Difference between revisions of "Signal Representation"

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The book focuses on the mathematical description of typical signals in communications engineering, which can alternatively be in the time or frequency domain.
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===Brief summary===
*The spectral transformations which are exclusively applicable to causal signals and systems are not treated in this book <br>&nbsp; &nbsp; (for example:&nbsp; Laplace transform,&nbsp; z-transform,&nbsp; Hilbert transform).
 
*Here we refer to the book&nbsp;[[Lineare_zeitinvariante_Systeme|$\text{Linear and Time Invariant Systems}$]]&nbsp;.
 
  
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{{BlueBox|TEXT=The book focuses on the mathematical description of typical signals in Communications Engineering,&nbsp; which can be done alternatively in the time or frequency domain:
 +
# Components of communication systems and classification of different signals.
 +
# The Fourier series for the description of periodic signals  with the special case&nbsp; &raquo;harmonic oscillation&laquo;&nbsp; and the limiting case&nbsp; &raquo;direct current signal&laquo;.
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# The laws of the Fourier transform for describing aperiodic&nbsp; $($impulsive$)$&nbsp; signals and their spectra;&nbsp; first and second Fourier integral.
 +
# Peculiarities of band-pass signals and their description by the analytical signal and the equivalent low-pass signal.
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# Discrete Fourier transform for the description of discrete-time signals;&nbsp; application for spectral analysis;&nbsp; FFT as an efficient computer implementation.
  
The subject matter corresponds to a&nbsp; $\text{lecture with two semester hours per week (SWS) and one additional SWS exercise}$. 
 
  
Here is a table of contents based on the&nbsp; $\text{five main chapters}$&nbsp; with a total of&nbsp; $\text{19 individual chapters}$.
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The spectral transforms&nbsp; $($Laplace transform,&nbsp; z-transform,&nbsp; Hilbert transform$)$&nbsp; applicable exclusively to causal signals and systems are not treated in this book.&nbsp; Here we refer to the book&nbsp; [[Lineare_zeitinvariante_Systeme|&raquo;Linear and Time Invariant Systems&laquo;]].
  
===Inhalt===
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&rArr; &nbsp; First a&nbsp; &raquo;'''content overview'''&laquo;&nbsp; on the basis of the&nbsp; &raquo;'''five main chapters'''&laquo;&nbsp; with a total of&nbsp; &raquo;'''19 individual chapters'''&laquo;&nbsp; and&nbsp; &raquo;'''127 sections'''&laquo;.}}
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===Contents===
 
{{Collapsible-Kopf}}
 
{{Collapsible-Kopf}}
{{Collapse1| header=Grundbegriffe der Nachrichtentechnik
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{{Collapse1| header=Basic Terms of Communications Engineering
 
| submenu=  
 
| submenu=  
*[[/Prinzipien der Nachrichtenübertragung/]]
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*[[/Principles of Communication/]]
*[[/Klassifizierung von Signalen/]]
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*[[/Signal Classification/]]
*[[/Zum Rechnen mit komplexen Zahlen/]]
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*[[/Calculating with Complex Numbers/]]
 
}}
 
}}
{{Collapse2 | header=Periodische Signale
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{{Collapse2 | header=Periodic Signals
 
|submenu=
 
|submenu=
*[[/Allgemeine Beschreibung/]]
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*[[/General Description/]]
*[[/Gleichsignal - Grenzfall eines periodischen Signals/]]
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*[[/Direct Current Signal - Limit Case of a Periodic Signal/]]
*[[/Harmonische Schwingung/]]
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*[[/Harmonic Oscillation/]]
*[[/Fourierreihe/]]
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*[[/Fourier Series/]]
 
}}
 
}}
{{Collapse3 | header=Aperiodische Signale - Impulse
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{{Collapse3 | header=Aperiodic Signals - Pulses
 
|submenu=
 
|submenu=
*[[/Fouriertransformation und -rücktransformation/]]
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*[[/The Fourier Transform and its Inverse/]]
*[[/Einige Sonderfälle impulsartiger Signale/]]
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*[[/Special Cases of Pulses/]]
*[[/Gesetzmäßigkeiten der Fouriertransformation/]]
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*[[/The Fourier Transform Theorems/]]
*[[/Faltungssatz und Faltungsoperation/]]
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*[[/The Convolution Theorem and Operation/]]
 
