# Continuous- and Discrete-Time Signals and Systems - Theory and Computational Examples
This repository collects didactically edited [Jupyter](https://jupyter.org/)
notebooks that introduce the theory of linear, time-invariant (LTI) signals and
systems.
Please take a look at the [static version](http://nbviewer.ipython.org/github/spatialaudio/signals-and-systems-lecture/blob/master/index.ipynb)
for a first glance.
The continuous-time case, as well as the temporally sampled (discrete-time)
case is covered.
The theory is accompanied by a series of computational examples and exercises
written in [IPython 3](http://ipython.org/).
The notebooks constitute the lecture notes to the bachelor's course
[Signals and Systems](http://www.int.uni-rostock.de/Signal-und-Systemtheorie.428.0.html)
given by [Sascha Spors](http://www.int.uni-rostock.de/Staff-Info.23+B6JmNIYXNoPWUxOTliMTNjY2U2MDcyZjJiZTI0YTc4MmFkYTE5NjQzJnR4X2pwc3RhZmZfcGkxJTVCYmFja0lkJTVEPTMmdHhfanBzdGFmZl9waTElNUJzaG93VWlkJTVEPTExMQ__.0.html) at the University of Rostock, Germany.
The contents are provided as [Open Educational Resource](https://de.wikipedia.org/wiki/Open_Educational_Resources)
, so feel free to fork, share, teach and learn.
You can give the project a [Star](https://github.com/spatialaudio/signals-and-systems-lecture/stargazers)
if you like the notebooks.
## Getting Started
The Jupyter notebooks are accessible in various ways
* Online as [static web pages](http://nbviewer.ipython.org/github/spatialaudio/signals-and-systems-lecture/blob/master/index.ipynb)
* Online for [interactive usage](https://mybinder.org/v2/gh/spatialaudio/signals-and-systems-lecture/master?filepath=index.ipynb) with [binder](https://mybinder.org/)
* Local for interactive usage on your computer
Other online services (e.g. [Google Colaboratory](https://colab.research.google.com),
[Microsoft Azure](https://azure.microsoft.com/), ...) provide environments for
interactive execution of Jupyter notebooks as well.
Local execution on your computer requires a local Jupyter/IPython installation.
The [Anaconda distribution](https://www.continuum.io/downloads) can be
considered as a convenient starting point.
Then, you'd have to [clone/download the notebooks from Github](http://github.com/spatialaudio/signals-and-systems-lecture).
Use a [Git](http://git-scm.org/) client to clone the notebooks and then start
your local Jupyter server. For manual installation under OS X/Linux please
refer to your packet manager.
## Concept and Contents
An understanding of the underlying mechanisms and the limitations of basic
signal processing methods is essential for the design of more complex techniques,
such as for example the recent contributions on indirect [detection of supermassive
black holes](https://en.wikipedia.org/wiki/Messier_87)
heavily relying on system identification and image processing.
The present notebooks cover the fundamentals of linear and time-invariant
signals and systems.
A focus is laid on a detailed mathematical treatise.
The discussion of the mathematical background is important to understand the
underlying principles in a more general manner.
The materials contain a series of computational examples and exercises to
interpret the theoretical findings and foster understanding.
The examples are designed to be explored in an interactive manner.
Furthermore, an outlook to practical applications is given whenever possible.
The material is organized in two major blocks, namely
* continuous-time and
* discrete-time (temporal sampling)
signals and systems.
The two blocks become interrelated by the discussion of the ideal temporal
sampling process and its inherent implications on sampled signals.
The didactical layouts for the two blocks are quite similar:
* introduction into signals and LTI systems
* standard signals and operations
* characterization of LTI systems in the time-domain
* spectral representation of signals (Laplace and Fourier transform vs. z- and discrete-time Fourier transform)
* spectral representation of LTI systems
* properties of LTI systems
This allows to observe the similarities and differences between the
continuous- and discrete-time case but otherwise for reading a
block without having studied the other one.
## Usage and Contributing
The contents are provided as [Open Educational Resource](https://de.wikipedia.org/wiki/Open_Educational_Resources).
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).
Feel free to use the entire collection, parts or even single notebooks for your
own purposes.
I am curious on the usage of the provided resources, so feel free to drop a
line or report to [Sascha.Spors@uni-rostock.de](mailto:Sascha.Spors@uni-rostock.de).
Our long-term vision is to lay the grounds for a **community driven concise and
reliable resource** covering the entire theory of signals and systems revised
by research and engineering professionals.
We aim at linking the strengths of both, the good old-fashioned text books
and the interactive playground of computational environments.
Open Educational Resources in combination with open source tools (Jupyter,
Python) and well-established tools for data literacy (git) provide the unique
possibility for collaborative and well-maintained resources.
