Cross-Spectrum-Based Post-Filter Utilizing Noisy and Robust Beamformers

This chapter reviews a post-filtering technique that can provide additional attenuation of spatial noise, interferers, and diffuse sound to the output of a beamformer with minimal spectral artifacts. It provides the notation, the signal model, and background on practical beamforming techniques where an arbitrary target directivity pattern is desired. The chapter focuses on the two variations of the non-linear directional filtering algorithm including the design principles for the weight coefficients for the constant and the adaptive beamformers. It also focuses on implementation examples with simulated and real microphone arrays in reverberant environments with single- or multiple-talker scenarios. The post-filters employs the cross-spectrum of signals originating from coincident beamformers. The cross-spectrum aims to estimate the target signal energy originating from a specific look direction by using two beamformers with the same phase and unity gain towards that direction.