Microelectromechanical systems (MEMS) are under development as radio-frequency (RF) switches for a broad range of applications, where active and passive components can be switched into or out of RF circuits. Optical interferometry is well-suited to the characterization of MEMS structures due to its wide dynamic range, its fine resolution, and its non-invasive qualities. However, RF MEMS operate at frequencies ranging from a few megahertz to tens of gigahertz. These high operating frequencies offer challenges in the demodulation of the interferometric system. Our demodulation system consists of photodetecting the optical interferometric signal, converting the analog electronic signal to a digital signal, and digitally processing the signal to compute the MEMS structure's vibration amplitude. In this paper, we present a digital signal processing algorithm for demodulating an interferometer developed for characterizing RF MEMS. Our algorithm is based on a phase-generated carrier modulation system and assumes that the target structure is oscillating at a fixed frequency. A key feature of our algorithm is that it permits determination of a structure’s vibration amplitude, where the structure's vibration frequency is greater than the analog-to-digital converter's (ADC's) sample frequency. Therefore, commercially-available low-cost ADCs and microprocessor systems may be used for real-time demodulation. Both simulation and experimental results will be presented.