniques
When array geometry is cylinder and estimated primary source location is , predicted driving signal is obtained as
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Normalization
Algorithm
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Discretize secondary source distribution
Amplitude distribution for prior
Algorithm
1. Detect source location ( )2. Calculate amplitude distribution3. Calculate as 4. Eigenvalue decomposition of 5. Obtain transform filter as
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Simulation Experiments Simulation using cylindrical arrays of microphones and
loudspeakers under free-field assumption Proposed method is compared with WFR filtering method Microphone array:– Radius: 0.12 m, # of microphones: 32 in x 6 in
Loudspeaker array:– Radius: 1.5 m, # of loudspeakers: 32 in x 12 in
Evaluation w/ signal-to-distortion ratio (SDR) at radius
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[Koyama+ IEEE TASLP 2014]
Reproduced and original pressure distribution
Reproduced pressure distribution (x-y-plane)
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Pres
sure
Erro
rProposed WFR
Source location: (2.0 m, 155 deg, -0.4) m, Source signal: 1.6 kHz
Reproduced pressure distribution (y-z-plane)
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Pres
sure
Erro
rProposed WFR
Source location: (2.0 m, 155 deg, -0.4) m, Source signal: 1.6 kHz
Relationship between distance and SDR
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Source location: (2.0 m, 155 deg, -0.4) m, Source signal: 1.6 kHz
Almost the same reproduction accuracy even when prior source
location was perturbed
Conclusion Source-location-informed sound field recording and
reproduction for several types of array geometries– Signal conversion method that takes into account prior information on
primary source locations– Spatial basis functions and their coefficients are optimized– Two requirements:
1. Relationship between desired and received sound pressures can be obtained
2. Amplitude distribution of driving signals of secondary sources can be predicted from prior source locations
– Simulation results using cylindrical arrays indicated that region of high reproduction accuracy of proposed method was larger than that of WFR filtering method
July 19, 2016Thank you for your attention!