Applets:Period Duration of Periodic Signals - Revision history

Hwang at 18:05, 21 March 2023

2023-03-21T18:05:06Z

Javier: Text replacement - "„" to """

2021-05-28T14:40:51Z

Text replacement - "„" to """

Javier: Text replacement - "”" to """

2021-05-28T14:40:19Z

Text replacement - "”" to """

Guenter at 13:21, 29 March 2021

2021-03-29T13:21:14Z

Guenter at 12:46, 24 February 2021

2021-02-24T12:46:08Z

Guenter at 16:09, 9 January 2021

2021-01-09T16:09:17Z

Guenter at 16:00, 9 January 2021

2021-01-09T16:00:13Z

Guenter at 16:02, 19 November 2020

2020-11-19T16:02:54Z

Guenter at 16:02, 19 November 2020

2020-11-19T16:02:16Z

Guenter at 16:01, 19 November 2020

2020-11-19T16:01:09Z

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 *The first German version was created in 2004 by&nbsp; [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#Ji_Li_.28Bachelorarbeit_EI_2003.2C_Diplomarbeit_EI_2005.29|Ji Li]]&nbsp;  as part of her diploma thesis with “FlashMX – Actionscript” (Supervisor: [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.28am_LNT_seit_1974.29|Günter Söder]]).
 *In 2017 the program was redesigned by [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#David_Jobst_.28Ingenieurspraxis_Math_2017.29|David Jobst]] (Bachelor thesis LB, Supervisor:&nbsp;  [[Biographies_and_Bibliographies/Beteiligte_der_Professur_Leitungsgebundene_%C3%9Cbertragungstechnik#Tasn.C3.A1d_Kernetzky.2C_M.Sc._.28bei_L.C3.9CT_seit_2014.29|Tasnád Kernetzky]] ) via "HTML5".
-* The English version was done in 2020 by&nbsp; [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Carolin_Mirschina_.28Ingenieurspraxis_Math_2019.2C_danach_Werkstudentin.29|Carolin Mirschina]].&nbsp; Translation with www.DeepL.com/Translator (free version).
+* The English version was done in 2020 by&nbsp; [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Carolin_Mirschina_.28Ingenieurspraxis_Math_2019.2C_danach_Werkstudentin.29|Carolin Mirschina]].&nbsp;

@@ Line 133: / Line 133: @@
 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  At the bottom of the graphic field you will find the following buttons:
-&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; '''(1)''' &nbsp; &nbsp; Zoom funktions:&nbsp; &nbsp; &bdquo;$+$" (Zoom In),&nbsp; &nbsp;  &bdquo;$-$" (Zoom Out),&nbsp; &nbsp; $\rm o$ (Reset)
+&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; '''(1)''' &nbsp; &nbsp; Zoom funktions:&nbsp; &nbsp; "$+$" (Zoom In),&nbsp; &nbsp;  "$-$" (Zoom Out),&nbsp; &nbsp; $\rm o$ (Reset)
-&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; '''(2)''' &nbsp; &nbsp; Move with&nbsp; &nbsp; "←"&nbsp; &nbsp; (Section to the left, ordinate to the right),&nbsp; &nbsp;  &bdquo;$\uparrow$"&nbsp; &nbsp; &bdquo;$\downarrow$", &nbsp; &nbsp; &bdquo;$\rightarrow$"
+&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; '''(2)''' &nbsp; &nbsp; Move with&nbsp; &nbsp; "←"&nbsp; &nbsp; (Section to the left, ordinate to the right),&nbsp; &nbsp;  "$\uparrow$"&nbsp; &nbsp; "$\downarrow$", &nbsp; &nbsp; "$\rightarrow$"
 &nbsp; &nbsp; '''(H)''' &nbsp; &nbsp; Task selection according to the task number
@@ Line 153: / Line 153: @@
 This interactive calculation tool was designed and implemented at the&nbsp; [https://www.ei.tum.de/en/lnt/home/ Institute for Communications Engineering]&nbsp; at the&nbsp; [https://www.tum.de/en Technical University of Munich].
 *The first German version was created in 2004 by&nbsp; [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#Ji_Li_.28Bachelorarbeit_EI_2003.2C_Diplomarbeit_EI_2005.29|Ji Li]]&nbsp;  as part of her diploma thesis with “FlashMX – Actionscript” (Supervisor: [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.28am_LNT_seit_1974.29|Günter Söder]]).
-*In 2017 the program was redesigned by [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#David_Jobst_.28Ingenieurspraxis_Math_2017.29|David Jobst]] (Bachelor thesis LB, Supervisor:&nbsp;  [[Biographies_and_Bibliographies/Beteiligte_der_Professur_Leitungsgebundene_%C3%9Cbertragungstechnik#Tasn.C3.A1d_Kernetzky.2C_M.Sc._.28bei_L.C3.9CT_seit_2014.29|Tasnád Kernetzky]] ) via &bdquo;HTML5".
+*In 2017 the program was redesigned by [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#David_Jobst_.28Ingenieurspraxis_Math_2017.29|David Jobst]] (Bachelor thesis LB, Supervisor:&nbsp;  [[Biographies_and_Bibliographies/Beteiligte_der_Professur_Leitungsgebundene_%C3%9Cbertragungstechnik#Tasn.C3.A1d_Kernetzky.2C_M.Sc._.28bei_L.C3.9CT_seit_2014.29|Tasnád Kernetzky]] ) via "HTML5".
 * The English version was done in 2020 by&nbsp; [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Carolin_Mirschina_.28Ingenieurspraxis_Math_2019.2C_danach_Werkstudentin.29|Carolin Mirschina]].&nbsp; Translation with www.DeepL.com/Translator (free version).

