# Signals and Systems

Modul group: Fundamentals of systems engineering

The concepts of signals and systems are powerful tools for any engineer dealing with information bearing, measurable physical quantitites. Areas of applications include, among others, communications engineering, signal processing, control engineering, and systems engineering.

##### On-campus lectures:

to be determined (participants with very long journeys and high travel expenses can take part via online meetings)

Oral examination towards the end of the semester (according to individual agreement) in Ulm (personal attendance necessary)

# Signals and Systems

Modul group: Fundamentals of systems engineering

The concepts of signals and systems are powerful tools for any engineer dealing with information bearing, measurable physical quantitites. Areas of applications include, among others, communications engineering, signal processing, control engineering, and systems engineering.

##### On-campus lectures:

to be determined (participants with very long journeys and high travel expenses can take part via online meetings)

Oral examination towards the end of the semester (according to individual agreement) in Ulm (personal attendance necessary)

### Module Description

The Description of the module you find here.

### Contents of the module

• basic properties of discrete-time and continuous-time systems
• z-transformation
• linear time-invariant systems, convolution integral
• Fourier transformation, discrete Fourier transformation, Fourier series
• sampling theorem
• probability theory, random variables and stochastic processes
• stochastic signals and linear time-invariant systems

### Learning aims of the course

1. The students will be able to classify, interpret, and compare signals and systems with respect to their characteristic properties. They can explain and apply analytical and numerical methods to analyze and synthesize signals and systems in time and frequency domain. Suitable signal transformations can be chosen and calculated with the help of transformation tables.
2. The students are able to recognize stochastic signals and analyze them based on their characteristic properties. They can calculate and interpret the influence of linear time-invariant systems on stochastic signals.

### Learning setting

The online part of the study programme takes place in self studies and in form of group work. For the self study part video lectures with detailed information about the contents and an elaborated script is offered. The script is developed especially for extra-occupational learners in regard to the didactic concept of Ulm University. It contains learning stopps, multiple and single choice tests, quizzes, exercises, etc. Lecture notes and further materials and forums are available in a modern web-based e-learning environment.

Tutorials for solving problems and exercises are offered by your mentor typically bi-weekly and held via video conferences. These seminars will help you handling the exercises and working on the learning matters. An online forum for exchange with the other students will also be available.

### Requirements

Solid knowledge of advanced mathematics at least on the level of a bachelor’s degree in engineering is required. Especially the following topics are very important:

• Linear algebra
• Analysis (series, functions, derivatives, integrals, complex numbers)

### Technical preconditions for e-Learning

Recommended requirements:

• A desktop computer or notebook, with Windows 7 or more recent, Linux or macOS 10.9, dual-core or more, 2 GHz or more
• Current version of Mozilla Firefox, Google Chrome, Safari (or more recent)
• Current version of Adobe Flash Plugin in the browser (needed only for online-consultation hours and online-webinars)
• Broadband access to the internet via xDSL, Cable, LTE or a similar technology with a minimum data rate of 2 Mbit/s downstream and 384 kbit/s upstream. For interactive sessions (e.g. video conferences or the usage of our remote-tool server) a reliable internet connection without packet loss is required.

### Activity confirmation

Regular participation in online seminars will help you solving exercises, which have to be loaded up to the learning management system after request of the mentor. Passing the exercises successfully is recommended for participation in the final examination at Ulm University.

### Certificate

After finishing your exame successfully you will get a certificate and a supplement, which will list the contents of the module and the competencies you have acquired. In the supplement the responsible person for the module confirms you the equivalent of 6 credit points (ECTS).

### Study fees

It is possible to book this course as a certificate course for 1.170 Euros (participation fee) completely in English language. In the following you can find more information (in German language).

Die Höhe der Studiengebühren bzw. der für die Belegung von Einzelmodulen im Kontaktstudium fälligen Entgelte finden Sie hier.

### Lecturer

Dr. Werner Teich
Institute of Communications Engineering

### Mentor

Dipl.-Inf. Steffen Moser
Institute of Embedded Systems/Real-Time Systems

### Counselor

Dipl.-Soz. Ursula Müller
E-Mail: ursula.mueller(at)uni-ulm.de

Gefördert von:

### Lecturer

Dr. Werner Teich
Institute of Communications Engineering

### Mentor

Dipl.-Inf. Steffen Moser
Institute of Embedded Systems/Real-Time Systems

### Counselor

Dipl.-Soz. Ursula Müller
E-Mail: ursula.mueller(at)uni-ulm.de

### Contents of the module

• basic properties of discrete-time and continuous-time systems
• z-transformation
• linear time-invariant systems, convolution integral
• Fourier transformation, discrete Fourier transformation, Fourier series
• sampling theorem
• probability theory, random variables and stochastic processes
• stochastic signals and linear time-invariant systems

### Learning aims of the course

1. The students will be able to classify, interpret, and compare signals and systems with respect to their characteristic properties. They can explain and apply analytical and numerical methods to analyze and synthesize signals and systems in time and frequency domain. Suitable signal transformations can be chosen and calculated with the help of transformation tables.
2. The students are able to recognize stochastic signals and analyze them based on their characteristic properties. They can calculate and interpret the influence of linear time-invariant systems on stochastic signals.

### Requirements

Solid knowledge of advanced mathematics at least on the level of a bachelor’s degree in engineering is required. Especially the following topics are very important:

• Linear algebra
• Analysis (series, functions, derivatives, integrals, complex numbers)

### Activity confirmation

Regular participation in online seminars will help you solving exercises, which have to be loaded up to the learning management system after request of the mentor. Passing the exercises successfully is recommended for participation in the final examination at Ulm University.

### Certificate

After finishing your exame successfully you will get a certificate and a supplement, which will list the contents of the module and the competencies you have acquired. In the supplement the responsible person for the module confirms you the equivalent of 6 credit points (ECTS).

### Study fees

It is possible to book this course as a certificate course for 1.170 Euros (participation fee) completely in English language. In the following you can find more information (in German language).

Die Höhe der Studiengebühren bzw. der für die Belegung von Einzelmodulen im Kontaktstudium fälligen Entgelte finden Sie hier.