Objectives and competences
The objective of this course is for students to be able to demonstrate understanding of theoretical basis of statistical signal processing algorithms, classify different stochastic processes, and apply statistical signal processing algorithms in processing different stochastic signals.
Content (Syllabus outline)
• Probability theory: event, probability and conditional probability, independent events.
• Random variable and random vector: basic concept, distribution function of random variable, density function of random variable, Gaussian random variable, conditional distribution/conditional density function, operations on random variables, concept of random vector, joint distribution and density, conditional distribution/conditional density function of random vector, statistical independence, operations on random vectors.
• Random process: basic concept, classification of random processes, first-/second-order stationary process, wide-sense stationarity, ergodicity, correlation and covariance, Gauss and Poisson random processes.
• Spectrum estimation: power spectrum density, bandwidth, noise definition, white and coloured noises.
• Linear systems with random inputs: linear system, transfer function, random signal response, spectral characteristics, noise bandwidth, modelling of noise sources.
• Filtering of random processes: elements of deterministic signal filtering, filtering of random processes, comparison of deterministic and random case.
• Markov processes: definition and examples of Markov processes, calculation of transition and state probabilities in Markov chains, characterisation of Markov chains, continuous time Markov processes, hidden Markov models.
Learning and teaching methods
• lectures,
• tutorial,
• lab work,
• seminar work.
Intended learning outcomes - knowledge and understanding
On completion of this course the student will be able to
• explain the fundamentals of random signals,
• recognise characteristics of different random processes and conduct spectral analysis of random process,
• demonstrate knowledge and understanding of filtering random process with linear system,
• design digital filter and conduct filtering of random processes,
• explain the basics of Markov processes.
Intended learning outcomes - transferable/key skills and other attributes
• Communication skills: oral lab work defence, manner of expression at written exam.
• Use of information technology: use of statistical signal processing software tools.
• Problem solving: designing and implementing digital systems for random signal processing.
Readings
• G. Grimmett, D. Stirzaker, Probability and Random Processes: Fourth Edition, Oxford University Press, Oxford, 2020.
• R. M. Gray, L. D. Davisson: An Introduction to Statistical Signal Processing, Cambridge University Press, Cambridge, 2004.
• U. Spagnolini: Statistical Signal Processing in Engineering, John Wiley & Sons, Chichester, 2018..
• S. Miller, D. Childers: Probability and Random Processes: With Applications to Signal Processing and Communications, Elsevier Academic Press, Burlington, 2012.
Prerequisits
Recommended is basic knowledge of mathematics, programming, and signal processing.
