In this paper we investigate the application of a rotational-shear interferometer, toward the problem of simultaneously estimating the directions of well-localized sources, and their spectral profiles. Rotational shear makes possible the acquisition of a spectrum estimate, without the mechanical scan required in using a Michelson interferometer in Fourier-transform spectroscopy. The spectrum and angle estimates are obtained computationally. The interferometric data enables the application of super-resolution direction-finding techniques commonly used in radar and sonar array processing.