  This paper is concerned with a direct sampling method for imaging the support
of a frequency-dependent source term embedded in a homogeneous and isotropic
medium. The source term is given by the Fourier transform of a time-dependent
source whose radiating period in the time domain is known.
  The time-dependent source is supposed to be stationary in the sense that its
compact support does not vary along the time variable.
  Via a multi-frequency direct sampling method, we show that the smallest strip
containing the source support and perpendicular to the observation direction
can be recovered from far-field patterns at a fixed observation angle. With
multiple but sparse observation directions, the shape of the convex hull of the
source support can be recovered. The frequency-domain analysis performed here
can be used to handle inverse time-dependent source problems.
  Our algorithm has low computational overhead and is robust against noise.
Numerical experiments in both two and three dimensions have proved our
theoretical findings.
