Analysis of Multi-Rate Filters and Signal Design for Projected Image Superimposition

A technique for increasing the addressable resolution of digital projectors is to rapidly move the projected images by fractions of pixel lengths, using optomechanical actuators. In order to achieve real resolution improvements it is necessary to pre-process each shifted version (subframes), to compensate for the interference between adjacent pixels. We show that when the ratio between pixel size and subframe shifts is a rational number the system can be partially characterized by a linear multi-rate system. Using this result we analyze the signal design problem, which is a type of multi-rate inverse filtering problem. We discuss the existence of exact solutions, and some solutions that can yield good approximations when the exact inverse does not exist.