The computation of the radio emissions produced by an extended air shower at the location of the detector is a fundamental problem in the indirect detection of cosmic rays. Conventionally, simulation programs compute and sum the contributions from all particles in the shower, and then propagate this field through the environment and the signal processing chain of the experiment. This contribution presents a complementary formulation, which encodes all properties of the detector and its environment in a specially constructed electric field distribution, the ``weighting field’’. Once the weighting field is known for a particular situation, the electrical signal produced in the detector can be computed very efficiently by convolving the weighting field with the trajectories of the charged particles in the shower.