Directional Sources and Beamforming
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1 156 th meeting of the Acoustical Society of America Miami, Florida, November 13, 2008 Directional Sources and Beamforming Christian Bouchard David I. Havelock Institute for Microstructural Sciences National Research Council of Canada Ottawa ON K1A 0R6 CANADA Martin Bouchard University of Ottawa Ottawa ON K1N 6N5 CANADA
2 Directional Sources and Beamforming Beamforming The directionality of some real world sources that deviate from an ideal point source Performance measures used to evaluate the properties of a beamformer Validity of assuming a point source Challenges for beamforming on non-point sources
3 Directional Sources and Beamforming Beamforming The directionality of some real world sources that deviate from an ideal point source Performance measures used to evaluate the properties of a beamformer Validity of assuming a point source Challenges for beamforming on non-point sources
4 Beamforming Discrete array of L sensors t s t n t p1 1 1 t s t n t p2 2 2 Beamformer Filter 1 Filter 2 yt p L t s t n t L L Filter L w Filter bank design will depend on array geometry, on source directivity, orientation, and position as well as array output optimization criterion y f w * f p f l H l f pf l
5 Beamforming on a Point Source Wave crest Point source Discrete array of L sensors t s t n t p1 1 1 t s t n t p2 2 2 Filter 1 Filter 2 Beamformer yt p L t s t n t L L Filter L Wave trough Must know how the source radiates to coherently sum the received signals at the microphones: source model y f w * f p f f pf Conventional beamforming: point source as source model l w H l l
6 Directional Sources and Beamforming Beamforming The directionality of some real world sources that deviate from an ideal point source Performance measures used to evaluate the properties of a beamformer Validity of assuming a point source Challenges for beamforming on non-point sources
7 Aeroacoustics Example: Solid object in an air flow Air flow
8 Measurements of Flute Directivity, With G Fingering (IRCAM) Fundamental 410 Hz Overtone, 820 Hz Mouth hole Tone holes From: A. Rousseau, Institut de Recherche et Coordination Acoustique/Musique (IRCAM), Département d acoustique instrumentale (IRCAM), Paris, May 1996.
9 Measurements of Flute Directivity, With G Fingering (IRCAM) Fundamental 410 Hz Overtone, 820 Hz From: A. Rousseau, Institut de Recherche et Coordination Acoustique/Musique (IRCAM), Département d acoustique instrumentale (IRCAM), Paris, May 1996.
10 Measurements of Flute Directivity, With G Fingering (IRCAM) Overtone, 1628 Hz Overtone, 3160 Hz From: A. Rousseau, Institut de Recherche et Coordination Acoustique/Musique (IRCAM), Département d acoustique instrumentale (IRCAM), Paris, May 1996.
11 Directional Sources and Beamforming Beamforming The directionality of some real world sources that deviate from an ideal point source Performance measures used to evaluate the properties of a beamformer Validity of assuming a point source Challenges for beamforming on non-point sources
12 Performance measures: Array Gain Improvement in SNR SNR at output of the array Array gain SNR at input of the array w H w H H K sk s K wk H K E nk n K w H s K sk / L H E n K nk / K L White-noise gain is maximized when the source model and the source have the same directivity position orientation Maximum white-noise gain equals the number of microphones
13 Performance measures: Directivity factor Definition for a point source in the far-field of a receiving array: Directivity factor, T T Array output power for direction of arrival T, T Array output power due to spherically isotropic noise Possible definition for directional sources Directivity factor Source directivity and orientation, rt,, Array output power for a given source located at rt, θt, T Source Power at center of array Array output power due to spherically isotropic noise T T
14 Directional Sources and Beamforming Beamforming The directionality of some real world sources that deviate from an ideal point source Performance measures used to evaluate the properties of a beamformer Validity of assuming a point source Challenges for beamforming on non-point sources
15 Beamforming on a Point Source Array Geometry and Source 120 White-Noise Gain (Linear) Conventional beamforming Number of microphones
16 Beamforming on a Quadrupole Array Geometry and Source White-Noise Gain (Linear) Conventional beamforming Number of microphones
17 Beamforming on a Quadrupole Array Geometry and Source White-Noise Gain (Linear) Quadrupole source model Conventional beamforming Number of microphones
18 Directional Sources and Beamforming Beamforming The directionality of some real world sources that deviate from an ideal point source Performance measures used to evaluate the properties of a beamformer Validity of assuming a point source Challenges for beamforming on non-point sources
19 Challenges for Beamforming on Non- Point Sources Often necessary to estimate the source directivity and orientation The source model needs to be computationally efficient (finite template sets?) Source directivity estimators may be affected by the presence of interferers Source directivity may change with frequency Array located in a directional null
20 156 th meeting of the Acoustical Society of America Miami, Florida, November 13, 2008 Directional Sources and Beamforming Christian Bouchard David I. Havelock Institute for Microstructural Sciences National Research Council of Canada Ottawa ON K1A 0R6 CANADA Martin Bouchard University of Ottawa Ottawa ON K1N 6N5 CANADA
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