Trigonometric Interpolation Beamforming for a Circular Microphone Array

Polynomial beamforming has previously been proposed for addressing the non-trivial problem of integrating acoustic echo cancellation with adaptive microphone beamforming. This paper demonstrates a design example for a circular array where traditional polynomial beamforming approaches exhibit severe (over 10 dB) directivity index (DI) oscillations at the edges of the design interval, leading to severe DI degradation for certain look directions. A solution, based on trigonometric interpolation, is proposed that stabilizes the oscillations significantly, resulting in a DI that deviates only about 1 dB from that of a fixed beamformer over all look directions.