Difference between revisions of "Theory of Stochastic Signals"
From LNTwww
| (26 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
| − | + | ===Brief summary=== | |
| − | This third book of our learning tutorial deals in detail with stochastic signals and their | + | {{BlaueBox|TEXT=This third book of our learning tutorial deals in detail with stochastic signals and their modelling. Knowledge of stochastic signal theory is an important prerequisite for understanding the following books, which focus on transmission aspects. |
| − | + | # Fundamentals and definitions of probability theory; set-theoretic description; Statistical dependence; Markov chains. | |
| − | + | # Properties of discrete-valued random variables and their computational generation. Examples: Binomial and Poisson distribution. Moments calculation. | |
| + | # Description of continuous-valued random variables: Probability density function, distribution function, moment calculation. special distributions. | ||
| + | # Two- and multi-dimensional random variables: Autocorrelation function, power-spectral density, correlation coefficient, cross-correlation function. | ||
| + | # Filtering of stochastic signals ⇒ »Stochastic System Theory«; digital filters; properties of matched filter and Wiener–Kolmogorov filter. | ||
| − | + | Knowledge of the first two $\text{LNTwww}$-books, which describe the [[Signal Representation|»representation of deterministic signals«]] as well as the [[Linear_and_Time_Invariant_Systems|"description of linear and time-invariant systems»]], are helpful for the understanding of the present book, but not required. | |
| + | |||
| + | ⇒ First a »'''content overview'''« on the basis of the »'''five main chapters'''« with a total of »'''28 individual chapters'''« and »'''166 sections'''«:}} | ||
| + | |||
| − | |||
| − | |||
===Content=== | ===Content=== | ||
| Line 41: | Line 45: | ||
|submenu= | |submenu= | ||
*[[/Two-Dimensional Random Variables/]] | *[[/Two-Dimensional Random Variables/]] | ||
| − | *[[/Two-Dimensional Gaussian Random Variables/]] | + | *[[/Two-Dimensional Gaussian Random Variables/]] |
| − | *[[/Linear Combinations of Random Variables/]] | + | *[[/Linear Combinations of Random Variables/]] |
| − | *[[/Auto Correlation Function | + | *[[/Auto-Correlation Function/]] |
| − | *[[/Power Density | + | *[[/Power-Spectral Density/]] |
| − | *[[/Cross-Correlation Function and Cross Power Density/]] | + | *[[/Cross-Correlation Function and Cross Power-Spectral Density/]] |
| − | *[[/Generalization to N-Dimensional Random Variables/]] | + | *[[/Generalization to N-Dimensional Random Variables/]] |
}} | }} | ||
{{Collapse5 | header=Filtering of Stochastic Signals | {{Collapse5 | header=Filtering of Stochastic Signals | ||
| Line 58: | Line 62: | ||
{{Collapsible-Fuß}} | {{Collapsible-Fuß}} | ||
| − | In addition to these theory pages, we also offer | + | ===Exercises and multimedia=== |
| − | + | ||
| − | + | {{BlaueBox|TEXT= | |
| − | + | In addition to these theory pages, we also offer exercises and multimedia modules on this topic, which could help to clarify the teaching material: | |
| − | + | ||
| − | + | $(1)$ [https://en.lntwww.de/Category:Theory_of_Stochastic_Signals:_Exercises $\text{Exercises}$] | |
| + | |||
| + | $(2)$ [[LNTwww:Learning_videos_to_"Theory_of_Stochastic_Signals"|$\text{Learning videos}$]] | ||
| + | |||
| + | $(3)$ [[LNTwww:Applets_to_"Theory_of_Stochastic_Signals"|$\text{Applets}$]] }} | ||
| + | |||
| + | |||
| + | ===Further links=== | ||
| − | $( | + | {{BlaueBox|TEXT= |
| + | $(4)$ [[LNTwww:Bibliography_to_"Theory_of_Stochastic_Signals"|$\text{Bibliography}$]] | ||
| − | $( | + | $(5)$ [[LNTwww:Imprint_for_the_book_"Stochastic_Signal_Theory"|$\text{Impressum}$]]}} |
<br><br> | <br><br> | ||
| − | |||
{{Display}} | {{Display}} | ||
Latest revision as of 12:24, 3 April 2023
Brief summary
This third book of our learning tutorial deals in detail with stochastic signals and their modelling. Knowledge of stochastic signal theory is an important prerequisite for understanding the following books, which focus on transmission aspects.
- Fundamentals and definitions of probability theory; set-theoretic description; Statistical dependence; Markov chains.
- Properties of discrete-valued random variables and their computational generation. Examples: Binomial and Poisson distribution. Moments calculation.
- Description of continuous-valued random variables: Probability density function, distribution function, moment calculation. special distributions.
- Two- and multi-dimensional random variables: Autocorrelation function, power-spectral density, correlation coefficient, cross-correlation function.
- Filtering of stochastic signals ⇒ »Stochastic System Theory«; digital filters; properties of matched filter and Wiener–Kolmogorov filter.
Knowledge of the first two $\text{LNTwww}$-books, which describe the »representation of deterministic signals« as well as the "description of linear and time-invariant systems», are helpful for the understanding of the present book, but not required.
⇒ First a »content overview« on the basis of the »five main chapters« with a total of »28 individual chapters« and »166 sections«:
Content
Exercises and multimedia
In addition to these theory pages, we also offer exercises and multimedia modules on this topic, which could help to clarify the teaching material:
$(1)$ $\text{Exercises}$
$(2)$ $\text{Learning videos}$
$(3)$ $\text{Applets}$
Further links
