Applets:Physical Signal & Analytic Signal - Versionsgeschichte

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Textersetzung - „Biografien_und_Bibliografien/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.28am_LNT_seit_1974.29“ durch „Biografien_und_Bibliografien/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.28am_LNT_von_1974-2024.29“

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Höfler am 26. Oktober 2023 um 09:38 Uhr

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Tasnad am 1. April 2021 um 14:10 Uhr

2021-04-01T14:10:13Z

Tasnad am 9. Juni 2020 um 20:07 Uhr

2020-06-09T20:07:34Z

Guenter am 5. Mai 2020 um 08:56 Uhr

2020-05-05T08:56:16Z

Guenter am 29. August 2018 um 13:53 Uhr

2018-08-29T13:53:55Z

Tasnad am 24. August 2018 um 11:38 Uhr

2018-08-24T11:38:53Z

Tasnad: Tasnad verschob die Seite Applets:Physical Signal & Analytical Signal nach Applets:Physical Signal & Analytic Signal

2018-08-24T11:36:42Z

Tasnad verschob die Seite Physical Signal & Analytical Signal nach Physical Signal & Analytic Signal

@@ Zeile 291: / Zeile 291: @@
 ==About the Authors==
 This interactive calculation was designed and realized at the  [http://www.lnt.ei.tum.de/startseite Lehrstuhl für Nachrichtentechnik] of the  [https://www.tum.de/ Technical University of Munich] .
-*The original version was created in 2005 by [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#Ji_Li_.28Bachelorarbeit_EI_2003.2C_Diplomarbeit_EI_2005.29|Ji Li]] as part of her Diploma thesis using  &bdquo;FlashMX&ndash;Actionscript&rdquo; (Supervisor: [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.28am_LNT_seit_1974.29|Günter Söder]]).
+*The original version was created in 2005 by [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#Ji_Li_.28Bachelorarbeit_EI_2003.2C_Diplomarbeit_EI_2005.29|Ji Li]] as part of her Diploma thesis using  &bdquo;FlashMX&ndash;Actionscript&rdquo; (Supervisor: [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.28am_LNT_von_1974-2024.29|Günter Söder]]).
 *In 2018 this Applet was redesigned and updated to &bdquo;HTML5&rdquo; by [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#Xiaohan_Liu_.28Bachelorarbeit_2018.29|Xiaohan Liu]] as part of her Bachelor's thesis (Supervisor: [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_LÜT-Angehörige#Dr.-Ing._Tasn.C3.A1d_Kernetzky_.28bei_L.C3.9CT_von_2014-2022.29|Tasnád Kernetzky]]).

@@ Zeile 292: / Zeile 292: @@
 This interactive calculation was designed and realized at the  [http://www.lnt.ei.tum.de/startseite Lehrstuhl für Nachrichtentechnik] of the  [https://www.tum.de/ Technical University of Munich] .
 *The original version was created in 2005 by [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#Ji_Li_.28Bachelorarbeit_EI_2003.2C_Diplomarbeit_EI_2005.29|Ji Li]] as part of her Diploma thesis using  &bdquo;FlashMX&ndash;Actionscript&rdquo; (Supervisor: [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.28am_LNT_seit_1974.29|Günter Söder]]).
-*In 2018 this Applet was redesigned and updated to &bdquo;HTML5&rdquo; by [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#Xiaohan_Liu_.28Bachelorarbeit_2018.29|Xiaohan Liu]] as part of her Bachelor's thesis (Supervisor: [[Biographies_and_Bibliographies/LNTwww_members_from_LÜT#Dr.-Ing._Tasn.C3.A1d_Kernetzky_.28at_L.C3.9CT_from_2014-2022.29|Tasnád Kernetzky]]).
+*In 2018 this Applet was redesigned and updated to &bdquo;HTML5&rdquo; by [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#Xiaohan_Liu_.28Bachelorarbeit_2018.29|Xiaohan Liu]] as part of her Bachelor's thesis (Supervisor: [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_LÜT-Angehörige#Dr.-Ing._Tasn.C3.A1d_Kernetzky_.28bei_L.C3.9CT_von_2014-2022.29|Tasnád Kernetzky]]).
 ==Once again:&nbsp; Open Applet in new Tab==
 {{LntAppletLinkEn|physAnSignal_en}}

