Design of robust differential microphone arrays with the Jacobi–Anger expansion |
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Authors: | Liheng Zhao Jacob Benesty Jingdong Chen |
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Institution: | 1. INRS-EMT, University of Quebec, 800 de la Gauchetiere Ouest, Suite 6900, Montreal, QC H5A 1K6, Canada;2. Center of Intelligent Acoustics and Immersive Communications, Northwestern Polytechnical University, 127 Youyi West Rd, Xi’an, Shaanxi 710072, China |
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Abstract: | Due to their small size, differential microphone arrays (DMAs) are very attractive. Moreover, they have been effective in combating noise and reverberation. Recently, a new class of DMAs of different orders have been developed with the MacLaurin’s series and the frequency-independent patterns. However, the MacLaurin’s series does not approximate well the exponential function, which appears in the general definition of the beampattern, when the intersensor spacing is not small enough. To circumvent this problem, we propose in this paper to approximate the exponential function with the Jacobi–Anger expansion. Based on this approximation and the frequency-independent Chebyshev patterns, we derive first-, second-, and third-order DMAs. Furthermore, in order to improve the robustness of DMAs against white noise amplification, we propose to use more microphones combined with minimum-norm filters. It is also shown that the Jacobi–Anger expansion is optimal from a mean-squared error perspective. Simulations are carried out to evaluate the performance of the proposed DMAs. |
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Keywords: | Differential microphone arrays (DMAs) Robust DMAs Beampattern Beamforming White noise gain Directivity factor First-order DMA Second-order DMA Third-order DMA Jacobi&ndash Anger expansion |
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