Electrochemical pressure impedance spectroscopy (EPIS) is an emerging tool for the diagnosis of polymer electrolyte membrane fuel cells (PEMFC). It is based on analyzing the frequency response of the cell voltage with respect to an excitation of the gas-phase pressure. Several experimental studies in the past decade have shown the complexity of EPIS signals, and so far there is no agreement on the interpretation of EPIS features. The present study contributes to shed light into the physicochemical origin of EPIS features, by using a combination of pseudo-two-dimensional modeling and analytical interpretation. Using static simulations, the contributions of cathode equilibrium potential, cathode overpotential, and membrane resistance on the quasi-static EPIS response are quantified. Using model reduction, the EPIS responses of individual dynamic processes are predicted and compared to the response of the full model. We show that the EPIS signal of the PEMFC studied here is dominated by the humidifier. The signal is further analyzed by using transfer functions between various internal cell states and the outlet pressure excitation. We show that the EPIS response of the humidifier is caused by an oscillating oxygen molar fraction due to an oscillating mass flow rate.