@@ Zeile 292: / Zeile 292: @@
 This interactive calculation was designed and realized at the  [http://www.lnt.ei.tum.de/startseite Lehrstuhl für Nachrichtentechnik] of the  [https://www.tum.de/ Technical University of Munich] .
 *The original version was created in 2005 by [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#Ji_Li_.28Bachelorarbeit_EI_2003.2C_Diplomarbeit_EI_2005.29|Ji Li]] as part of her Diploma thesis using  &bdquo;FlashMX&ndash;Actionscript&rdquo; (Supervisor: [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.28am_LNT_seit_1974.29|Günter Söder]]).
-*In 2018 this Applet was redesigned and updated to &bdquo;HTML5&rdquo; by [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#Xiaohan_Liu_.28Bachelorarbeit_2018.29|Xiaohan Liu]] as part of her Bachelor's thesis (Supervisor: [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_LÜT-Angehörige#Dr.-Ing._Tasn.C3.A1d_Kernetzky_.28bei_L.C3.9CT_von_2014-2022.29|Tasnád Kernetzky]]).
+*In 2018 this Applet was redesigned and updated to &bdquo;HTML5&rdquo; by [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#Xiaohan_Liu_.28Bachelorarbeit_2018.29|Xiaohan Liu]] as part of her Bachelor's thesis (Supervisor: [[Biographies_and_Bibliographies/LNTwww_members_from_LÜT#Dr.-Ing._Tasn.C3.A1d_Kernetzky_.28at_L.C3.9CT_from_2014-2022.29|Tasnád Kernetzky]]).
 ==Once again:&nbsp; Open Applet in new Tab==
 {{LntAppletLinkEn|physAnSignal_en}}

@@ Zeile 292: / Zeile 292: @@
 This interactive calculation was designed and realized at the  [http://www.lnt.ei.tum.de/startseite Lehrstuhl für Nachrichtentechnik] of the  [https://www.tum.de/ Technical University of Munich] .
 *The original version was created in 2005 by [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#Ji_Li_.28Bachelorarbeit_EI_2003.2C_Diplomarbeit_EI_2005.29|Ji Li]] as part of her Diploma thesis using  &bdquo;FlashMX&ndash;Actionscript&rdquo; (Supervisor: [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.28am_LNT_seit_1974.29|Günter Söder]]).
-*In 2018 this Applet was redesigned and updated to &bdquo;HTML5&rdquo; by [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#Xiaohan_Liu_.28Bachelorarbeit_2018.29|Xiaohan Liu]] as part of her Bachelor's thesis (Supervisor: [[Biografien_und_Bibliografien/Beteiligte_der_Professur_Leitungsgebundene_%C3%9Cbertragungstechnik#Tasn.C3.A1d_Kernetzky.2C_M.Sc._.28bei_L.C3.9CT_seit_2014.29|Tasnád Kernetzky]]).
+*In 2018 this Applet was redesigned and updated to &bdquo;HTML5&rdquo; by [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#Xiaohan_Liu_.28Bachelorarbeit_2018.29|Xiaohan Liu]] as part of her Bachelor's thesis (Supervisor: [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_LÜT-Angehörige#Dr.-Ing._Tasn.C3.A1d_Kernetzky_.28bei_L.C3.9CT_von_2014-2022.29|Tasnád Kernetzky]]).
 ==Once again:&nbsp; Open Applet in new Tab==
 {{LntAppletLinkEn|physAnSignal_en}}

← Nächstältere Version		Version vom 1. April 2021, 14:10 Uhr
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	{{LntAppletLinkEn\|physAnSignal_en}}		{{LntAppletLinkEn\|physAnSignal_en}}
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−	~~[[Category:Applets\|^Verzerrungen^]]~~

