The inhomogeneous plasma parametric decay instability (PDI) is studied in the present paper both experimentally and theoretically for different types of pump wave frequency modulation. It is shown that the theory conclusion on weak sensitivity of inhomogeneous plasma PDI to the pump frequency modulation holds only for modulation faster than the decay wave transient time. In the case of slower modulation, both harmonic and stochastic, the PDI resonant enhancement may take place instead. The expression for amplification in the resonance is derived and several mechanisms of the singularity saturation are studied.