Aims and motivation for the course

We aim to:

• Develop a theory which can characterize the behavior of real-world Random Signals and Processes ;
• Use standard Probability Theory for this.

• Analysis of signals;
• Inference of underlying system parameters from noisy observed data;
• Design of optimal systems (digital and analogue signal recovery, signal classification, estimation ...);
• Predicting system performance (error-rates, signal-to-noise ratios, ...).

Probability theory is used to give a mathematical description of the behavior of real-world systems which involve elements of randomness . Such a system might be as simple as a coin-flipping experiment, in which we are interested in whether'Heads' or 'Tails' is the outcome, or it might be more complex, as in the study of random errors in a coded digital data stream(e.g. a CD recording or a digital mobile phone).

The basics of probability theory should be familiar from the IB Probability and Statistics course. Here we summarize the mainresults from that course and develop them into a framework that can encompass random signals and processes.