A known problem for observer design in engineering applications is the mismatch between the theoretical output and the available output due to sampled measurements and sensor nonlinearities. This paper presents an observer redesign method that addresses this problem. Our main assumption is the existence of an observer based on the theoretical output, that is, the continuous and non-transformed output. The proposed observer then results in an interconnected system consisting of the original observer dynamics coupled with a switched subsystem. The asymptotic convergence of the proposed observer is shown by using the small-gain theorem for switched systems together with Linear Matrix Inequalities (LMI's). Our method is illustrated for uniformly observable systems.