How narrow is narrowband?

The ‘narrowband’ assumption is often made in the analysis of array signal processing algorithms. The author provides a definition for the notion of narrowband, and the derivation of an expression which is useful in determining if a particular scenario qualifies as narrowband. The expression derived correctly predicts where the narrowband assumption fails for some super-resolution algorithms, the Cramer–Rao bound on angle estimation and the signal-to-interference plus noise performance of adaptive beamformers.