Theory of Stochastic Signals

$\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

Probability Calculation

• Some Basic Definitions
• Set Theory Basics
• Statistical Dependence and Independence
• Markov Chains

Discrete Random Variables

• From Random Experiment to Random Variable
• Moments of a Discrete Random Variable
• Binomial Distribution
• Poisson Distribution
• Generation of Discrete Random Variables

Continuous Random Variables

• Probability Density Function
• Cumulative Distribution Function
• Expected Values and Moments
• Uniformly Distributed Random Variables
• Gaussian Distributed Random Variables
• Exponentially Distributed Random Variables
• Further Distributions

Random Variables with Statistical Dependence

• Two-Dimensional Random Variables
• Two-Dimensional Gaussian Random Variables
• Linear Combinations of Random Variables$ *[[/Auto-Correlation Function/]]$\hspace{0.5cm}\Rightarrow \hspace{0.5cm}\text{Not yet translated}$ *[[/Power-Spectral Density/]]$\hspace{0.5cm}\Rightarrow \hspace{0.5cm}\text{Not yet translated}$ *[[/Cross-Correlation Function and Cross Power Density/]]$\hspace{0.5cm}\Rightarrow \hspace{0.5cm}\text{Not yet translated}$ *[[/Generalization to N-Dimensional Random Variables/]]$\hspace{0.5cm}\Rightarrow \hspace{0.5cm}\text{Not yet translated}$ '"`UNIQ--html-0000000C-QINU`"' '"`UNIQ--html-0000000D-QINU`"' Filtering of Stochastic Signals '"`UNIQ--html-0000000E-QINU`"' *[[/Stochastic System Theory/]] *[[/Digital Filters/]] *[[/Creation of Predefined ACF Properties/]] *[[/Matched Filter/]] *[[/Wiener–Kolmogorow Filter/]] '"`UNIQ--html-0000000F-QINU`"' '"`UNIQ--html-00000010-QINU`"' 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/Category:Theory_of_Stochastic_Signals:_Exercises $\text{Exercises}$] *[[LNTwww:Learning_videos_to_Stochastic_Signal_Theory|$\text{Learning videos}$]] *[[LNTwww:Applets_to_Stochastic_Signal_Theory|$\text{Applets}$]] <br><br> $\text{Other links:}$ $(1)$    [[LNTwww:Bibliography_to_Stochastic_Signal_Theory|$\text{Bibliography to the book}$]] $(2)$    [[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)