Cosine beamforming

In various application areas, e.g., seismology, astronomy and geodesy,arrays of sensors are used to characterize incoming wavefields due todistant sources. Beamforming is a general term for phased-adjustedsummations over the different array elements, for untangling thedirectionality and elevation angle of the incoming waves. Forcharacterizing noise sources, beamforming is conventionally applied witha temporal Fourier and a 2D spatial Fourier transform, possibly withadditional weights. These transforms become aliased for higherfrequencies and sparser array-element distributions. As a partialremedy, we derive a kernel for beamforming crosscorrelated data and callit cosine beamforming (CBF). By applying beamforming not directly to the data, but to crosscorrelated data, the sampling is effectivelyincreased. We show that CBF, due to this better sampling, suffers lessfrom aliasing and yields higher resolution than conventionalbeamforming. As a flip-side of the coin, the CBF output shows moresmearing for spherical waves than conventional beamforming.