To increase the reliability of turboprop and turboshaft engines in extreme operating conditions, filtering protections such as Inlet Particle Separators (IPS) can be installed at the intake. The flow inside an IPS is highly 3D and unsteady, with fluctuations especially pronounced when transonic conditions are reached. In this paper, we aim at providing the transonic analysis of an industrial IPS designed for aerodynamic lab testing. As a first step, we define the threshold beyond which sonic conditions are reached in the boundary cross sections of the IPS by means of a 1D semi-empirical model. Second, we select a critical configuration, and we perform CFD simulations to analyze the locations and evolution of the transonic flow inside the IPS. Different models are presented, i.e. steady and unsteady Reynolds-Averaged Navier-Stokes, Detached Eddy Simulation and Large Eddy Simulation, characterized by three levels of resolution. The results show the evolution of some transonic shocks: the steady-state model is only providing information on averaged quantities, while the time-resolved simulations offer a more precise overview in the time domain. The analysis in the frequency domain reveals the frequencies of the transonic fluctuations. Finally, we discuss three alternative designs to effectively improve the operating range and mitigate the risks related to the transonic instabilities, comparing the differences in separation efficiency with respect to the baseline case. The results prove that the optimal design choice is given by the trade-off between operating range, pressure losses and separation efficiency.