Signals and Systems¶

This repository contains a collection of Jupyter notebooks providing notes and examples to the bachelors course Signals and Systems read by Sascha Spors, Institute of Communications Engineering, Universität Rostock. The notebooks contain computational examples written in IPython 3, which are best explored in an interactive manner.

Table of Contents¶

The contents are still under development. Parts of the notebooks may be revised throughout summer 2019. You are invited to contribute by reporting errors and suggestions as issues on GitHub or directly to Sascha.Spors@uni-rostock.de.

Part 1: Continuous Signals and Systems¶

Signals and Systems¶

Signals¶

• Standard Signals
• Operations

Characterization of Systems in the Time Domain¶

• Impulse Response
• Convolution
• Step Response
• Eigenfunctions and the Transfer Function
• Example: Analysis of a Passive Electrical Network
• Example: Analysis of a Damped Spring Pendulum

The Laplace-Transform¶

• Definition
• Properties
• Theorems
• Summary of Properties, Theorems and Transforms
• Inverse Transform
• Analysis of Passive Electrical Networks

The Fourier-Transform¶

• Definition
• Properties
• Theorems
• Summary of Properties, Theorems and Transforms

Characterization of Systems in the Spectral Domain¶

• The Transfer Function
• The Bode Plot
• Phase and Group Delay
• Combination of Systems

Properties of LTI-Systems¶

• Causality and Stability
• Classes of Systems
• Idealized Systems

Periodic Signals¶

• Spectrum
• Relation between Spectrum and Fourier Series
• Convolution of a Periodic with an Aperiodic Signal

Sampling of Signals¶

• Ideal Sampling and Reconstruction

Part 2: Time-Discrete Signals and Systems¶

Discrete Signals¶

• Standard Signals
• Operations

Characterization of Discrete Systems in the Time Domain¶

• Difference Equation
• Impulse Response
• Linear Convolution
• Example: Convolution of an Audio Signal with a Room Impulse Response
• Eigenfunctions and the Transfer Function

The $z$-Transform¶

• Definition
• Properties
• Theorems
• Summary of Properties, Theorems and Transforms

The Discrete-Time Fourier Transform¶

• Definition
• Properties
• Theorems
• Summary of Properties, Theorems and Transforms

The Discrete Fourier Transform¶

• Definition
• Properties
• Theorems
• Summary of Properties, Theorems and Transforms
• The Fast Fourier Transform
• Fast Convolution

Characterization of Discrete Systems in the Spectral Domain¶

• The Transfer Function
• Example: Measurement of an Electroacoustic Transfer Function
• Magnitude and Phase
• Phase and Group Delay
• Combination of Systems

Properties of Discrete LTI-Systems¶

References¶

The contents base on the following literature:

• Bernd Girod, Rudolf Rabenstein, Alexander Stenger, Einführung in die Systemtheorie, B.G. Teubner Verlag, 2007.
• Bernd Girod, Rudolf Rabenstein, Alexander Stenger, Signals and Systems, Wiley, 2001
• Thomas Frey, Martin Bossert, Signal- und Systemtheorie, Vieweg+Teubner, 2008.
• Alan Oppenheim, Alan Willsky, Hamid Nawab, Signals and Systems, Prentice-Hall,1996.
• Norbert Fliege, Markus Gaida, Signale und Systeme: Grundlagen und Anwendungen mit MATLAB, Schlembach Verlag, 2008.
• Mark Wickert, Signals and Systems for Dummies, 2013.

Contributors¶

• Sascha Spors (Author)
• Frank Schultz (Proofreading)
• Till Rettberg (Proofreading)
• Matthias Geier (Proofreading)

Copyright

The notebooks are provided as Open Educational Resource. Feel free to use the notebooks for your own educational purposes. The text is licensed under Creative Commons Attribution 4.0, the code of the IPython examples under the MIT license. Please attribute the work as follows: Signals and Systems by Sascha Spors.