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-{{LntAppletLinkEn|physAnSignal}}
+{{LntAppletLinkEn|physAnSignal_en}}
 ==Applet Description==
@@ Zeile 296: / Zeile 296: @@
 ==Once again:&nbsp; Open Applet in new Tab==
-{{LntAppletLinkEn|physAnSignal}}
+{{LntAppletLinkEn|physAnSignal_en}}
 [[Category:Applets|^Verzerrungen^]]

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 ::&nbsp;$x_+(t= 20 \ {\rm &micro; s}) = x_+(t= 0) =  1.5\ \text{V}\hspace{0.3cm}\Rightarrow\hspace{0.3cm}x(t= 20 \ {\rm &micro; s})  =  1.5\ \text{V,}$
 ::&nbsp;$x_+(t= 5 \ {\rm &micro; s})  =  {\rm j} \cdot 1.5\ \text{V}\hspace{0.3cm}\Rightarrow\hspace{0.3cm}x(t= 5 \ {\rm &micro; s}) = {\rm Re}[x_+(t= 5 \ {\rm &micro; s})] =  0$.
 {{BlaueBox|TEXT=
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 ::The signal $x(t)$ is now a sine signal with a smaller amplitude. The analytic signal now starts because of $\varphi_{\rm T} = 90^\circ$ &nbsp; &rArr; &nbsp; $\phi_{\rm T} = -90^\circ$ at $x_+(t= 0) = -{\rm j} \cdot A_{\rm T}$. <br>After that, $x_+(t)$ rotates again in a mathematically positive direction, but twice as fast because of $T_0 = 10 \ \rm &micro; s$ as in $\rm (1)$.
 {{BlaueBox|TEXT=
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 ::In the phase diagram, the (red) carrier rotates faster than the (green) lower sideband and slower than the (blue) upper sideband. The analytic signal $x_+(t)$ results as the geometric sum of the three rotating pointers. It seems that the blue pointer is leading the carrier and the green pointer is following the carrier.
 {{BlaueBox|TEXT=
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 ::Until the time $t=2.5 \ \rm &micro; s$, the red carrier has rotated by $90^\circ$, the blue one by $108^\circ$ and the green one by $72^\circ$. We have $x(t=2.5 \ \rm &micro; s) = {\rm Re}\big [x_+(t= 2.5 \ \rm &micro; s)\big] = 0$, because now the pointer group points in the direction of the imaginary axis. The other sought signal values are $x(t=5 \ \rm &micro; s) = {\rm Re}\big [x_+(t= 5 \ \rm &micro; s)\big] = -1.647\ \text{V}$ and $x(t=10 \ \rm &micro; s) = {\rm Re}\big [x_+(t= 10 \ \rm &micro; s)\big] = 1.247\ \text{V}$.
 ::For $x_+(t)$ a spiral shape results, alternating with a smaller radius and then with a larger radius.
@@ Zeile 228: / Zeile 224: @@
 ::The parameter selection $\varphi_{\rm T} = \varphi_{\rm U} = \varphi_{\rm O}=90^\circ$ describes the signals $x_{\rm T}(t) = A_{\rm T}\cdot \sin\left(2\pi f_{\rm T}\cdot t\right)$ and $x_{\rm N}(t) = A_{\rm N}\cdot \cos\left(2\pi f_{\rm N}\cdot t\right)$. If, in addition, the message $x_{\rm N}(t)$ is sinusoidal, then $\varphi_{\rm O}=\varphi_{\rm T} - 90^\circ = 0$ and $\varphi_{\rm U}=\varphi_{\rm T} + 90^\circ = 180^\circ$ must be set.
 {{BlaueBox|TEXT=
@@ Zeile 238: / Zeile 233: @@
 ::With $A_{\rm T} = 0$ &nbsp; &rArr; &nbsp; $m \to \infty$ results in a [https://en.wikipedia.org/wiki/Double-sideband_suppressed-carrier_transmission ''DSB&ndash;AM without carrier''].  For this, one also needs coherent demodulation.
 {{BlaueBox|TEXT=
@@ Zeile 250: / Zeile 244: @@
 :: $A_{\rm U} = 0.8\ \text{V}$, $A_{\rm O} = 0$ is a USB modulation. The blue pointer is missing and the green pointer rotates slower compared to the red carrier.
 {{BlaueBox|TEXT=
@@ Zeile 301: / Zeile 294: @@
 *In 2018 this Applet was redesigned and updated to &bdquo;HTML5&rdquo; by [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#Xiaohan_Liu_.28Bachelorarbeit_2018.29|Xiaohan Liu]] as part of her Bachelor's thesis (Supervisor: [[Biografien_und_Bibliografien/Beteiligte_der_Professur_Leitungsgebundene_%C3%9Cbertragungstechnik#Tasn.C3.A1d_Kernetzky.2C_M.Sc._.28bei_L.C3.9CT_seit_2014.29|Tasnád Kernetzky]]).
-==Once again: Open Applet in new Tab==
+==Once again:&nbsp; Open Applet in new Tab==
 {{LntAppletLinkEn|physAnSignal}}
 [[Category:Applets|^Verzerrungen^]]