@@ Line 133: / Line 133: @@
 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  At the bottom of the graphic field you will find the following buttons:
-&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; '''(1)''' &nbsp; &nbsp; Zoom funktions:&nbsp; &nbsp; &bdquo;$+$&rdquo; (Zoom In),&nbsp; &nbsp;  &bdquo;$-$&rdquo; (Zoom Out),&nbsp; &nbsp; $\rm o$ (Reset)
+&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; '''(1)''' &nbsp; &nbsp; Zoom funktions:&nbsp; &nbsp; &bdquo;$+$" (Zoom In),&nbsp; &nbsp;  &bdquo;$-$" (Zoom Out),&nbsp; &nbsp; $\rm o$ (Reset)
-&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; '''(2)''' &nbsp; &nbsp; Move with&nbsp; &nbsp; "←"&nbsp; &nbsp; (Section to the left, ordinate to the right),&nbsp; &nbsp;  &bdquo;$\uparrow$&rdquo;&nbsp; &nbsp; &bdquo;$\downarrow$&rdquo;, &nbsp; &nbsp; &bdquo;$\rightarrow$&rdquo;
+&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; '''(2)''' &nbsp; &nbsp; Move with&nbsp; &nbsp; "←"&nbsp; &nbsp; (Section to the left, ordinate to the right),&nbsp; &nbsp;  &bdquo;$\uparrow$"&nbsp; &nbsp; &bdquo;$\downarrow$", &nbsp; &nbsp; &bdquo;$\rightarrow$"
 &nbsp; &nbsp; '''(H)''' &nbsp; &nbsp; Task selection according to the task number
@@ Line 153: / Line 153: @@
 This interactive calculation tool was designed and implemented at the&nbsp; [https://www.ei.tum.de/en/lnt/home/ Institute for Communications Engineering]&nbsp; at the&nbsp; [https://www.tum.de/en Technical University of Munich].
 *The first German version was created in 2004 by&nbsp; [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#Ji_Li_.28Bachelorarbeit_EI_2003.2C_Diplomarbeit_EI_2005.29|Ji Li]]&nbsp;  as part of her diploma thesis with “FlashMX – Actionscript” (Supervisor: [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.28am_LNT_seit_1974.29|Günter Söder]]).
-*In 2017 the program was redesigned by [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#David_Jobst_.28Ingenieurspraxis_Math_2017.29|David Jobst]] (Bachelor thesis LB, Supervisor:&nbsp;  [[Biographies_and_Bibliographies/Beteiligte_der_Professur_Leitungsgebundene_%C3%9Cbertragungstechnik#Tasn.C3.A1d_Kernetzky.2C_M.Sc._.28bei_L.C3.9CT_seit_2014.29|Tasnád Kernetzky]] ) via &bdquo;HTML5&rdquo;.
+*In 2017 the program was redesigned by [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#David_Jobst_.28Ingenieurspraxis_Math_2017.29|David Jobst]] (Bachelor thesis LB, Supervisor:&nbsp;  [[Biographies_and_Bibliographies/Beteiligte_der_Professur_Leitungsgebundene_%C3%9Cbertragungstechnik#Tasn.C3.A1d_Kernetzky.2C_M.Sc._.28bei_L.C3.9CT_seit_2014.29|Tasnád Kernetzky]] ) via &bdquo;HTML5".
 * The English version was done in 2020 by&nbsp; [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Carolin_Mirschina_.28Ingenieurspraxis_Math_2019.2C_danach_Werkstudentin.29|Carolin Mirschina]].&nbsp; Translation with www.DeepL.com/Translator (free version).

@@ Line 1: / Line 1: @@
-{{LntAppletLink|signalPeriod_en}}  &nbsp; &nbsp;  &nbsp;
+{{LntAppletLinkEnDe|signalPeriod_en|signalPeriod}}
@@ Line 16: / Line 15: @@
 ==Theoretical background==
 <br>
-A ''periodic signal''&nbsp; $x(t)$&nbsp; is present exactly when it is not constant and if for all arbitrary values of&nbsp; $t$&nbsp; and all integer values of&nbsp; $i$&nbsp; with an appropriate&nbsp; $T_{0}$&nbsp; applies: &nbsp;
+A periodic signal&nbsp; $x(t)$&nbsp; is present exactly when it is not constant and if for all arbitrary values of&nbsp; $t$&nbsp; and all integer values of&nbsp; $i$&nbsp; with an appropriate&nbsp; $T_{0}$&nbsp; applies: &nbsp;
 :$$x(t+i\cdot T_{0}) = x(t).$$
 *$T_0$&nbsp; is called the&nbsp; '''period duration''' &nbsp; and&nbsp; $f_0 = 1/T_0$&nbsp; the&nbsp; '''basic frequency'''.
@@ Line 160: / Line 159: @@
 ==Once again: Open Applet in new Tab==
-{{LntAppletLink|signalPeriod_en}}  &nbsp; &nbsp;  &nbsp;
+{{LntAppletLinkEnDe|signalPeriod_en|signalPeriod}}
 <br><br>

