Stochastic signals

Published: 3 January 2022

Applications of stochastic signals are found in many areas such as. electrical engineering, signal processing, image processing, communication technology, control technology, measurement systems, medicine and economics. This course will give you a good understanding of how to implement, evaluate and analyze stochastic signals.

The teaching consists of lectures, laboratory work and a seminar assignment.

Course content:

Use mathematical and statistical methods to process randomly varying signals, disturbances and noise. Estimate random parameters, estimate signals and parameters from noise, separate random composite signals, calculate estimation errors, calculate the statistical effect of linear time-invariant systems on random signals, develop detectors for noise signals, calculate and estimate the spectral content of random signals. Students should be able to implement, evaluate, and analyze the above concepts in Matlab, as well as present and demonstrate the results in written group reports.

At the end of the course you will be able to:

• Stochastic variables, functions of stochastic variables, distribution functions, density functions
• Expected values and moments, stochastic vectors, central limit value theorem
• Parameter estimation, Maximum Likelihood estimation, linear estimation
• Minimum mean squared error (MMSE) estimation, linear MMSE estimation, statistical orthogonality,
• Bayesian decision theory, hypothesis testing and detection, likelihood ratio test
• Stochastic sequences, stochastic processes, stationary
• Autocorrelation, cross-correlation
• Linear time-invariant systems and weakly stationary sequences and processes, filtering random signals
• Spectral density, white noise
• Ergodicity, Wiener filter, spectral estimation