Course starts on Oct. 4, 2018 - don't miss - fun guaranteed!
Knowledge of the theory, mathematical description, and basic processing of random variables, random vectors, und random signals (stochastic processes) as well as its practical application. The theory presented in the lectures is illustrated by problems in exercise classes.
1. One random variable: Cumulative distribution function (cdf) and probability density function (pdf), discrete random variables, transformation of random variables, conditional cdf and pdf, moments, characteristic function, inequalities, conditional expectation, special distributions
2. Two random variables: Joint cdf and pdf, discrete random variables, transformation of random variables, conditional cdf and pdf, moments, correlation, covariance, statistical independence, orthogonality and uncorrelatedness, characteristic function, conditional expectation, special distributions, complex random variables, circular symmetry
3. Random vectors: cdf and pdf, discrete random vectors, transformation of random vectors, conditional cdf and pdf, mean, correlation matrix, covariance matrix, statistical independence, orthogonality and uncorrelatedness, characteristic function, conditional expectation, special distributions, complex random vectors, Karhunen-Loeve decomposition, whitening transformation, innovations representation, MMSE estimation, LMMSE estimation (Wiener filter), ML estimation
4. Random signals (stochastic processes): pdf, stationarity, second-order description (mean, autocorrelation function), cyclostationarity, power spectral density, cross-correlation function und cross-power spectral density, effects of linear systems, time averages und ergodicity, discrete-time random signals, special random signals, complex random signals and circular symmetry, whitening filter, innovations filter, Wold decomposition, AR, MA and ARMA processes, LMMSE estimation (Wiener filter), linear prediction
