The medium-frequency unsteadiness in a pressure-induced turbulent separation bubble is examined by means of linear stability analysis (LSA). Two flow databases, an experimental and a numerical, are investigated, allowing for the extraction of characteristic frequencies as well as their respective amplification from the experiment, and the calculation of local stability analysis based on mean velocity profiles obtained from direct numerical simulation. This circumvents the need for a velocity profile curve fit often required when dealing with experimental data. Three different assumptions are used, inviscid LSA, where all terms related to viscosity are neglected, quasi-laminar LSA, where only the molecular viscosity is considered, and finally, LSA including effects of Reynolds shear stress through an eddy-viscosity model. Along the separation bubble, a quasi-constant neutral frequency associated with Kelvin-Helmholtz instabilities is predicted by the inviscid LSA, which is found to be consistent with the characteristic frequencies extracted from the power spectral density (PSD) of unsteady wall-pressure measurements in the downstream part of the flow. Spectral Proper Orthogonal Decomposition (SPOD) of velocity data confirms that this quasi-constant frequency represents the initial roll-up of the shear layer bounding the recirculation zone. Although the flow is fully turbulent, the introduction of an eddy-viscosity model is found to exhibit a damping effect both on the onset of instability as well as on the bandwidth of amplified frequencies, indicating that the underlying phenomenon to the shedding mode must be inviscid.