Parameter selection for audio beamforming
An audio beamformer receives signals from microphones of an array and processes the signals to produce a directional audio signal that emphasizes sound from a selected direction. The beamformer is implemented using weights or other parameters that are calculated to account for effects upon the received audio signals by the surfaces upon which the microphones are positioned.
1. A method comprising:
receiving multiple frequency domain input signals, each input signal corresponding to a microphone of a microphone array, wherein each microphone is on a surface;
selecting a focus direction;
determining a correction vector for a first input signal corresponding to a first microphone of the microphone array, the correction vector indicating magnitude differences and phase differences at multiple frequencies of the first input signal caused by the surface in comparison to a free-field input signal that would be produced by the first microphone in free space in response to a sound wave arriving from the focus direction;
calculating filter weights corresponding to the multiple frequencies of the first input signal based at least in part on the correction vector and based at least in part on the focus direction;
multiplying frequency components of the first input signal by the filter weights to produce a first filtered signal corresponding to the first input signal; and
summing multiple filtered signals corresponding respectively to the input signals to produce a directional frequency domain signal, the multiple filtered signals comprising the first filtered signal.
2. The method of claim 1 , wherein determining the correction vector comprises mathematically modeling diffraction and scattering effects caused by the surface upon the first input signal at multiple frequencies and for multiple focus directions.
3. The method of claim 1 , wherein determining the correction vector comprises experimentally measuring diffraction and scattering effects caused by the surface upon the first input signal at multiple frequencies and for multiple focus directions.
4. The method of claim 1 , wherein the correction vector comprises correction values corresponding respectively to different frequencies ω, each correction value comprising a m (ω, Θ d )e jφ m (ω, Θ d ) , where:
a m (ω, Θ d ) is the magnitude difference of the first input signal caused by the surface at frequency ω in response to a sound wave arriving from the focus direction Θ d , and
φ m (ω, Θ d ) is the phase difference of the first input signal caused by the surface at frequency ω in response to the sound wave arriving from the focus direction Θ d .
5. The method of claim 1 , wherein calculating the frequency-domain filter weights comprises calculating
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~
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v
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m
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ω
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Θ
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;
where:
{tilde over (v)} m (ω, Θ d ) is an array manifold vector that is calculated based at least in part on the correction vector;
{tilde over (Ψ)} NN Diff is a normalized noise correlation matrix for spherically diffuse noise;
the superscript H indicates a Hermitian matrix transposition operation; and
the superscript −1 indicates an inverse matrix operation.
6. A method of determining filter weights of a beamformer that processes multiple input signals, each input signal corresponding to a microphone of a microphone array, wherein each microphone is on a surface, the method comprising:
determining a correction vector for a first input signal corresponding to a first microphone of the microphone array, the correction vector indicating differences, at multiple frequencies of the first input signal, caused by the surface in comparison to a free-field input signal that would be produced by the first microphone in free space in response to a sound wave arriving from a focus direction; and
calculating the filter weights corresponding to the first input signal using the correction vector.
7. The method of claim 6 , wherein calculating the filter weights corresponding to the first input signal comprises calculating
A exp(− jk T p );
where:
p is a position of the first microphone;
A is the correction vector;
the operator exp indicates an exponentiation operation;
j is an imaginary unit;
k is a unit vector corresponding to the focus direction; and
the superscript T indicates a matrix transposition operation.
8. The method of claim 7 , wherein calculating the filter weights further comprises calculating
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where:
{tilde over (Ψ)} NN Diff is a normalized noise correlation matrix for spherically diffuse noise;
{tilde over (v)} is A exp(−jk T p);
the superscript H indicates a Hermitian matrix transposition operation; and
the superscript −1 indicates an inverse matrix operation.
9. The method of claim 6 , wherein determining the correction vector comprises mathematically modeling diffraction and scattering effects caused by the surface upon the first input signal at multiple frequencies and for multiple focus directions.
10. The method of claim 6 , wherein determining the correction vector comprises experimentally measuring diffraction and scattering effects caused by the surface upon the first input signal at multiple frequencies and for multiple focus directions.
11. The method of claim 6 , wherein the differences include magnitude differences and phase differences.
12. The method of claim 6 , wherein the filter weights are for use in a beamformer that multiplies frequency components of the input signal by the filter weights.
13. The method of claim 6 , wherein the filter weights are for use in a superdirective beamformer.
14. One or more computer-readable media storing computer-executable instructions that, when executed by one or more processors, cause the one or more processors to perform acts comprising:
determining first diffraction and scattering effects caused by a surface on a first input signal received from a microphone array, the first diffraction and scattering effects comprising a first difference in magnitude and a first difference in phase caused by the surface in comparison to a free-field input signal that would be produced by the microphone array in free space in response to a sound wave arriving at the microphone array;
determining second diffraction and scattering effects caused by the surface on a second input signal received from the microphone array, the second diffraction and scattering effects comprising a second difference in magnitude and a second difference in phase caused by the surface in comparison to the free-field input signal that would be produced by the microphone array in free space in response to the sound wave arriving at the microphone array;
calculating parameters for use by an audio beamformer to process the first input signal and the second input signal received from the microphone array and to produce a directionally focused output signal;
wherein the calculating is based at least in part on the determined first diffraction and scattering effects and second diffraction and scattering effects caused by the surface.
15. The one or more computer-readable media of claim 14 , wherein the first diffraction and scattering effects comprise ae jφ , where:
a represents a magnitude of the first diffraction and scattering effects, and
φ represents a phase of the first diffraction and scattering effects.
16. The one or more computer-readable media of claim 14 , wherein each parameter comprises a weight that is calculated as:
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;
where:
{tilde over (Ψ)} NN Diff is a normalized noise correlation matrix for spherically diffuse noise;
{tilde over (v)} is an array manifold vector that accounts for the first diffraction and scattering effects;
the superscript H indicates a Hermitian matrix transposition operation; and
the superscript −1 indicates an inverse matrix operation.
17. The one or more computer-readable media of claim 14 , wherein calculating the parameters comprises calculating weights for use in a superdirective audio beamformer.
18. The one or more computer-readable media of claim 14 , wherein determining the first diffraction and scattering effects and the second diffraction and scattering effects comprises mathematically modeling the first diffraction and scattering effects and the second diffraction and scattering effects.
19. The one or more computer-readable media of claim 14 , wherein determining the first diffraction and scattering effects and the second diffraction and scattering effects comprises experimentally measuring the first diffraction and scattering effects and the second diffraction and scattering effects.