Signal processing techniques using special purpose digital hardware and general purpose digital computers are playing an increasingly important role. The course deals with some introductory and some advanced topics in the area. In particular, it presents the characterization of random discrete time signals. It provides an introduction to traditional and modern statistical discrete time signal processing frameworks, including processing with second-, higher-, and fractional lower-order statistics. It discusses sampling and multirate signal conversion; linear prediction and optimum linear filters; least squares methods for system modeling and design; theory and applications of adaptive filters. It also deals with applications in signal and image processing and analysis.