@@ Line 114: / Line 114: @@
 ==Applet Manual==
-[[File:Anleitung_Periodendauer.png|right|frame|Bildschirmabzug der englischen Version]]
+[[File:Anleitung_Periodendauer.png|right|frame|Screenshot]]
 &nbsp; &nbsp; '''(A)''' &nbsp; &nbsp; Parameter input for harmonic oscillation 1

@@ Line 55: / Line 55: @@
 ==Exercises==
-[[File:Aufgaben_2D-Gauss.png|right]]
+* First select the number&nbsp; (<b>1</b>, <b>2</b>, ... )&nbsp; of the exercise.&nbsp; The number&nbsp; '''0'''&nbsp; corresponds to a&nbsp; "Reset":&nbsp; Same setting as at the program start.
-* First select the number&nbsp; (<b>1</b>, <b>2</b>, ... )&nbsp; of the exercise. <br>
+* An exercise description is displayed.&nbsp; Parameter values are adjusted.&nbsp; Solution after pressing "Show solution".<br>
-* An exercise description is displayed.&nbsp; Parameter values are adjusted.<br>
+* $A_1'$&nbsp; and&nbsp; $A_2'$&nbsp; denote the signal amplitudes normalized to&nbsp; $1\ \rm V$.&nbsp;   $f_0'$,&nbsp; $f_1'$&nbsp; and&nbsp; $f_2'$&nbsp; are the frequencies normalized to&nbsp; $1\ \rm kHz$.
 <br clear=all>
 {{BlaueBox|TEXT=

@@ Line 118: / Line 118: @@
 ==Applet Manual==
-[[File:Exercise_impuls.png |right|frame|Screenshot]]
+[[File:Anleitung_Periodendauer.png|right|frame|Bildschirmabzug der englischen Version]]
-&nbsp; &nbsp; '''(B)''' &nbsp; &nbsp; Bereich der graphischen Darstellung
+&nbsp; &nbsp; '''(A)''' &nbsp; &nbsp; Parameter input for harmonic oscillation 1
-&nbsp; &nbsp; '''(C)''' &nbsp; &nbsp; Variationsmöglichkeit für die  graphische Darstellung
+&nbsp; &nbsp; '''(B)''' &nbsp; &nbsp; Parameter input for harmonic oscillation 2 and time&nbsp; $t_*$.
-&nbsp; &nbsp; '''(D)''' &nbsp; &nbsp; Abspeichern und Zurückholen von Parametersätzen
+&nbsp; &nbsp; '''(C)''' &nbsp; &nbsp; Numerical output of the main result&nbsp; $T_0$; graphical illustration by red line
-&nbsp; &nbsp; '''(E)''' &nbsp; &nbsp; Numerikausgabe des Hauptergebnisses $T_0$; graphische Verdeutlichung durch rote Linie
+&nbsp; &nbsp; '''(D)''' &nbsp; &nbsp; Save parameter sets
-&nbsp; &nbsp; '''(F)''' &nbsp; &nbsp; Ausgabe von $x_{\rm max}$ und der Signalwerte $x(t_*) = x(t_* + T_0)= x(t_* + 2T_0)$
+&nbsp; &nbsp; '''(E)''' &nbsp; &nbsp; Retrieve parameter sets
-&nbsp; &nbsp; '''(G)''' &nbsp; &nbsp; Darstellung der Signalwerte $x(t_*) = x(t_* + T_0)= x(t_* + 2T_0)$ durch grüne Punkte
+&nbsp; &nbsp; '''(F)''' &nbsp; &nbsp; Output of&nbsp; $x_{\rm max}$&nbsp; and the signal values&nbsp; $x(t_*) = x(t_* + T_0)= x(t_* + 2T_0)$
-&nbsp; &nbsp; '''(H)''' &nbsp; &nbsp; Einstellung der Zeit $t_*$ für die Signalwerte $x(t_*) = x(t_* + T_0)= x(t_* + 2T_0)$
+&nbsp; &nbsp; '''(G)''' &nbsp; &nbsp; Graphic field for displaying the signals
-'''Details zum obigen Punkt (C)'''
+&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; The signal values&nbsp; $x(t_*) = x(t_* + T_0)= x(t_* + 2T_0)$&nbsp; are marked by green dots
-&nbsp; &nbsp; '''(*)''' &nbsp; Verschieben mit &bdquo;$\leftarrow$&rdquo; (Ausschnitt nach links, Ordinate nach rechts),  &bdquo;$\uparrow$&rdquo; &bdquo;$\downarrow$&rdquo; und &bdquo;$\rightarrow$&rdquo;
+&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  At the bottom of the graphic field you will find the following buttons: