A correspondence between input estimation (deconvolution) and feedforward is discussed from a polynomial point of view. Optimal estimation and feedforward control filters are derived from a spectral factorization and a polynomial equation. Simple loop transformations are used for transforming one problem into the other. The close relationship cannot be explained by the well-known duality between optimal state estimation and feedback control. Instead, it rests on the fact that both the problems discussed are open loop. They can be seen as two interpretations of one underlying design problem. Several other open-loop problems can be described in this framework.