Difference between revisions of "Kontinuierliche und diskrete Spektren (Lernvideo)"
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| − | Contrast the spectral properties of a triangular pulse $g(t)$ with continuous spectrum $G(f)$ and a periodic triangular signal $x(t)$ with line spectrum $X(f)$. The relation results from the convolution corresponding to $x(t)= g(t) \star p(t)$, where $p(t)$ denotes a Dirac delta pulse (infinite sum of equidistantly shifted Dirac delta pulses). The relation in the spectral domain is $X(f)= G(f) \cdot P(f)$. The spectral function $P(f)$ of the Dirac pulse $p(t)$ is also a Dirac delta pulse, but now in the frequency domain (Duration 6:19). | + | Contrast the spectral properties of a triangular pulse $g(t)$ with continuous spectrum $G(f)$ and a periodic triangular signal $x(t)$ with line spectrum $X(f)$. The relation results from the convolution corresponding to $x(t)= g(t) \star p(t)$, where $p(t)$ denotes a Dirac delta pulse (infinite sum of equidistantly shifted Dirac delta pulses). The relation in the spectral domain is $X(f)= G(f) \cdot P(f)$. The spectral function $P(f)$ of the Dirac delta pulse $p(t)$ is also a Dirac delta pulse, but now in the frequency domain (Duration 6:19). |
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| − | Using the same example, we now compare the spectral value $G(f = f_{\rm B})$ of the triangular pulse at the fixed reference frequency $f_{\rm B}$ with the Dirac weight of the periodic triangular signal $x(t)$ at the frequency $f = f_{\rm B}$ . Many significant similarities are found, but also some fundamental differences. The results depend among others on the period duration $T_0$ of the signal $x(t)$ (duration 5:12). | + | Using the same example, we now compare the spectral value $G(f = f_{\rm B})$ of the triangular pulse at the fixed reference frequency $f_{\rm B}$ with the Dirac delta weight of the periodic triangular signal $x(t)$ at the frequency $f = f_{\rm B}$ . Many significant similarities are found, but also some fundamental differences. The results depend among others on the period duration $T_0$ of the signal $x(t)$ (duration 5:12). |
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| − | This educational video was conceived and realized in | + | This educational video was conceived and realized in 2005 at the [http://www.lnt.ei.tum.de/startseite "Chair of Communications Engineering"] of the [https://www.tum.de/ "Technical University of Munich"]. |
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Latest revision as of 19:00, 18 March 2023
!!! The learning video is in German language (images and sound). There is an English summary at the end of this file !!!
Teil 1
Gegenübergestellt werden die Spektraleigenschaften eines Dreieckimpulses $g(t)$ mit kontinuierlichem Spektrum $G(f)$ und eines periodischen Dreiecksignals $x(t)$ mit Linienspektrum $X(f)$. Der Zusammenhang ergibt sich aus der Faltung entsprechend $x(t)= g(t) \star p(t)$, wobei $p(t)$ einen Diracpuls (unendliche Summe von äquidistant verschobenen Diracimpulsen) bezeichnet. Der Zusammenhang im Spektralbereich lautet $X(f)= G(f) \cdot P(f)$. Die Spektralfunktion $P(f)$ des Diracpulses $p(t)$ ist ebenfalls ein Diracpuls, aber nun im Frequenzbereich (Dauer 6:19).
Teil 2
Anhand des gleichen Beispiels wird nun der Spektralwert $G(f = f_{\rm B})$ des Dreieckimpulses bei der festen Bezugsfrequenz $f_{\rm B}$ mit dem Diracgewicht des periodischen Dreiecksignals $x(t)$ bei der Frequenz $f = f_{\rm B}$ verglichen. Dabei ergeben sich viele signifikante Gemeinsamkeiten, aber auch einige grundlegende Unterschiede. Die Ergebnisse hängen unter Anderem von der Periodendauer $T_0$ des Signals $x(t)$ ab (Dauer 5:12).
Dieses Lernvideo wurde 2005 am "Lehrstuhl für Nachrichtentechnik" der "Technischen Universität München" konzipiert und realisiert.
Buch und Regie: »Günter Söder« und »Klaus Eichin«, Sprecher und Realisierung: »Thorsten Kalweit«.
Im Zuge der LNTwww-Neugestaltung (Version 3) wurden diese Lernvideos 2016/2017 von »Tasnád Kernetzky« und einigen Studenten in moderne Formate konvertiert, um von möglichst vielen Browsern (wie Firefox, Chrome, Safari) als auch von Smartphones wiedergegeben werden zu können.
English summary:
Continuous and discrete spectra
Part 1
Contrast the spectral properties of a triangular pulse $g(t)$ with continuous spectrum $G(f)$ and a periodic triangular signal $x(t)$ with line spectrum $X(f)$. The relation results from the convolution corresponding to $x(t)= g(t) \star p(t)$, where $p(t)$ denotes a Dirac delta pulse (infinite sum of equidistantly shifted Dirac delta pulses). The relation in the spectral domain is $X(f)= G(f) \cdot P(f)$. The spectral function $P(f)$ of the Dirac delta pulse $p(t)$ is also a Dirac delta pulse, but now in the frequency domain (Duration 6:19).
Part 2
Using the same example, we now compare the spectral value $G(f = f_{\rm B})$ of the triangular pulse at the fixed reference frequency $f_{\rm B}$ with the Dirac delta weight of the periodic triangular signal $x(t)$ at the frequency $f = f_{\rm B}$ . Many significant similarities are found, but also some fundamental differences. The results depend among others on the period duration $T_0$ of the signal $x(t)$ (duration 5:12).
This educational video was conceived and realized in 2005 at the "Chair of Communications Engineering" of the "Technical University of Munich".
