#!/usr/bin/env python # coding: utf-8 # # Signals and Systems # # This repository contains a collection of [Jupyter](https://jupyter.org/) notebooks providing notes and examples to the bachelors course [Signals and Systems](http://www.int.uni-rostock.de/Signal-und-Systemtheorie.428.0.html) read by [Sascha Spors](http://www.int.uni-rostock.de/Staff-Info.23+B6JmNIYXNoPWUxOTliMTNjY2U2MDcyZjJiZTI0YTc4MmFkYTE5NjQzJnR4X2pwc3RhZmZfcGkxJTVCYmFja0lkJTVEPTMmdHhfanBzdGFmZl9waTElNUJzaG93VWlkJTVEPTExMQ__.0.html), Institute of Communications Engineering, Universität Rostock. The notebooks contain computational examples written in [IPython 3](http://ipython.org/), 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 2021. You are invited to contribute by reporting errors and suggestions as [issues](https://github.com/spatialaudio/signals-and-systems-lecture/issues) on GitHub or directly to [Sascha.Spors@uni-rostock.de](mailto:Sascha.Spors@uni-rostock.de). # ### Part 1: Continuous Signals and Systems # *** # # Signals and Systems # # Signals # * [Standard Signals](continuous_signals/standard_signals.ipynb) # * [Operations](continuous_signals/operations.ipynb) # # Characterization of Systems in the Time Domain # * [Impulse Response](systems_time_domain/impulse_response.ipynb) # * [Convolution](systems_time_domain/convolution.ipynb) # * [Step Response](systems_time_domain/step_response.ipynb) # * [Eigenfunctions and the Transfer Function](systems_time_domain/eigenfunctions.ipynb) # * [Example: Analysis of a Passive Electrical Network](systems_time_domain/network_analysis.ipynb) # * [Example: Analysis of a Damped Spring Pendulum](systems_time_domain/spring_pendulum_analysis.ipynb) # # The Laplace-Transform # * [Definition](laplace_transform/definition.ipynb) # * [Properties](laplace_transform/properties.ipynb) # * [Theorems](laplace_transform/theorems.ipynb) # * [Summary of Properties, Theorems and Transforms](laplace_transform/table_theorems_transforms.ipynb) # * [Inverse Transform](laplace_transform/inverse.ipynb) # * [Analysis of Passive Electrical Networks](laplace_transform/network_analysis.ipynb) # # The Fourier-Transform # * [Definition](fourier_transform/definition.ipynb) # * [Properties](fourier_transform/properties.ipynb) # * [Theorems](fourier_transform/theorems.ipynb) # * [Summary of Properties, Theorems and Transforms](fourier_transform/table_theorems_transforms.ipynb) # # Characterization of Systems in the Spectral Domain # * [The Transfer Function](systems_spectral_domain/transfer_function.ipynb) # * [The Bode Plot](systems_spectral_domain/bode_plot.ipynb) # * [Phase and Group Delay](systems_spectral_domain/phase_group_delay.ipynb) # * [Combination of Systems](systems_spectral_domain/combination.ipynb) # # Properties of LTI-Systems # * [Causality and Stability](systems_properties/causality_stability.ipynb) # * [Classes of Systems](systems_properties/classes.ipynb) # * [Idealized Systems](systems_properties/idealized_systems.ipynb) # # Periodic Signals # * [Spectrum](periodic_signals/spectrum.ipynb) # * [Relation between Spectrum and Fourier Series](periodic_signals/fourier_series.ipynb) # * [Convolution of a Periodic with an Aperiodic Signal](periodic_signals/convolution.ipynb) # # Sampling of Signals # * [Ideal Sampling and Reconstruction](sampling/ideal.ipynb) # ### Part 2: Time-Discrete Signals and Systems # *** # # Discrete Signals # * [Standard Signals](discrete_signals/standard_signals.ipynb) # * [Operations](discrete_signals/operations.ipynb) # # Characterization of Discrete Systems in the Time Domain # * [Difference Equation](discrete_systems_time_domain/difference_equation.ipynb) # * [Impulse Response](discrete_systems_time_domain/impulse_response.ipynb) # * [Linear Convolution](discrete_systems_time_domain/linear_convolution.ipynb) # * [Example: Convolution of an Audio Signal with a Room Impulse Response](discrete_systems_time_domain/convolution_room_IR.ipynb) # * [Eigenfunctions and the Transfer Function](discrete_systems_time_domain/eigenfunctions.ipynb) # # The $z$-Transform # * [Definition](z_transform/definition.ipynb) # * [Properties](z_transform/properties.ipynb) # * [Theorems](z_transform/theorems.ipynb) # * [Summary of Properties, Theorems and Transforms](z_transform/table_theorems_transforms.ipynb) # # The Discrete-Time Fourier Transform # * [Definition](discrete_time_fourier_transform/definition.ipynb) # * [Properties](discrete_time_fourier_transform/properties.ipynb) # * [Theorems](discrete_time_fourier_transform/theorems.ipynb) # * [Summary of Properties, Theorems and Transforms](discrete_time_fourier_transform/table_theorems_transforms.ipynb) # # The Discrete Fourier Transform # * [Definition](discrete_fourier_transform/definition.ipynb) # * [Properties](discrete_fourier_transform/properties.ipynb) # * [Theorems](discrete_fourier_transform/theorems.ipynb) # * [Summary of Properties, Theorems and Transforms](discrete_fourier_transform/table_theorems_transforms.ipynb) # * [The Fast Fourier Transform](discrete_fourier_transform/fast_fourier_transform.ipynb) # * [Fast Convolution](discrete_fourier_transform/fast_convolution.ipynb) # # Characterization of Discrete Systems in the Spectral Domain # * [The Transfer Function](discrete_systems_spectral_domain/transfer_function.ipynb) # * [Example: Measurement of an Electroacoustic Transfer Function](discrete_systems_spectral_domain/measurement_acoustic_transfer_function.ipynb) # * [Magnitude and Phase](discrete_systems_spectral_domain/magnitude_phase.ipynb) # * [Phase and Group Delay](discrete_systems_spectral_domain/phase_group_delay.ipynb) # * [Combination of Systems](discrete_systems_spectral_domain/combination.ipynb) # # 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** # # This notebook is provided as [Open Educational Resource](https://en.wikipedia.org/wiki/Open_educational_resources). Feel free to use the notebook for your own purposes. The text is licensed under [Creative Commons Attribution 4.0](https://creativecommons.org/licenses/by/4.0/), the code of the IPython examples under the [MIT license](https://opensource.org/licenses/MIT). Please attribute the work as follows: *Sascha Spors, Continuous- and Discrete-Time Signals and Systems - Theory and Computational Examples*.