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

July 19, 2016

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]

July 19, 2016

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!