Difference between revisions of "Signal Representation"
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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: | {{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: | ||
# Components of communication systems and classification of different signals. | # Components of communication systems and classification of different signals. | ||
| − | # Fourier series for the description of periodic signals with the special case | + | # The Fourier series for the description of periodic signals with the special case »harmonic oscillation« and the limiting case »direct current signal«. |
| − | # | + | # The laws of the Fourier transform for describing aperiodic $($impulsive$)$ signals and their spectra; first and second Fourier integral. |
| − | # Peculiarities of band-pass signals and their description by the | + | # Peculiarities of band-pass signals and their description by the analytical signal and the equivalent low-pass signal. |
# Discrete Fourier transform for the description of discrete-time signals; application for spectral analysis; FFT as an efficient computer implementation. | # 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 [[Lineare_zeitinvariante_Systeme| | + | 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«]]. |
| − | ⇒ First a »'''content overview'''« on the basis of the »'''five main chapters'''« with a total of »'''19 individual chapters'''«.}} | + | ⇒ 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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{{Collapse3 | header=Aperiodic Signals - Pulses | {{Collapse3 | header=Aperiodic Signals - Pulses | ||
|submenu= | |submenu= | ||
| − | *[[/Fourier Transform and its Inverse/]] | + | *[[/The Fourier Transform and its Inverse/]] |
*[[/Special Cases of Pulses/]] | *[[/Special Cases of Pulses/]] | ||
| − | *[[/Fourier Transform Theorems/]] | + | *[[/The Fourier Transform Theorems/]] |
*[[/The Convolution Theorem and Operation/]] | *[[/The Convolution Theorem and Operation/]] | ||
}} | }} | ||
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{{BlaueBox|TEXT= | {{BlaueBox|TEXT= | ||
| − | $(4)$ [[LNTwww:Bibliography_to_Signal_Representation|$\text{Bibliography | + | $(4)$ [[LNTwww:Bibliography_to_Signal_Representation|$\text{Bibliography}$]] |
| − | $(5)$ [[LNTwww: | + | $(5)$ [[LNTwww:Imprint_for_the_book_"Signal_Representation"|$\text{Impressum}$]]}} |
<br><br> | <br><br> | ||
Latest revision as of 19:31, 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:
- Components of communication systems and classification of different signals.
- The Fourier series for the description of periodic signals with the special case »harmonic oscillation« and the limiting case »direct current signal«.
- The laws of the Fourier transform for describing aperiodic $($impulsive$)$ signals and their spectra; first and second Fourier integral.
- Peculiarities of band-pass signals and their description by the analytical signal and the equivalent low-pass signal.
- 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
