# Signal Processing 2

##### Signal Processing 2

Course No. 389.170
2020W, VU, 3.0h, 4.5EC

###### Announcements
• Welcome to Signal Processing 2 (389.170), winter term 2021/22.
• The course starts on October 1, 2021, at 10:30 in lecture hall EI4.
• Check the TISS news for further announcements.
###### General Information

Lecturer: Gerald MATZ, Ao.Univ.Prof. Dipl.-Ing. Dr.techn.

Assistant: Thomas DITTRICH, Univ.Ass. Dipl.-Ing.

Course type: VU – lectures and exercises

Credits: 4.5 ECTS

Course language: English

Time and place: Thursday 11:00-12:00 (primarily online exercises, otherwise lectures in lecture hall EI4) and Friday 10:30-12:00 (lectures in lecture hall EI4)

Lecture notes: Detailed lecture notes will be made available

Administrative details: Leaflet (PDF), slides (PDF), schedule (TXT)

Corresponding TISS page: TISS – 389.170

###### Course Contents

1. One random variable:

Cumulative distribution function (cdf) and probability density function (pdf), discrete random variables, transformation of random variables, conditional cdf and pdf, moments, characteristic function, inequalities, conditional expectation, special distributions

2. Two random variables:

Joint cdf and pdf, discrete random variables, transformation of random variables, conditional cdf and pdf, moments, correlation, covariance, statistical independence, orthogonality and uncorrelatedness, characteristic function, conditional expectation, special distributions, complex random variables, circular symmetry

3. Random vectors:

cdf and pdf, discrete random vectors, transformation of random vectors, conditional cdf and pdf, mean, correlation matrix, covariance matrix, statistical independence, orthogonality and uncorrelatedness, characteristic function, conditional expectation, special distributions, complex random vectors, Karhunen-Loeve decomposition, whitening transformation, innovations representation, MMSE estimation, LMMSE estimation (Wiener filter), ML estimation

4. Random signals (stochastic processes):

pdf, stationarity, second-order description (mean, autocorrelation function), cyclostationarity, power spectral density, cross-correlation function und cross-power spectral density, effects of linear systems, time averages und ergodicity, discrete-time random signals, special random signals, complex random signals and circular symmetry, whitening filter, innovations filter, Wold decomposition, AR, MA and ARMA processes, LMMSE estimation (Wiener filter), linear prediction

The theory presented in the lectures is illustrated by problems in exercise classes.

###### Exercise Classes

The problem sets and more information will be available online in TWUEL.

###### Written Exam

Students who are admitted may register for the written exam via TISS. There are typically four exam dates per year (see examination dates). Please de-register in TISS or via email in case you cannot attend an exam you registered for.

The written exam consists of four problems and lasts three hours. As of now, we are planning to make an exam at the end of the semester on site at the university. For this exam a copy of the lecture notes will be provided during the exam. Additionally, a calculator may be used. The use of other documents or electronic devices is not permitted.

As it is possible that the situation changes throughout the semester, we might adapt the modalities of the exam.

The result of the written exam will be sent to your generic student address (e<matriculation_number>@student.tuwien.ac.at) in a signed email and uploaded to TUWEL.

You are encouraged to prepare for the written exam using the following sample exams: 14.10.201415.03.2012, 17.03.2011, 15.03.2010, 19.01.2009, 23.01.2008

###### Office Hours

Specific questions regarding exam problems and exercise problems can be discussed during office hours. Due to the special situation with COVID-19 office hours are online and by appointment.