Spatial filtering using compact microphone arrays is essential in many audio applications. Traditional fixed beamformers implement spatial filtering by applying a linear combination of filtered microphone signals to achieve a desired directivity pattern. However, the achievable pattern—defined by sidelobe levels, null positions, and mainlobe width—is constrained by the number of microphones and the array aperture. Spatial aliasing also becomes unavoidable at high frequencies when the inter-microphone spacing is not sufficiently small. These limitations often require large arrays with many microphones to obtain the desired directivity. In this work, we present a comprehensive study of these limitations in the context of a deep neural network-based method, termed neural directional filtering (NDF). Our two main contributions are as follows. First, we demonstrate that NDF can learn highly directive patterns without white noise amplification, achieving effective beamforming orders that significantly exceed the number of microphones. Second, we show that the directivity patterns realized by NDF remain frequency-invariant, even at frequencies well above the spatial aliasing threshold. These results suggest that NDF can overcome fundamental limitations of fixed beamforming and achieve spatial selectivity that would otherwise require large, compact microphone arrays.
Huang et al. (Wed,) studied this question.