This text for advanced undergraduates and graduate students provides a concise introduction to increasingly important topics in electrical engineering: digital filtering, filter design, and applications in the form of the Kalman and Wiener filters. The first half focuses on digital filtering, covering FIR and IIR filter design and other concepts. The second half addresses filtering noisy data to extract a signal, with chapters on nonrecursive (FIR Wiener) estimation, recursive (Kalman) estimation, and optimum estimation of vector signals. The treatment is presented in tutorial form, but readers are assumed to be familiar with basic circuit theory, statistical averages, and elementary matrices. Central topics are developed gradually, including both worked examples and problems with solutions, and this second edition features new material and problems.