# course: System Theory 2: Signal Transformations

- number:
- 141218
- teaching methods:
- lecture with tutorials
- responsible person:
- Prof. Dr.-Ing. Aydin Sezgin
- Lecturers:
- Prof. Dr.-Ing. Aydin Sezgin (ETIT), M. Sc. Simon Tewes (ETIT)
- language:
- german
- HWS:
- 5
- CP:
- 6
- offered in:
- winter term

## dates in winter term

- start: Monday the 07.10.2019
- lecture Mondays: from 10:15 to 11.45 o'clock in HGB 10
- lecture Tuesdays: from 12:15 to 13.45 o'clock in HID
- tutorial Fridays: from 10:15 to 11.45 o'clock in HID
- extra tutorial (alternativ) Wednesdays: from 12:15 to 13.45 o'clock in ID 03/419
- extra tutorial (alternativ) Wednesdays: from 14:15 to 15.45 o'clock in ID 03/445
- extra tutorial (alternativ) Wednesdays: from 14:15 to 15.45 o'clock in ID 03/471
- extra tutorial (alternativ) Thursdays: from 10:15 to 11.45 o'clock in ID 04/445

## Exam

Form of exam: | written |

Registration for exam: | FlexNow |

Date: | 14.08.2019 |

Begin: | 08:30 |

Duration: | 120min |

Room : | HID |

## goals

The system theory is a general mathematical description of physical waveforms (signals), signal processing techniques and transferring/transformation of signals between systems, in addition to the description of systems themselves, which represents the main learning content in this course. The students, who are familiar with basic methods to describe and analyses the analog and digital systems, as well as the development of basic circuits for analog and digital signal processing.They will be able to understand all the tasks and techniques related to the analysis and interpretation of linear time-invariant analog and digital (discrete time) systems.

## content

If an engineer want to design a system, let us say a system for exchanging information over large distances, he should be able first to determine which type of signals can be used in such a system to enable such kind of communication systems. In this course the mathematical models for signals as well as systems and signal processing systems will be explained. More precisely the following subjects will be covered: Introduction:

Basics of signal and systems: Linear and time invariant systems: LTI-systems, causality and stability.

Continuous and discrete signals: real/complex, symmetry, periodic, bounded and finite signals discontinuous and carrier form elementary signals and their properties. classification of signals. Discrete time LTI-systems determining the response characteristics of a system by Z- transform. response characteristics of a system in time domain: discrete convolution Transfer function, impulse response and basic structures Properties: stability, eigenfunctions , IIR and FIR systems Initial value problems

Z-transform, time discrete and discrete Fourier-transform Definition and existence properties and computation rules Inverse Z-transform. Continuous LTI-Systems Generalized functions: distributions, Dirac-impulse determining the response characteristics of a system by Laplace-transform response characteristics of a system in time domain: continuous convolution Transfer function, impulse response and basic structures Properties: stability and eigenfunctions state-space representation The Laplace and Fourier-transform, Fourier series Definition and existence properties and computation rules Inverse transformation. relations between different transformations Spectral description of LTI systems Transfer function and frequency response Filter and all-pass filters. Discretization of continuous signals signals sampling and signal reconstruction

## requirements

keine

## recommended knowledge

The content of mathematics 1 and 2 lectures Materials

## materials

### miscellaneous:

## literature

- M. Bossert, , T. Frey, "Signal- und Systemtheorie, 2. Auflage", Vieweg Verlag, 2008

## miscellaneous

The lecture has at the first half of the semester 6 (SWS) (4 hours for the lecture) in the second half of the semester it is 4 SWS(2 hours of them for the lecture). In the second half of the semester the appointment at Monday is dropped.