Applets:Physical Signal & Equivalent Lowpass Signal - Versionsgeschichte

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2026-03-16T12:39:21Z

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← Nächstältere Version		Version vom 16. März 2026, 14:39 Uhr
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	{{LntAppletLinkEn\|physAnLPSignal_en}}		{{LntAppletLinkEn\|physAnLPSignal_en}}
			[[en:Applets:Physical_Signal_&_Equivalent_Lowpass_Signal]]

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2026-02-25T13:19:29Z

Fix MathJax: add space after \cdot before letter

← Nächstältere Version		Version vom 25. Februar 2026, 15:19 Uhr
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	The '''analytic signal''' $x_+(t)$ belonging to the physical signal $x(t)$ is the time function whose spectrum fulfills the following property:		The '''analytic signal''' $x_+(t)$ belonging to the physical signal $x(t)$ is the time function whose spectrum fulfills the following property:
	[[Datei:Ortskurve_2.png\|right\|frame\|spectral functions $X(f)$, $X_+(f)$ and $X_{\rm TP}(f)$ \|class=fit]]		[[Datei:Ortskurve_2.png\|right\|frame\|spectral functions $X(f)$, $X_+(f)$ and $X_{\rm TP}(f)$ \|class=fit]]
	:$$X_+(f)=\big[1+{\rm sign}(f)\big] \cdot X(f) = \left\{ {2 \~~cdotX~~(f) \; \hspace{0.2cm}\rm for\hspace{0.2cm} {\it f} > 0, \atop {\,\,\,\, \rm 0 \; \hspace{0.9cm}\rm for\hspace{0.2cm} {\it f} < 0.} }\right.$$		:$$X_+(f)=\big[1+{\rm sign}(f)\big] \cdot X(f) = \left\{ {2 \cdot X(f) \; \hspace{0.2cm}\rm for\hspace{0.2cm} {\it f} > 0, \atop {\,\,\,\, \rm 0 \; \hspace{0.9cm}\rm for\hspace{0.2cm} {\it f} < 0.} }\right.$$

	The ''Signum function'' is for positive values of $f$ equal to $+1$ and for negative $f$ values equal to $-1$.		The ''Signum function'' is for positive values of $f$ equal to $+1$ and for negative $f$ values equal to $-1$.

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2026-02-24T13:40:28Z

Join multi-line formulas for MW 1.43 parser compat

← Nächstältere Version		Version vom 24. Februar 2026, 15:40 Uhr
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	The associated equivalent lowpass–signal is $f_{\rm O}\hspace{0.01cm}' = f_{\rm O}- f_{\rm T} > 0$,   $f_{\rm U}\hspace{0.01cm}' = f_{\rm U}- f_{\rm T} < 0$  and  $f_{\rm T}\hspace{0.01cm}' = 0$:		The associated equivalent lowpass–signal is $f_{\rm O}\hspace{0.01cm}' = f_{\rm O}- f_{\rm T} > 0$,   $f_{\rm U}\hspace{0.01cm}' = f_{\rm U}- f_{\rm T} < 0$  and  $f_{\rm T}\hspace{0.01cm}' = 0$:

	:$$x_{\rm TP}(t) = x_\text{TP, T}(t) + x_\text{TP, O}(t) + x_\text{TP, U}(t) = A_{\rm T}\cdot {\rm e}^{-{\rm j} \varphi_{\rm T} } \hspace{0.1cm}+ \hspace{0.1cm} A_{\rm O}\cdot {\rm e}^{-{\rm j} \varphi_{\rm O} } \cdot {\rm e}^{ {\rm j}\hspace{0.05cm}\cdot \hspace{0.05cm}2\pi \hspace{0.05cm}\cdot \hspace{0.05cm}f_{\rm O}\hspace{0.01cm}'\hspace{0.05cm}\cdot \hspace{0.05cm}t}\hspace{0.1cm}+ \hspace{0.1cm}		:$$x_{\rm TP}(t) = x_\text{TP, T}(t) + x_\text{TP, O}(t) + x_\text{TP, U}(t) = A_{\rm T}\cdot {\rm e}^{-{\rm j} \varphi_{\rm T} } \hspace{0.1cm}+ \hspace{0.1cm} A_{\rm O}\cdot {\rm e}^{-{\rm j} \varphi_{\rm O} } \cdot {\rm e}^{ {\rm j}\hspace{0.05cm}\cdot \hspace{0.05cm}2\pi \hspace{0.05cm}\cdot \hspace{0.05cm}f_{\rm O}\hspace{0.01cm}'\hspace{0.05cm}\cdot \hspace{0.05cm}t}\hspace{0.1cm}+ \hspace{0.1cm}A_{\rm U}\cdot {\rm e}^{-{\rm j} \varphi_{\rm U} } \cdot {\rm e}^{ {\rm j}\hspace{0.05cm}\cdot \hspace{0.05cm}2\pi \hspace{0.05cm}\cdot \hspace{0.05cm}f_{\rm U}\hspace{0.01cm}'\hspace{0.05cm}\cdot \hspace{0.05cm}t} . $$
	A_{\rm U}\cdot {\rm e}^{-{\rm j} \varphi_{\rm U} } \cdot {\rm e}^{ {\rm j}\hspace{0.05cm}\cdot \hspace{0.05cm}2\pi \hspace{0.05cm}\cdot \hspace{0.05cm}f_{\rm U}\hspace{0.01cm}'\hspace{0.05cm}\cdot \hspace{0.05cm}t} . $$

