A fundamental challenge in digital control arises when the controlled plant is subjected to a fast disturbance dynamics but is only equipped with a relatively slow sensor. Such intrinsic difficulties are, however, commonly encountered in many novel applications such as laser- and electron-beam-based additive manufacturing, human-machine interaction, etc. This paper provides a discrete- time regulation scheme for exact sampled-data rejection of disturbances beyond Nyquist frequency. By introducing a model-based multirate predictor and a forward-model disturbance observer, we show that the inter-sample disturbances can be fully attenuated despite the limitations in sampling and sensing. The proposed control scheme offers several advantages in stability assurance and lucid design intuitions. Verification of the algorithm is conducted on a motion control platform that shares the general characteristics in several advanced manufacturing systems.