  High-quality microwave amplifiers and notch-filters can be made from
microwave optomechanical systems in which a mechanical resonator is coupled to
a microwave cavity by radiation pressure. These amplifiers and filters rely on
optomechanically induced transparency (OMIT) and absorption (OMIA),
respectively. Such devices can amplify microwave signals with large,
controllable gain, high dynamic range and very low noise. Furthermore,
extremely narrowband filters can be constructed with this technique. We briefly
review previous measurements of microwave OMIT and OMIA before reporting our
own measurements of these phenomena, which cover a larger parameter space than
has been explored in previous works. We find excellent agreement between our
measurements and the predictions of input/output theory, thereby guiding
further development of microwave devices based on nanomechanics.