Jupyter has been chosen due to its seamless integration of text, math and code.
The contents are represented future prove, as simple markdown layout allows for
conversion into many other formats (html, PDF, ...).
The git version management system features tracking of the changes and
authorship.
You are invited to contribute on different levels.
The lowest level is to provide feedback in terms of a
[Star](https://github.com/spatialaudio/signals-and-systems-lecture/stargazers)
if you like the contents.
Please consider reporting errors or suggestions for improvements as
[issues](https://github.com/spatialaudio/digital-signal-processing-lecture/issues).
We are always looking forward to new examples and exercises, as well as
reformulation of existing and novel sub-sections or sections.
Authorship of each considerable contribution will be clearly stated.
One way of introducing reformulated and new material is to handle them as
a tracked [pull request](https://github.com/spatialaudio/signals-and-systems-lecture/pulls).
We are currently working on an accompanying
[exercise repository](https://github.com/spatialaudio/signals-and-systems-exercises)
to gain knowledge and experience on manual calculation of prototypical signal
and systems problems.
This will be online very soon.
## Build Status
The computational examples in the notebooks are automatically build and checked for errors by continuous integration using github actions.
连续和离散时间信号和系统-理论和计算示例.zip
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连续和离散时间信号和系统-理论和计算示例.zip （135个子文件） 
convolution.ipynb 3.68MB linear_convolution.ipynb 1.59MB convolution_room_IR.ipynb 1.41MB theorems.ipynb 1.01MB measurement_acoustic_transfer_function.ipynb 849KB definition.ipynb 802KB definition.ipynb 788KB standard_signals.ipynb 747KB ideal.ipynb 671KB theorems.ipynb 604KB idealized_systems.ipynb 553KB theorems.ipynb 513KB impulse_response.ipynb 481KB standard_signals.ipynb 453KB bode_plot.ipynb 376KB spectrum.ipynb 366KB operations.ipynb 360KB network_analysis.ipynb 347KB theorems.ipynb 312KB spring_pendulum_analysis.ipynb 308KB causality_stability.ipynb 301KB classes.ipynb 291KB difference_equation.ipynb 267KB fourier_series.ipynb 250KB definition.ipynb 235KB magnitude_phase.ipynb 217KB properties.ipynb 207KB transfer_function.ipynb 206KB combination.ipynb 188KB properties.ipynb 183KB network_analysis.ipynb 179KB inverse.ipynb 171KB phase_group_delay.ipynb 169KB impulse_response.ipynb 169KB operations.ipynb 162KB eigenfunctions.ipynb 141KB phase_group_delay.ipynb 129KB transfer_function.ipynb 124KB fast_convolution.ipynb 118KB combination.ipynb 112KB fast_fourier_transform.ipynb 99KB theorems.ipynb 86KB definition.ipynb 84KB properties.ipynb 82KB definition.ipynb 73KB eigenfunctions.ipynb 24KB properties.ipynb 16KB properties.ipynb 14KB index.ipynb 12KB table_theorems_transforms.ipynb 6KB table_theorems_transforms.ipynb 6KB table_theorems_transforms.ipynb 6KB table_theorems_transforms.ipynb 5KB table_theorems_transforms.ipynb 5KB convolution.ipynb 4KB step_response.ipynb 3KB LICENSE 19KB README.md 7KB
sinc_interpolation.png 79KB analog_discrete_digital.png 65KB mapping_s_z_plane.png 45KB radix2_DIT_FFT_4.png 37KB influence_pole_zero.png 34KB radix2_DIT_FFT_1.png 33KB ROC.png 30KB sampling_unit_circle.png 29KB DTFT_axis.png 23KB DTFT_finite_length_signal.png 20KB DFT_axis.png 19KB DTFT_periodic_continuation.png 17KB symmetries.png 16KB radix2_DIT_FFT_2.png 16KB spectrum_sampled_signal.png 15KB integration_as_convolution.png 15KB aliasing.png 15KB symmetries.png 15KB symmetries.png 14KB ROC.png 14KB ideal_reconstruction.png 14KB integration_paths.png 13KB ideal_sampling.png 13KB FT_axis.png 12KB LTI_system_time_spectral_domain.png 11KB LTI_system_time_spectral_domain.png 11KB pz_plot.png 11KB LTI_system.png 10KB damped_spring.png 10KB parallel.png 9KB parallel.png 9KB feedback.png 9KB feedback.png 9KB LTI_system_Fourier_domain.png 9KB pz_plot.png 9KB LTI_system_Laplace_domain.png 9KB spectrum_lowpass_signal.png 7KB BIBO_stability.png 7KB concatenation.png 7KB lowpass_laplace_domain.png 6KB radix2_DIT_FFT_3.png 6KB concatenation.png 6KB共 135 条
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