The problem of resolving the fine details of a signal from its coarse scale measurements or, as it is commonly referred to in the literature, the super-resolution problem arises naturally in engineering and physics in a variety of settings. We suggest a unified convex optimization approach for super-resolution. The key is the construction of an interpolating polynomial based on localized kernels. We also show that the localized kernels act as the connecting thread to another wide-spread problem of stream of pulses.