Stationary stochastic Processes

The aim of this course is that the student shall acquire a toolbox containing concepts and models for description and handling of stationary stochastic processes within many different areas, such as, signal processing, automatic control, information theory, economics, biology, chemistry, and medicine. The mathematical and statistical elements are therefore illustrated using a wide variety of examples from different areas of application. The course shall also give the student the ability to identify the presence of stationary processes in other courses in the education, use the knowledge of stationary processes in other courses, and translate the concepts and tools between different courses, building on stationary processes. The course covers models for stochastic dependence, concepts for description of stationary stochastic processes in the time domain such as expectation, covariance, and cross-covariance functions, and concepts of description of stationary stochastic processes in the frequency domain such as effect spectrum and cross spectrum. Some important types of processes are introduced: Gaussian processes, Wiener processes, white noise and Gaussian fields in time and space. The course also covers stochastic processes in linear filters: relationships between in- and out-signals, auto regression and moving average (AR, MA, ARMA), and differentiation and integration of stochastic processes. Finally, the basics in statistical signal processing are introduced, including estimation of expectations, covariance function, spectrum, and applications of linear filters: frequency analysis and optimal filters. The course consists of two modules: Module 1 (6 ECTS) *Theory* and Module 2 (1.5 ECTS) *Computer labs*.