Cognitive: Acquaintance with randomness and its impact in signal transmission; image, speech, and audio processing; language processing. Thorough grasp of the concepts of random variable, random vector, stochastic signal, moments of random variables with emphasis on the autocorrelation. Augmenting and revising linear system theory so that it allows for the analysis of linear systems excited by stochastic signals.
Skills: Promoting analytical and programming skills in signal processing. Building the foundations for undertaking advanced studies in image, speech, audio, and biomedical signal processing as well as further reading in pattern recognition and statistical learning theory. Programming applications to speech, music, and telecommunications in MATLAB.
Course Content (Syllabus)
Probability theory. Repeated trials. Random variables. Functions of random variables. Joint statistics. Moments and conditional statistics. Stochastic signals. Basic categories of stochastic signals (Gaussian, Markov, Stationary, Ergodic) . Statistical auto-correlation and cross-correlation function. Input-output relationship of linear systems with stochastic excitation. Theory of optimal linear systems. Mean square estimation.
Students are graded taking into account their achievements in the compulsory home-work assigned to them, their attendance and active participation in the lectures and tutorials, and the assessment of the mid-term and final progress exams.
Compulsory homework includes solving two problems per chapter of Papoulis’ textbook taught and working out two computer-based projects in MATLAB assigned to each student during the semester.
During the mid-term and final progress exams, students are requested to provide short answers in 10-15 questions/problems covering the topics taught in the course.
Homework assignment and deadlines are announced in the course web page at http://pileas.csd.auth.gr. Students pass the course, if their total grade is greater than on equal to five (5). Details on the grading procedure are announced in the course web page, which supersede any prior arrangement.
Course Bibliography (Eudoxus)
Papoulis A., Pillai S. (translated in Greek) «Πιθανότητες, Τυχαίες Μεταβλητές και Στοχαστικές Διαδικασίες», 4η Έκδοση, Εκδόσεις Τζιόλα, Θεσσαλονίκη, 2005.
Πανάς Σ. «Ανάλυση Στοχαστικού Σήματος», University Studio Press, Θεσσαλονίκη, 1985.
Additional bibliography for study
S. M. Kay, Intuitive Probability and Random Processes Using MATLAB}. New York, N.Y.: Springer 2006. (e-book accessible through www.lib.auth.gr)
T. Dutoit and F. Marques, Applied Signal Processing. A MATLAB-Based Proof of Concept. New York, N.Y.: Springer, 2009 (e-book accessible through www.lib.auth.gr)
R. E. Ziemer, Elements of Engineering Probability and Statistics. Upper Saddle River, N.J.: Prentice-Hall, 1997.
D. P. Bertsekas and J. N. Tsitsiklis, Introduction to Probability. Belmont, MA: Athena Scientific, 2002.
C. S. Burrus, J. H. McClellan, A. V. Oppenheim, T. W. Parks, R. W. Schafer, and H. W. Schuessler, Computer-Based Exercises for Signal Processing. Englewood Cliffs, N.J.: Prentice-Hall, 1994.