A stylized compressed sensing radar is proposed in which the time-frequency plane is discretized into an N by N grid. Assuming that the number of targets K is small (i.e. KLtN2), then we can transmit a sufficiently ldquoincoherentrdquo pulse and employ the techniques of compressed sensing to reconstruct the target scene. A theoretical upper bound on the sparsity K is presented. Numerical simulations verify that even better performance can be achieved in practice. By comparing traditional uncertainty principles with those of compressed sensing, this novel approach reveals great potential for better resolution over classical radar.