}}
 
}}
{{Collapse4 | header=Bandpassartige Signale
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{{Collapse4 | header=Band-Pass Signals
 
|submenu=
 
|submenu=
*[[/Unterschiede und Gemeinsamkeiten von TP- und BP-Signalen/]]
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*[[/Differences and Similarities of Low-Pass and Band-Pass Signals/]]
*[[/Analytisches Signal und zugehörige Spektralfunktion/]]
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*[[/Analytical Signal and its Spectral Function/]]
*[[/Äquivalentes Tiefpass-Signal und zugehörige Spektralfunktion/]]
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*[[/Equivalent Low-Pass Signal and its Spectral Function/]]
 
}}
 
}}
{{Collapse5 | header=Zeit- und frequenzdisktrete Signaldarstellung
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{{Collapse5 | header=Time-Discrete and Frequency-Discrete Signal Representation
 
|submenu=
 
|submenu=
*[[/Zeitdiskrete Signaldarstellung/]]
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*[[/Discrete-Time Signal Representation/]]
*[[/Diskrete Fouriertransformation (DFT)/]]
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*[[/Discrete Fourier Transform (DFT)/]]
*[[/Fehlermöglichkeiten bei Anwendung der DFT/]]
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*[[/Possible Errors when using DFT/]]
*[[/Spektralanalyse/]]
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*[[/Spectrum Analysis/]]
*[[/Fast-Fouriertransformation (FFT)/]]
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*[[/Fast Fourier Transform (FFT)/]]
 
}}
 
}}
 
{{Collapsible-Fuß}}
 
{{Collapsible-Fuß}}
  
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===
*[https://en.lntwww.de/Kategorie:Aufgaben_zu_Signaldarstellung $\text{Aufgaben}$]
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*[[LNTwww:Lernvideos_zu_Signaldarstellung|$\text{Lernvideos}$]]
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{{BlaueBox|TEXT=
*[[LNTwww:HTML5_zu_Signaldarstellung|$\text{Neu gestaltete Applets}$]]&nbsp; (based on HTML5 and JavaScript, also executable on smartphones)
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In addition to these theory pages,&nbsp; we also offer exercises and multimedia modules on this topic,&nbsp; which could help to clarify the teaching material:
<br><br>
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$\text{Further links:}$
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$(1)$&nbsp; &nbsp; [https://en.lntwww.de/Category:Signal_Representation:_Exercises  $\text{Exercises}$]
<br><br>
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$(1)$&nbsp; &nbsp; [[LNTwww:Literaturempfehlung_zu_Signaldarstellung|$\text{Literaturempfehlungen zum Buch}$]]
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$(2)$&nbsp; &nbsp; [[LNTwww:Learning_Videos_Related_to_Signal_Representation|$\text{Learning videos}$]]
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$(3)$&nbsp; &nbsp; [[LNTwww:Applets_Related_to_Signal_Representation|$\text{Applets}$]]&nbsp;}}
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===Further links===
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{{BlaueBox|TEXT=
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$(4)$&nbsp; &nbsp; [[LNTwww:Bibliography_to_Signal_Representation|$\text{Bibliography}$]]
  
$(2)$&nbsp; &nbsp; [[LNTwww:Weitere_Hinweise_zum_Buch_Signaldarstellung|$\text{Allgemeine Hinweise zum Buch}$]] &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_"Signal_Representation"|$\text{Impressum}$]]}}
 
<br><br>
 
<br><br>
  

Latest revision as of 18:31, 24 March 2023

Brief summary

The book focuses on the mathematical description of typical signals in Communications Engineering,  which can be done alternatively in the time or frequency domain:

  1. Components of communication systems and classification of different signals.
  2. The Fourier series for the description of periodic signals with the special case  »harmonic oscillation«  and the limiting case  »direct current signal«.
  3. The laws of the Fourier transform for describing aperiodic  $($impulsive$)$  signals and their spectra;  first and second Fourier integral.
  4. Peculiarities of band-pass signals and their description by the analytical signal and the equivalent low-pass signal.
  5. Discrete Fourier transform for the description of discrete-time signals;  application for spectral analysis;  FFT as an efficient computer implementation.


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  »Linear and Time Invariant Systems«.

⇒   First a  »content overview«  on the basis of the  »five main chapters«  with a total of  »19 individual chapters«  and  »127 sections«.


Contents

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