Stochastic Signals & Systems

COURSE CONTENT

1. Introduction to stochastic signals and systems
2. Fundamental notions of stochastic signals in the time domain
3. Non-parametric estimation of stochastic signals in the time domain
4. Fundamental notions of stochastic signals in the frequency domain
5. Non-parametric estimation of stochastic signals in the frequency domain
6. Theory of stationary and linear stochastic signals and systems
7. Theory and properties of parametric ARMA models
8. ARMA models originating from the sampling of continuous time models
9. Introduction to non-stationary and seasonal stochastic signals
10. Theory of optimal prediction
11. Identification, estimation, and validation of stochastic parametric models
12. Introductory remarks on vector stochastic signals

LEARNING OUTCOMES

The course constitutes a comprehensive introduction into discrete-time stochastic signals and systems, with reference to random vibration. Upon successful completion of the course the student will be in position to:

• Understand the form and basic notions of stationary stochastic signals and systems in the time and frequency domains
• Appreciate their applications in mechanical & aeronautical engineering, as well as in other scientific disciplines
• Mathematically describe stationary, and certain non-stationary, stochastic signals
• Comprehend the basic notions of estimation, as well as the estimation of mathematical models of stochastic signals in the time and frequency domains
• Thoroughly analyze mathematical models for stationary stochastic signals and systems in the time and frequency domains
• Relate the mathematical models to underlying physical systems and their properties
• Perform stochastic signal prediction
• Validate an estimated model
• Model and analyze stationary stochastic signals and systems from the engineering practice using realizations and proper software (such as MATLAB/SIMULINK, R)