Difference between revisions of "Signal Representation"
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| − | + | ===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: | ||
| + | # 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 [[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'''« and »'''127 sections'''«.}} |
| + | |||
| + | |||
| + | ===Contents=== | ||
{{Collapsible-Kopf}} | {{Collapsible-Kopf}} | ||
{{Collapse1| header=Basic Terms of Communications Engineering | {{Collapse1| header=Basic Terms of Communications Engineering | ||
| Line 14: | Line 20: | ||
*[[/Principles of Communication/]] | *[[/Principles of Communication/]] | ||
*[[/Signal Classification/]] | *[[/Signal Classification/]] | ||
| − | *[[/Calculating | + | *[[/Calculating with Complex Numbers/]] |
}} | }} | ||
{{Collapse2 | header=Periodic Signals | {{Collapse2 | header=Periodic Signals | ||
| Line 23: | Line 29: | ||
*[[/Fourier Series/]] | *[[/Fourier Series/]] | ||
}} | }} | ||
| − | {{Collapse3 | header=Aperiodic Signals - | + | {{Collapse3 | header=Aperiodic Signals - Pulses |
|submenu= | |submenu= | ||
| − | *[[/Fourier Transform and | + | *[[/The Fourier Transform and its Inverse/]] |
| − | *[[/Special Cases of | + | *[[/Special Cases of Pulses/]] |
| − | *[[/Fourier Transform Theorems/]] | + | *[[/The Fourier Transform Theorems/]] |
*[[/The Convolution Theorem and Operation/]] | *[[/The Convolution Theorem and Operation/]] | ||
}} | }} | ||
| − | {{Collapse4 | header= | + | {{Collapse4 | header=Band-Pass Signals |
|submenu= | |submenu= | ||
| − | *[[/Differences and Similarities of | + | *[[/Differences and Similarities of Low-Pass and Band-Pass Signals/]] |
| − | *[[/Analytical Signal and | + | *[[/Analytical Signal and its Spectral Function/]] |
| − | *[[/Equivalent Low Pass Signal and | + | *[[/Equivalent Low-Pass Signal and its Spectral Function/]] |
}} | }} | ||
| − | {{Collapse5 | header=Time and Frequency-Discrete Signal Representation | + | {{Collapse5 | header=Time-Discrete and Frequency-Discrete Signal Representation |
|submenu= | |submenu= | ||
| − | *[[/Time | + | *[[/Discrete-Time Signal Representation/]] |
*[[/Discrete Fourier Transform (DFT)/]] | *[[/Discrete Fourier Transform (DFT)/]] | ||
| − | *[[/Possible Errors | + | *[[/Possible Errors when using DFT/]] |
*[[/Spectrum Analysis/]] | *[[/Spectrum Analysis/]] | ||
*[[/Fast Fourier Transform (FFT)/]] | *[[/Fast Fourier Transform (FFT)/]] | ||
| Line 46: | Line 52: | ||
{{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:Signal_Representation:_Exercises $\text{Exercises}$] | |
| − | + | ||
| − | $( | + | $(2)$ [[LNTwww:Learning_Videos_Related_to_Signal_Representation|$\text{Learning videos}$]] |
| + | |||
| + | $(3)$ [[LNTwww:Applets_Related_to_Signal_Representation|$\text{Applets}$]] }} | ||
| + | |||
| + | |||
| + | ===Further links=== | ||
| + | |||
| + | {{BlaueBox|TEXT= | ||
| + | $(4)$ [[LNTwww:Bibliography_to_Signal_Representation|$\text{Bibliography}$]] | ||
| − | $( | + | $(5)$ [[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:
- 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
