Abstract: A stylized compressed sensing radar is proposed in which the time-frequency plane is discretized into an $N$ by $N$ grid. Assuming the number of targets $K$ is small (i.e., $K$ much less than $N^2$), then we can transmit a sufficiently ``incoherent'' 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. This novel compressed sensing approach offers great potential for better resolution over classical radar.