System Theory 3 - Stochastic Signals

Number: 141224
Type of Event: Lecture with Exercises
Module Representative: Prof. Dr.-Ing. Georg Schmitz
Lecturer: Prof. Dr.-Ing. Georg Schmitz, research assistants
Language: German
SWS: 5
CP: 6

APPOINTMENTS IN SUMMER SEMESTER
Start: Tuesday, 04/05/2022
Lecture: Tuesday, 10:15 - 11.45 AM, HID
Exercise: Mondays, 08:15 - 09.45 AM, ID 04/459 and ID 04/471
Computer Exercise: Fridays, 10:15 - 11.45 AM, CIP-Pool 2

GOALS

The students have subject-specific knowledge of the mathematical treatment of stochastic models for discrete and continuous measured signals. The students understand the necessity of stochastic signal models and their relation to practical problems (measurement accuracy, reliability). They have the qualification to analyze signal transmission and processing problems for random signals, to propose suitable solution methods, to explain them and to implement them in practice. The students know and understand in particular relevant methods for parameter estimation in signal processing and are able to transfer and apply them to new problems. Through the exercises and computer exercises the students are enabled to apply the acquired knowledge in a small team in practice, to explain and evaluate solution approaches and to represent them with supporting arguments. The important basic nomenclature of stochastic signals is also translated to English, so that students are able to understand the international literature in the field of statistical signal processing.

CONTENT

In signal processing dealing with noise and formulating models for signals with random fluctuations as speech or images is often a central task. The mathematical model for such signals are random processes. To treat such signals, profound knowledge of probability theory and random variables is a prerequisite. This course teaches the mathematical methods that are needed and based on that treats estimation theory and detection theory as the two main topics.

Introduction
- Definition of stochastic processes
- Probability distributions and densities for stochastic processes
- Moment functions, autocovariance, crosscovariance, autocorrelation, crosscorrelation
- properties of covarianve and correlation functions, stationarity and ergodicity, power spectral density, white noise processes
Detection theory
- binary decisions, Bayes-test, Maximum-a-posteriori (MAP) test, Maximum-Likelihood-test, MiniMax-test
- Receiver-Operating-Characteristics (ROC)
Parameter Estimation
- Estimates and estimators
- Bias, consistency, Cramér-Rao Lower Bound, efficiency
- Least squares estimators and Maximum Likelihood estimators
Random signals and systems
- Transfer by LTI systems
- Linear processes (AR, MA, ARMA)
- Yule-Walker-equations
- Wiener-filter
Statistics for random processes
- Estimation of the covariance function, spectral estimation with the periodogram, parameter estimation for linear processes

REQUIREMENTS

none

RECOMMENDED KNOWLEDGE

Contents of the courses in System Theory 1 and 2

LITERATURE

Kay, Steven M. "Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory", Prentice Hall, 1993
Kay, Steven M. "Fundamentals of Statistical Signal Processing, Volume II: Detection Theory ", Prentice Hall, 1998
Kay, Steven M. "Fundamentals of Statistical Signal Processing, Volume III: Practical Algorithm Development ", Prentice Hall, 2013
Kay, Steven M. "Intuitive Probability and Random Processes using MATLAB", Prentice Hall, 2005
Mertins, Alfred "Signaltheorie", Springer, 2013 http://www.springer.com/de/book/9783834813947
Kroschel, Kristian, Rigoll, Grhard, Schuller, Björn W. "Statistische Informationstechnik", Springer Verlag, 2011 http://www.springer.com/de/book/9783642159534
Hänsler, Eberhard "Statistische Signale. Grundlagen und Anwendungen", Springer, 2001
Böhme, Johann F. "Stochastische Signale", Teubner Verlag, 1998

MISCELLANEOUS

Registration is carried out via the E-Learning Portal Moodle of the Ruhr-Universität Bochum. The required information is provided in the first lecture.