We consider the problem of observer design for a class of systems described by an observable linear system perturbed by nonlinear, time-varying terms. In particular, we investigate conditions under which the effect of the nonlinear terms may be dominated by using sufficiently high gain. Our main tool is the transformation of the original system to a canonical form suitable for high-gain design, which is similar to canonical forms used elsewhere in the high-gain literature. We demonstrate that linear, nonsingular transformations to this canonical form can easily be constructed using available tools, but that many systems do not allow for such a transformation. Our main contribution is a constructive algorithm that aims to rectify this problem by dynamically shaping the output through the addition of stable output filters.