Difference between revisions of "Theory of Stochastic Signals"
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− | + | $\Rightarrow \hspace{0.5cm}\text{The translation of this book to English is in progress. The first $3$ chapters are completed.}$ | |
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+ | This third book of our learning tutorial deals in detail with stochastic signals and their modeling. | ||
+ | *Knowledge of $\text{stochastic signal theory}$ is an important prerequisite for understanding the following books, which focus on transmission aspects. | ||
+ | *Knowledge of the first two $\text{LNTwww}$ books, which include the representation of [[Signal Representation|$\text{ deterministic signals}$]] and the description of [[Linear_and_Time_Invariant_Systems|$\text{LTI systems}$]] ⇒ "linear and time-invariant systems" is helpful for understanding this book, but not required. | ||
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− | + | The course material corresponds to a $\text{lecture with three semester hours per week (sh/w) and two sh/w exercises}$. | |
+ | Here is a table of contents based on the $\text{five main chapters}$ with a total of $\text{28 individual chapters}$. | ||
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− | === | + | ===Content=== |
{{Collapsible-Kopf}} | {{Collapsible-Kopf}} | ||
− | {{Collapse1| header= | + | {{Collapse1| header=Probability Calculation |
| submenu= | | submenu= | ||
− | *[[/ | + | *[[/Some Basic Definitions/]] |
− | *[[/ | + | *[[/Set Theory Basics/]] |
− | *[[/ | + | *[[/Statistical Dependence and Independence/]] |
− | *[[/ | + | *[[/Markov Chains/]] |
}} | }} | ||
− | {{Collapse2 | header= | + | {{Collapse2 | header=Discrete Random Variables |
|submenu= | |submenu= | ||
− | *[[/ | + | *[[/From Random Experiment to Random Variable/]] |
− | *[[/ | + | *[[/Moments of a Discrete Random Variable/]] |
− | *[[/ | + | *[[/Binomial Distribution/]] |
− | *[[/ | + | *[[/Poisson Distribution/]] |
− | *[[/ | + | *[[/Generation of Discrete Random Variables/]] |
}} | }} | ||
− | {{Collapse3 | header= | + | {{Collapse3 | header=Continuous Random Variables |
|submenu= | |submenu= | ||
− | *[[/ | + | *[[/Probability Density Function/]] |
− | *[[/ | + | *[[/Cumulative Distribution Function/]] |
− | *[[/ | + | *[[/Expected Values and Moments/]] |
− | *[[/ | + | *[[/Uniformly Distributed Random Variables/]] |
− | *[[/ | + | *[[/Gaussian Distributed Random Variables/]] |
− | *[[/ | + | *[[/Exponentially Distributed Random Variables/]] |
− | *[[/ | + | *[[/Further Distributions/]] |
}} | }} | ||
− | {{Collapse4 | header= | + | {{Collapse4 | header=Random Variables with Statistical Dependence |
|submenu= | |submenu= | ||
− | *[[/ | + | *[[/Two-Dimensional Random Variables/]] |
− | *[[/ | + | *[[/Two-Dimensional Gaussian Random Variables/]] |
− | *[[/ | + | *[[/Linear Combinations of Random Variables/]] |
− | *[[/ | + | *[[/Auto-Correlation Function/]] |
− | *[[/ | + | *[[/Power-Spectral Density/]] |
− | *[[/ | + | *[[/Cross-Correlation Function and Cross Power-Spectral Density/]] |
− | *[[/ | + | *[[/Generalization to N-Dimensional Random Variables/]] |
}} | }} | ||
− | {{Collapse5 | header= | + | {{Collapse5 | header=Filtering of Stochastic Signals |
|submenu= | |submenu= | ||
− | *[[/ | + | *[[/Stochastic System Theory/]] |
− | *[[/ | + | *[[/Digital Filters/]] |
− | *[[/ | + | *[[/Creation of Predefined ACF Properties/]] |
− | *[[/Matched | + | *[[/Matched Filter/]] |
− | *[[/ | + | *[[/Wiener–Kolmogorow Filter/]] |
}} | }} | ||
{{Collapsible-Fuß}} | {{Collapsible-Fuß}} | ||
− | + | In addition to these theory pages, we also offer tasks and multimedia modules on this topic, which could help to clarify the teaching material: | |
− | *[https://en.lntwww.de/ | + | *[https://en.lntwww.de/Category:Theory_of_Stochastic_Signals:_Exercises $\text{Exercises}$] |
− | *[[LNTwww: | + | *[[LNTwww:Learning_videos_to_Stochastic_Signal_Theory|$\text{Learning videos}$]] |
− | *[[LNTwww: | + | *[[LNTwww:Applets_to_Stochastic_Signal_Theory|$\text{Applets}$]] |
− | + | <br><br> | |
+ | $\text{Other links:}$ | ||
− | + | $(1)$ [[LNTwww:Bibliography_to_Stochastic_Signal_Theory|$\text{Bibliography to the book}$]] | |
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− | $(1)$ [[LNTwww: | ||
− | $(2)$ [[LNTwww: | + | $(2)$ [[LNTwww:General_Notes_about_the_Book_"Stochastic_Signal_Theory"|$\text{General notes about the book}$]] (authors, other participants, materials as a starting point for the book, list of sources) |
<br><br> | <br><br> | ||
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{{Display}} | {{Display}} |
Revision as of 16:42, 17 March 2022
$\Rightarrow \hspace{0.5cm}\text{The translation of this book to English is in progress. The first $3$ chapters are completed.}$
This third book of our learning tutorial deals in detail with stochastic signals and their modeling.
- Knowledge of $\text{stochastic signal theory}$ is an important prerequisite for understanding the following books, which focus on transmission aspects.
- Knowledge of the first two $\text{LNTwww}$ books, which include the representation of $\text{ deterministic signals}$ and the description of $\text{LTI systems}$ ⇒ "linear and time-invariant systems" is helpful for understanding this book, but not required.
The course material corresponds to a $\text{lecture with three semester hours per week (sh/w) and two sh/w exercises}$.
Here is a table of contents based on the $\text{five main chapters}$ with a total of $\text{28 individual chapters}$.
Content
In addition to these theory pages, we also offer tasks and multimedia modules on this topic, which could help to clarify the teaching material:
$\text{Other links:}$
$(1)$ $\text{Bibliography to the book}$
$(2)$ $\text{General notes about the book}$ (authors, other participants, materials as a starting point for the book, list of sources)