Difference between revisions of "Theory of Stochastic Signals"

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===Brief summary===
 
===Brief summary===
  
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{{BlueBox|TEXT=The book focuses on the mathematical description of typical signals in Communications Engineering;,  which can be done alternatively in the time or frequency domain:
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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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# Components of communication systems and classification of different signals.
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# Fundamentals and definitions of probability theory;  set-theoretic description;  Statistical dependence;  Markov chains.
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# The Fourier series for the description of periodic signals  with the special case  "harmonic oscillation"  and the limiting case  "direct current signal".
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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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# The laws of the Fourier transform for describing aperiodic  $($impulsive$)$  signals and their spectra;  first and second Fourier integral.  
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# Description of continuous-valued random variables:  Probability density function,  distribution function,  moment calculation.  special distributions.
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# Peculiarities of band-pass signals and their description by the analytic signal and the equivalent low-pass signal.  
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# Two- and multi-dimensional random variables:  Autocorrelation function,  power density spectrum,  correlation coefficient,  cross-correlation function.
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# Discrete Fourier transform for the description of discrete-time signals;  application for spectral analysis;  FFT as an efficient computer implementation.
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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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The spectral transforms  $($Laplace transform,  z-transform,  Hilbert transform$)$  applicable exclusively to causal signals and systems are not treated in this book.  Here we refer to the book  [[Lineare_zeitinvariante_Systeme|"Linear and Time Invariant Systems"]].
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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  »'''19 individual chapters'''«  and  »'''127 sections'''«.}}
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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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This third book of our learning tutorial deals in detail with stochastic signals and their modeling.
 
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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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Here first a  »'''content overview'''«  on the basis of the  »'''five main chapters'''«  with a total of  »'''28 individual chapters«''':
 
  
  
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{{Collapsible-Fuß}}
 
{{Collapsible-Fuß}}
  
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===Exercises and multimedia===
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{{BlaueBox|TEXT=
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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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$(1)$    [https://en.lntwww.de/Category:Theory_of_Stochastic_Signals:_Exercises $\text{Exercises}$]
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$(1)$    [[LNTwww:Category:Theory_of_Stochastic_Signals:_Exercises| $\text{Exercises}$]]
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$(2)$    [[LNTwww:Learning_videos_to_Stochastic_Signal_Theory|$\text{Learning videos}$]]
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$(3)$    [[LNTwww:Applets_Related_to_Signal_Representation|$\text{Applets}$]] }}
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===Further links===
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{{BlaueBox|TEXT=
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$(4)$    [[LNTwww:Bibliography_to_Signal_Representation|$\text{Bibliography}$]]
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$(5)$    [[LNTwww:Imprint_for_the_book_"Signal_Representation"|$\text{Impressum}$]]}}
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<br><br>
 
In addition to these theory pages, we also offer tasks and multimedia modules on this topic, which could help to clarify the teaching material:
 
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 $\text{Exercises}$]
 
*[https://en.lntwww.de/Category:Theory_of_Stochastic_Signals:_Exercises $\text{Exercises}$]

Revision as of 17:50, 1 March 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 density spectrum,  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:

$(1)$    $\text{Exercises}$ $(1)$    $\text{Exercises}$

$(2)$    $\text{Learning videos}$

$(3)$    $\text{Applets}$ 


Further links

$(4)$    $\text{Bibliography}$

$(5)$    $\text{Impressum}$



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)




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