A numerical techniques cable of simulating blade-scale compression system flow instabilities over times scales spanning tens of rotor revolutions is presented. Simulations of stall inception, growth to fully-developed rotating stall, and evidence for hysteresis, secondary instabilities, and other nonlinear phenomena are presented. signal processing techniques for flow asymmetry characterization are discussed in the context of obtaining low-order representations of the flow disturbances with the ultimate goal of active stall suppression.