We consider the problem of estimating signal attacks injected into the actuators or sensors of control systems, assuming the attack is detectable, i.e., it can be seen at the output. We show that there exists a trade-off between attack rejection and control, and that the estimator design depends on the controller used. We use dual rate sampling to enhance detectability of the attacks and we provide different methods to design the estimator. The first method is by solving a model matching problem subject to causality constraints. The second method exploits dual rate sampling to accurately reconstruct the unknown input. The third method is using a dual rate unknown input observer. We provide conditions on the existence of these estimators, and show that dual rate unknown input observers always exist if the multirate system does not have a zero at 1.