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.  
 
This third book of our learning tutorial deals in detail with stochastic signals and their modeling.  
*Knowledge of stochastic signal theory is an important prerequisite for understanding the following books, which focus on transmission aspects.  
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*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|$\text{Linear Time-Invariant Systems}$]]  is helpful for understanding this book, but not required.
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*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.
  
  
The course material corresponds to a  $\text{lecture with three semester hours per week (SWS) and two SWS exercises}$.
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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, first, is an overview of the contents based on the  $\text{five main chapters}$  with a total of  $\text{28 individual chapters}$.  
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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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{{Collapse1| header=Probability Calculation
 
{{Collapse1| header=Probability Calculation
 
| submenu=  
 
| submenu=  
*[[/Einige grundlegende Definitionen/]]
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*[[/Some Basic Definitions/]]
*[[/Mengentheoretische Grundlagen/]]
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*[[/Set Theory Basics/]]
*[[/Statistische Abhängigkeit und Unabhängigkeit/]]
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*[[/Statistical Dependence and Independence/]]
*[[/Markovketten/]]
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*[[/Markov Chains/]]
 
}}
 
}}
 
{{Collapse2 | header=Discrete Random Variables
 
{{Collapse2 | header=Discrete Random Variables
 
|submenu=
 
|submenu=
*[[/Vom Zufallsexperiment zur Zufallsgröße/]]
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*[[/From Random Experiment to Random Variable/]]
*[[/Momente einer diskreten Zufallsgröße/]]
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*[[/Moments of a Discrete Random Variable/]]
*[[/Binomialverteilung/]]
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*[[/Binomial Distribution/]]
*[[/Poissonverteilung/]]
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*[[/Poisson Distribution/]]
*[[/Erzeugung von diskreten Zufallsgrößen/]]
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*[[/Generation of Discrete Random Variables/]]
 
}}
 
}}
 
{{Collapse3 | header=Continuous Random Variables
 
{{Collapse3 | header=Continuous Random Variables
 
|submenu=
 
|submenu=
*[[/Wahrscheinlichkeitsdichtefunktion/]]
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*[[/Probability Density Function/]]
*[[/Verteilungsfunktion/]]
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*[[/Cumulative Distribution Function/]]
 
*[[/Expected Values and Moments/]]
 
*[[/Expected Values and Moments/]]
*[[/Gleichverteilte Zufallsgrößen/]]
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*[[/Uniformly Distributed Random Variables/]]
*[[/Gaußverteilte Zufallsgrößen/]]
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*[[/Gaussian Distributed Random Variables/]]
 
*[[/Exponentially Distributed Random Variables/]]
 
*[[/Exponentially Distributed Random Variables/]]
*[[/Further distributions/]]
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*[[/Further Distributions/]]
 
}}
 
}}
 
{{Collapse4 | header=Random Variables with Statistical Dependence
 
{{Collapse4 | header=Random Variables with Statistical Dependence
 
|submenu=
 
|submenu=
*[[/Zweidimensionale Zufallsgrößen/]]
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*[[/Two-Dimensional Random Variables/]]
*[[/Zweidimensionale Gaußsche Zufallsgrößen/]]
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*[[/Two-Dimensional Gaussian Random Variables/]]
*[[/Linearkombinationen von Zufallsgrößen/]]
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*[[/Linear Combinations of Random Variables/]]
*[[/Auto Correlation Function (ACF)/]]
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*[[/Auto-Correlation Function/]]
*[[/Power Density Spectrum (PDS)/]]
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*[[/Power-Spectral Density/]]
*[[/Kreuzkorrelationsfunktion und Kreuzleistungsdichte/]]
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*[[/Cross-Correlation Function and Cross Power-Spectral Density/]]
*[[/Verallgemeinerung auf N-dimensionale Zufallsgrößen/]]
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*[[/Generalization to N-Dimensional Random Variables/]]
 
}}
 
}}
 
{{Collapse5 | header=Filtering of Stochastic Signals
 
{{Collapse5 | header=Filtering of Stochastic Signals
 
|submenu=
 
|submenu=
*[[/Stochastische Systemtheorie/]]
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*[[/Stochastic System Theory/]]
*[[/Digitale Filter/]]
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*[[/Digital Filters/]]
*[[/Erzeugung vorgegebener AKF-Eigenschaften/]]
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*[[/Creation of Predefined ACF Properties/]]
*[[/Matched-Filter/]]
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*[[/Matched Filter/]]
*[[/Wiener–Kolmogorow–Filter/]]
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*[[/Wiener–Kolmogorow Filter/]]
 
}}
 
}}
 
{{Collapsible-Fuß}}
 
{{Collapsible-Fuß}}
  
Neben diesen Theorieseiten bieten wir auch Aufgaben und multimediale Module an, die zur Verdeutlichung des Lehrstoffes beitragen könnten:
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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/Kategorie:Theory_of_Stochastic_Signals:_Exercises $\text{Exercises}$]
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*[https://en.lntwww.de/Category:Theory_of_Stochastic_Signals:_Exercises $\text{Exercises}$]
*[[LNTwww:Lernvideos_zu_Stochastische_Signaltheorie|$\text{Lernvideos}$]]
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*[[LNTwww:Learning_videos_to_Stochastic_Signal_Theory|$\text{Learning videos}$]]
*[[LNTwww:HTML5-Applets_zu_Stochastische_Signaltheorie|$\text{neu gestaltete Applets}$]], basierend auf HTML5, auch auf Smartphones lauffähig:
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*[[LNTwww:Applets_to_Stochastic_Signal_Theory|$\text{Applets}$]]
*[[LNTwww:SWF-Applets_zu_Stochastische_Signaltheorie|$\text{frühere Applets}$]], basierend auf SWF, lauffähig nur unter WINDOWS mit ''Adobe Flash Player''.
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<br><br>
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$\text{Other links:}$
  
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$(1)$&nbsp; &nbsp; [[LNTwww:Bibliography_to_Stochastic_Signal_Theory|$\text{Bibliography to the book}$]]
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$(2)$&nbsp; &nbsp; [[LNTwww:General_Notes_about_the_Book_"Stochastic_Signal_Theory"|$\text{General notes about the book}$]] &nbsp; (authors,&nbsp; other participants,&nbsp; materials as a starting point for the book,&nbsp; list of sources)
 
<br><br>
 
<br><br>
$\text{Weitere Links:}$
 
<br><br>
 
$(1)$&nbsp; &nbsp; [[LNTwww:Literaturempfehlung_zu_Stochastische_Signaltheorie|$\text{Literaturempfehlungen zum Buch}$]]
 
  
$(2)$&nbsp; &nbsp; [[LNTwww:Weitere_Hinweise_zum_Buch_Signaldarstellung|$\text{Allgemeine Hinweise zum Buch}$]] &nbsp; (Autoren,&nbsp; Weitere Beteiligte,&nbsp; Materialien als Ausgangspunkt des Buches,&nbsp; Quellenverzeichnis)
 
<br><br>
 
  
  
 
{{Display}}
 
{{Display}}

Revision as of 15:42, 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)