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$\hspace{0.5cm}\Rightarrow \hspace{0.5cm}\text{Not yet translated}$
• Linear Combinations of Random Variables$\hspace{0.5cm}\Rightarrow \hspace{0.5cm}\text{Not yet translated}$
• Auto Correlation Function (ACF)$\hspace{0.5cm}\Rightarrow \hspace{0.5cm}\text{Not yet translated}$
• 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$\hspace{0.5cm}\Rightarrow \hspace{0.5cm}\text{Not yet translated}$

Filtering of Stochastic Signals

• Stochastic System Theory
• Digital Filters
• Creation of Predefined ACF Properties
• Matched Filter
• Wiener–Kolmogorow Filter

In addition to these theory pages, we also offer tasks and multimedia modules on this topic, which could help to clarify the teaching material:

• $\text{Exercises}$
• $\text{Learning videos}$
• $\text{Applets}$

$\text{Other links:}$

$(1)$    $\text{Bibliography to the book}$

$(2)$    $\text{General notes about the book}$   (authors,  other participants,  materials as a starting point for the book,  list of sources)