Golden-Ratio Sampling for Scanning Circular Microphone Arrays

Circular microphone arrays have been recently studied for music recordings, beamforming, and sound-field analysis. Scanning circular arrays that use a single microphone to acquire measurements at a range of spatial sampling positions have been employed to gather an entire array data. Uniform sampling along the circle is typically used, but this scheme may not allow experimental flexibility. If, for any reason, the experiment was not completed in full, the data gathered may not be sufficient to perform the required processing. This paper presents an alternative spatial sampling scheme for scanning circular microphone arrays, which is more robust against uncertainty in the duration of the experiment. The proposed spatial sampling method is based on fixed-angle steps along the circle defined by the golden-ratio. Theoretical analysis of the golden-ratio sampling method is presented, supported by simulation examples, showing that experimental flexibility is achieved, but at the expanse of some reduction in numerical robustness.