The parametric approach to the design of observer based compensators has hitherto only been formulated in the time domain. It yields an explicit parametric expression for the state feedback matrix (observer gain) given the closed loop eigenvalues and the corresponding sets of invariant parameter vectors. Using the polynomial approach to the design of observer based compensators this contribution presents an equivalent parameterization in the frequency domain. By introducing the closed loop poles and the set of so-called pole directions as new design parameters, one obtains expressions in parametric form for the polynomial matrix (D) over tilde (s) ((D) over tilde (s)), parameterizing the state feedback (state observer) in the frequency domain. It is shown how the pole directions are related to the invariant parameter vectors used in the time domain approach. Another new result is the parametric design of reduced order observers both in the frequency domain, and derived from those results, in the time domain. The proposed design procedure is also used to provide a parametric solution for the optimal LQG control problem in the presence of partially perfect measurements. Simple examples demonstrate the design procedure.