Difference between revisions of "Theory of Stochastic Signals"

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This third book of our learning tutorial deals in detail with stochastic signals and their modeling.
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===Brief summary===
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*Knowledge of  $\text{stochastic signal theory}$  is an important prerequisite for understanding the following books, which focus on transmission aspects.
 
  
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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.
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{{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.
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# Fundamentals and definitions of probability theory;  set-theoretic description;  Statistical dependence;  Markov chains.
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# Properties of discrete-valued random variables and their computational generation.  Examples:  Binomial and Poisson distribution.  Moments calculation.
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# Description of continuous-valued random variables:  Probability density function,  distribution function,  moment calculation.  special distributions. 
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# Two- and multi-dimensional random variables:  Autocorrelation function,  power-spectral density,  correlation coefficient,  cross-correlation function. 
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# Filtering of stochastic signals   ⇒   »Stochastic System Theory«;  digital filters;  properties of matched filter and Wiener–Kolmogorov filter.
  
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Here first a  »'''content overview'''«  on the basis of the  »'''five main chapters'''«  with a total of  »'''28 individual chapters«''':
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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.
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⇒   First a  »'''content overview'''«  on the basis of the  »'''five main chapters'''«  with a total of  »'''28 individual chapters'''«  and  »'''166 sections'''«:}}
  
  
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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:
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===Exercises and multimedia===
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*[https://en.lntwww.de/Category:Theory_of_Stochastic_Signals:_Exercises $\text{Exercises}$]
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*[[LNTwww:Learning_videos_to_Stochastic_Signal_Theory|$\text{Learning videos}$]]
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{{BlaueBox|TEXT=
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*[[LNTwww:Applets_to_Stochastic_Signal_Theory|$\text{Applets}$]]
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In addition to these theory pages,  we also offer exercises and multimedia modules on this topic,  which could help to clarify the teaching material:
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<br><br>
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$\text{Other links:}$
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$(1)$&nbsp; &nbsp; [https://en.lntwww.de/Category:Theory_of_Stochastic_Signals:_Exercises $\text{Exercises}$]
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$(2)$&nbsp; &nbsp; [[LNTwww:Learning_videos_to_"Theory_of_Stochastic_Signals"|$\text{Learning videos}$]]
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$(3)$&nbsp; &nbsp; [[LNTwww:Applets_to_"Theory_of_Stochastic_Signals"|$\text{Applets}$]]&nbsp;}}
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===Further links===
  
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$(1)$&nbsp; &nbsp; [[LNTwww:Bibliography_to_Stochastic_Signal_Theory|$\text{Bibliography to the book}$]]
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{{BlaueBox|TEXT=
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$(4)$&nbsp; &nbsp; [[LNTwww:Bibliography_to_"Theory_of_Stochastic_Signals"|$\text{Bibliography}$]]
  
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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)
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$(5)$&nbsp; &nbsp; [[LNTwww:Imprint_for_the_book_"Stochastic_Signal_Theory"|$\text{Impressum}$]]}}
 
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{{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.

  1. Fundamentals and definitions of probability theory;  set-theoretic description;  Statistical dependence;  Markov chains.
  2. Properties of discrete-valued random variables and their computational generation.  Examples:  Binomial and Poisson distribution.  Moments calculation.
  3. Description of continuous-valued random variables:  Probability density function,  distribution function,  moment calculation.  special distributions.
  4. Two- and multi-dimensional random variables:  Autocorrelation function,  power-spectral density,  correlation coefficient,  cross-correlation function.
  5. 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

$(4)$    $\text{Bibliography}$

$(5)$    $\text{Impressum}$





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