# 389.170 Signal Processing 2 This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_21",{id:"j_id_21",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});This course is in at least 1 assigned curriculum part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_23",{id:"j_id_23",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});}); 2023W 2022W 2021W 2020W 2019W 2018W 2017W 2016W 2015W 2014W 2013W

2023W, VU, 3.0h, 4.5EC

## Properties

• Semester hours: 3.0
• Credits: 4.5
• Type: VU Lecture and Exercise
• Format: Presence

## Learning outcomes

After successful completion of the course, students are able to apply fundamental concepts in the area of probability theory, random variables, and stochastic processes to solve practical engineering problems.

## Subject of course

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

## Teaching methods

Theory lectures on the blackboard, discussion of real-world applications, numerical demonstrations, problem-solving exercises.

Recordings of the online lectures from the 20/21 semester are available on TUbe: https://portal.tuwien.tv/View.aspx?id=8756~4A~COLIdTaM

## Mode of examination

Written and oral

Course starts on Oct. 5, 2023 at 11am in lecture hall EI4 – don't miss!

## Course dates

DayTimeDateLocationDescription
Thu11:00 - 12:0005.10.2023 - 25.01.2024EI 4 Reithoffer HS Übung
Fri10:00 - 12:0006.10.2023 - 19.01.2024EI 4 Reithoffer HS Vorlesung
Signal Processing 2 - Single appointments
DayDateTimeLocationDescription
Thu05.10.202311:00 - 12:00EI 4 Reithoffer HS Übung
Fri06.10.202310:00 - 12:00EI 4 Reithoffer HS Vorlesung
Thu12.10.202311:00 - 12:00EI 4 Reithoffer HS Übung
Fri13.10.202310:00 - 12:00EI 4 Reithoffer HS Vorlesung
Thu19.10.202311:00 - 12:00EI 4 Reithoffer HS Übung
Fri20.10.202310:00 - 12:00EI 4 Reithoffer HS Vorlesung
Fri27.10.202310:00 - 12:00EI 4 Reithoffer HS Vorlesung
Fri03.11.202310:00 - 12:00EI 4 Reithoffer HS Vorlesung
Thu09.11.202311:00 - 12:00EI 4 Reithoffer HS Übung
Fri10.11.202310:00 - 12:00EI 4 Reithoffer HS Vorlesung
Thu16.11.202311:00 - 12:00EI 4 Reithoffer HS Übung
Fri17.11.202310:00 - 12:00EI 4 Reithoffer HS Vorlesung
Thu23.11.202311:00 - 12:00EI 4 Reithoffer HS Übung
Fri24.11.202310:00 - 12:00EI 4 Reithoffer HS Vorlesung
Thu30.11.202311:00 - 12:00EI 4 Reithoffer HS Übung
Fri01.12.202310:00 - 12:00EI 4 Reithoffer HS Vorlesung
Thu07.12.202311:00 - 12:00EI 4 Reithoffer HS Übung
Thu14.12.202311:00 - 12:00EI 4 Reithoffer HS Übung
Fri15.12.202310:00 - 12:00EI 4 Reithoffer HS Vorlesung
Thu21.12.202311:00 - 12:00EI 4 Reithoffer HS Übung

## Examination modalities

- active participation in exercises (solution of problems)

- three-hour written exam (4 problems)

- oral exam

## Exams

DayTimeDateRoomMode of examinationApplication timeApplication modeExam
Wed15:00 - 18:0022.01.2025 EI 5written30.12.2024 00:00 - 13.01.2025 00:00TISSSchriftliche Prüfung
Tue14:00 - 18:0018.03.2025 EI 7written24.02.2025 00:00 - 13.03.2025 00:00TISSSchriftliche Prüfung
Tue14:00 - 18:0013.05.2025 EI 9written21.04.2025 00:00 - 06.05.2025 00:00TISSSchriftliche Prüfung
Thu14:00 - 18:0026.06.2025 EI 9written05.06.2025 00:00 - 19.06.2025 00:00TISSSchriftliche Prüfung

## Course registration

Begin End Deregistration end
02.10.2023 00:00 20.10.2023 11:00

## Curricula

Study CodeObligationSemesterPrecon.Info
066 504 Master programme Embedded Systems Not specified
066 506 Energy Systems and Automation Technology Not specified
066 507 Telecommunications Not specified1. Semester
066 515 Automation and Robotic Systems Not specified
066 938 Computer Engineering Mandatory

## Literature

Detailed lecture notes for this course will be made available.

## Previous knowledge

basic knowledge of mathematics (particularly probability theory and linear algebra) and of signals and system theory (convolution, Fourier analysis, z transform)

English