The course gives a broad introduction to modelling by means of stochastic processes in electrical engineering applications. Problem formulation with mathematical models is an important part of the course.
Basic about time continuous and discrete-time stochastic processes, especially weakly stationary. Definitions such as distribution and density functions, expectation, mean power, variance, autocorrelationfunction, spectral density.Gaussian processes and white noise. Linear filtering of stochastic processes.
The notion of ergodicity: Estimation of the properties of processes from measurements.
Sampling and reconstruction: Transformation between continuous-time and discrete-time signals. Effect of sampling. Sampling theorem. Pulse amplitude modulation. Errors at reconstruction of stochastic signals.
Estimation theory: Linear estimation and the ortogonality principle. Prediction and Wiener filter. Model-based signal processing: Linear signal models, AR models. Spectral estimation.
Application of the above on simple electrotechnical applications.
A student who has passed the course should be able to:
- Show basic understanding of properties of stochastic processes.
- Analyse given issues in estimation or optimal filtering.
- Apply mathematical modelling on problems in electrical engineering.
- Demonstrate an understanding of sampling and reconstruction of weakly stationary stochastic processes.
- Develop simple programme code, e.g., by means of the tool Matlab, and use this code to simulate and analyse problems in the area, and report the implementation and the result.
- Use a given or individually formulated mathematical model for solving a given technical problem in the area and analyse the result and its plausibility.
A student who has completed the course with higher grades should in addition to the aims that apply to pass be able to:
- Show good understanding of properties of stochastic processes.
- Analyse given issues in filtering, sampling and reconstruction of weakly stationary stochastic processes.
- Analyse given issues in estimation and optimal filtering.
- Formulate mathematical models that are applicable and relevant at a given problem in the area. When it is missing explicitly given information in the problem, the student should be able to assess and compare different possibilities and make reasonable own assumptions to achieve an adequate modelling.
- Use a given or individually formulated mathematical model for solving a problem in the area e.g. problems that are built-up of several interacting partial problems or such that require more advanced mathematical modelling, and analyse the result and its plausibility.
