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This paper is devoted to the simultaneous synchronization and input reconstruction in nonlinear discrete-time models. To deal with these, we propose an observer-based approach for two classes of dynamical systems that describe a large wide of nonlinear models. First, we consider the general case of nonlinear dynamics where the inputs to be reconstructed introduce nonlinearly into the model. The second class of systems considered here is composed of linear and nonlinear parts. Sufficient conditions for asymptotic convergence are derived from useful regular transformations. High performances, easiness of implementation, and robustness against disturbances will be shown through simulation results of some well-known nonlinear chaotic models.