@@ Zeile 172: / Zeile 172: @@
 *The respective phase relationships can be seen in the following graphic.
-[[Datei:Zeigerdiagramm_2_neu.png|center|frame|Spectrum $X_+(f)$ of the analytic signal for different phase constellations |class=fit]]}}
+[[Datei:Zeigerdiagramm_5.png|center|frame|Spectrum $X_+(f)$ of the analytic signal for different phase constellations |class=fit]]}}
 ==Exercises==

@@ Zeile 21: / Zeile 21: @@
 \hspace{0.1cm}+\hspace{0.1cm} A_{\rm O}\cdot {\rm e}^{\hspace{0.05cm}{\rm j}\hspace{0.05cm}\cdot \hspace{0.05cm}(2\pi \hspace{0.05cm}\cdot \hspace{0.05cm}f_{\rm O}\hspace{0.05cm}\cdot \hspace{0.05cm}t- \varphi_{\rm O})}. $$
-[[Datei:Zeigerdiagramm_2a_version2.png|right|frame|Analytical signal at the time $t=0$]]
+[[Datei:Zeigerdiagramm_2a_version2.png|right|frame|Analytic signal at the time $t=0$]]
 The program displays $x_+(t)$ as the vectorial sum of three rotating pointers (all with counterclockwise) as a violet dot (see figure for start time $t=0$):
@@ Zeile 54: / Zeile 54: @@
 <br><br>
-===Analytical Signal &ndash; Frequency Domain===
+===Analytic Signal &ndash; Frequency Domain===
 The '''analytic signal''' $x_+(t)$ belonging to the physical signal $x(t)$ is the time function whose spectrum fulfills the following property:
@@ Zeile 76: / Zeile 76: @@
 <br clear=all>
-===Analytical Signal &ndash; Time Domain===
+===Analytic Signal &ndash; Time Domain===
 At this point, it is necessary to briefly discuss another spectral transformation.
@@ Zeile 115: / Zeile 115: @@
 <br><br>
-===Representation of the Harmonic Oscillation as an Analytical Signal===
+===Representation of the Harmonic Oscillation as an Analytic Signal===
 The spectral function $X(f)$ of a harmonic oscillation $x(t) = A\cdot\text{cos}(2\pi f_{\rm T}\cdot t - \varphi)$ is known to consist of two Dirac functions at the frequencies
@@ Zeile 147: / Zeile 147: @@
 <br><br>
-===Analytical Signal Representation of a Sum of Three Harmonic Oscillations===
+===Analytic Signal Representation of a Sum of Three Harmonic Oscillations===
 In our applet, we always assume a set of three rotating pointers. The physical signal is: