This monograph deals with approximation and noise cancellation of dynamical systems which include linear and nonlinear input/output relations. It will be of special interest to researchers, engineers and graduate students who have specialized in filtering theory and system theory. From noisy or noiseless data, reduction will be made. A new method which reduces noise or models information will be proposed. Using this method will allow model description to be treated as noise reduction or model reduction. As proof of the efficacy, this monograph provides new results and their extensions which can also be applied to nonlinear dynamical systems. To present the effectiveness of our method, many actual examples of noise and model information reduction are also provided.