Note: The lecture and practice documents are on ILIAS
Content of the lecture
1 Introduction
2. Probability theory
- signals
- Random experiment and event
- probability
- Conditional probability
3. A random variable
- random variable
- Distribution function and density
- Conditional distribution function and density
- Function of a random variable
- Expected value and moments
- Moments generating function
- Estimation of density and moments
4. Several random variables
- Multivariate distribution function and density
- Conditional distribution function and density
- Functions of random variables
- Expected value and moments
- Moments generating function
- Convergence of a sequence of random variables
- Estimation of moments
5. Stochastic processes
- definition
- Distribution function and density
- moments
- stationarity
- spectrum
- Estimation of moments and spectra
- Markov process
6. System theory with stochastic signals
- system
- Memoryless time invariant system
- Linear time invariant stable system