# System Theory II - Signal Transformations

Undergraduate Course, *Ruhr University Bochum*, 2019

- Lecturer: Prof. Dr.-Ing. Sezgin
- Language: German
- Credits: 6 CP
- Programs: B.Sc. Eletrical and Computer Engineering, B.Sc. IT-Security
- Examination: 100 % Written Exam (120 Minutes)

# Course Description

Before an engineer can develop a system that is intended to serve, for example, the exchange of information over greater distances, it must be clarified with what kind of signals such an exchange is even possible. Mathematical models for the signals and for the systems processing the signals are taught in the lecture. Specifically covered are:

- Introductino
- Basic concepts of signals and systems:
- Linearity and time invariance
- LTI systems, causality and stability

- Continuous and discrete signals
- Real/complex, symmetric, periodic, bounded and constrained signals
- Discontinuous and oscillatory elementary signals and their properties
- Classification of signals

- Discrete LTI systems
- Determination of the transmissino behaviour by means of z-transform
- Transform behavior in the time domain: Discrete convolution
- Transfer function, impulse response, basic structures
- Properties: stability, eigenfunctions, IIR and FIR systems
- Initial value problems

- The z-transform, discrete-time and discrete Fourier transforms
- Definition and existence
- Properties and calculation rules
- The inverse transform

- Continous LTI systems
- Generalized functions: Distributions, Dirac momentum
- Determination of the transfer behavior by Laplace transform
- Transfer behavior in the time domain: continuous convolution
- Transfer function, impulse response, basic structures
- Properties: stability, eigenfunctions
- State space representation

- The Laplace and Fourier transform, Fourier series
- Definition and existence
- Properties and calculation rules
- The inverse transformation
- Relationship of the transformations

- Spectral description of LTI systems
- Transfer function and frequency response
- Filters and all-passes

- Discretized continuous signals
- Signal sampling and signal reconstruction