  Microwave circuit electrodynamics of disordered superconductors is a very
active research topic spawning a wide range of experiments and applications.
For compact superconducting circuit elements, the transition to an insulating
state poses a limit to the maximum attainable kinetic inductance. It is
therefore vital to study the fundamental noise properties of thin films close
to this transition, particularly in situations where a good coherence and
temporal stability is required. In this paper, we present measurements on
superconducting granular aluminum microwave resonators with high normal state
resistances, where the influence of the superconductor to insulator phase
transition is visible. We trace fluctuations of the fundamental resonance
frequency and observe, in addition to a 1/f noise pattern, a distinct excess
noise, reminiscent of a random telegraph signal. The excess noise shows a
strong dependency on the resistivity of the films as well as the sample
temperature, but not on the applied microwave power.
