The course gives a broad overview of modeling using stochastic processes in electrical engineering applications. Formulating problems using mathematical modeling is an important part of the course.
Basics about continuous time an discrete time stochastic processes, especially weakly stationary processes. Definitions of probability distribution and density functions, statistical mean, mean power, variance, autocorrelation function, power spectral density, Gaussian processes and white noise. Linear filtering of stochastic processes.
Ergodicity: Estimation of statistical properties from measurements.
Sampling and reconstruction: Transformations between continuous and discrete time signals. Influence of sampling, sampling theorem. Pulse amplitude modulation. Errrors in the reconstruction of stochastic signals.
Estimation theory: Linear estimation, orthogonality conditions. Prediction and Wiener filtering. Model based signal processing: Linear signal models, AR-models. Spectral estimation.
Application of the above to simpler electrical engineering applications.