Regular Article: Computing Fourier Transforms and Convolutions on the 2-Sphere
Advances in Applied Mathematics
Detection, Estimation, and Modulation Theory: Radar-Sonar Signal Processing and Gaussian Signals in Noise
Spatial Aliasing in Spherical Microphone Arrays
IEEE Transactions on Signal Processing
Open-Sphere Designs for Spherical Microphone Arrays
IEEE Transactions on Audio, Speech, and Language Processing
Flexible and Optimal Design of Spherical Microphone Arrays for Beamforming
IEEE Transactions on Audio, Speech, and Language Processing
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Spherical arrays with array processing based on spherical harmonics have been recently studied for a wide range of applications that require three-dimensional beamforming. In this correspondence, a Dolph-Chebychev beampattern design, widely used in array processing due to the direct control over main-lobe width and maximum sidelobe level, is developed for spherical arrays within the spherical harmonics framework. We show that due to the similarity between the Legendre polynomials that define the spherical array beampattern and the Chebyshev polynomials that define the desired Dolph-Chebyshev beampattern, spherical array weights can be computed directly and accurately given desired main-lobe width or sidelobe level.