	[[Datei:Ortskurve_1.png\|right\|frame\|Equivalent low-pass signal currently $t=0$ for cosinusoidal carrier   ⇒   $\varphi_{\rm T} = 0$]]		[[Datei:Ortskurve_1.png\|right\|frame\|Equivalent low-pass signal currently $t=0$ for cosinusoidal carrier   ⇒   $\varphi_{\rm T} = 0$]]
Zeile 63:		Zeile 62:
	The '''analytic signal''' $x_+(t)$ belonging to the physical signal $x(t)$ is the time function whose spectrum fulfills the following property:		The '''analytic signal''' $x_+(t)$ belonging to the physical signal $x(t)$ is the time function whose spectrum fulfills the following property:
	[[Datei:Ortskurve_2.png\|right\|frame\|spectral functions $X(f)$, $X_+(f)$ and $X_{\rm TP}(f)$ \|class=fit]]		[[Datei:Ortskurve_2.png\|right\|frame\|spectral functions $X(f)$, $X_+(f)$ and $X_{\rm TP}(f)$ \|class=fit]]
	:$$X_+(f)=\big[1+{\rm sign}(f)\big] \cdot X(f) = \left\{ {2 \~~cdot~~		:$$X_+(f)=\big[1+{\rm sign}(f)\big] \cdot X(f) = \left\{ {2 \cdotX(f) \; \hspace{0.2cm}\rm for\hspace{0.2cm} {\it f} > 0, \atop {\,\,\,\, \rm 0 \; \hspace{0.9cm}\rm for\hspace{0.2cm} {\it f} < 0.} }\right.$$
	X(f) \; \hspace{0.2cm}\rm for\hspace{0.2cm} {\it f} > 0, \atop {\,\,\,\, \rm 0 \; \hspace{0.9cm}\rm for\hspace{0.2cm} {\it f} < 0.} }\right.$$

	The ''Signum function'' is for positive values of $f$ equal to $+1$ and for negative $f$ values equal to $-1$.		The ''Signum function'' is for positive values of $f$ equal to $+1$ and for negative $f$ values equal to $-1$.
Zeile 98:		Zeile 96:
	The associated equivalent low-pass signal is with $f_{\rm O}\hspace{0.01cm}' = f_{\rm O}- f_{\rm T} > 0$,   $f_{\rm U}\hspace{0.01cm}' = f_{\rm U}- f_{\rm T} < 0$  and  $f_{\rm T}\hspace{0.01cm}' = 0$:		The associated equivalent low-pass signal is with $f_{\rm O}\hspace{0.01cm}' = f_{\rm O}- f_{\rm T} > 0$,   $f_{\rm U}\hspace{0.01cm}' = f_{\rm U}- f_{\rm T} < 0$  and  $f_{\rm T}\hspace{0.01cm}' = 0$:

	:$$x_{\rm TP}(t) = x_\text{TP, T}(t) + x_\text{TP, O}(t) + x_\text{TP, U}(t) = A_{\rm T}\cdot {\rm e}^{-{\rm j} \varphi_{\rm T} } \hspace{0.1cm}+ \hspace{0.1cm} A_{\rm O}\cdot {\rm e}^{-{\rm j} \varphi_{\rm O} } \cdot {\rm e}^{ {\rm j}\hspace{0.05cm}\cdot \hspace{0.05cm}2\pi \hspace{0.05cm}\cdot \hspace{0.05cm}f_{\rm O}\hspace{0.01cm}'\hspace{0.05cm}\cdot \hspace{0.05cm}t}\hspace{0.1cm}+ \hspace{0.1cm}		:$$x_{\rm TP}(t) = x_\text{TP, T}(t) + x_\text{TP, O}(t) + x_\text{TP, U}(t) = A_{\rm T}\cdot {\rm e}^{-{\rm j} \varphi_{\rm T} } \hspace{0.1cm}+ \hspace{0.1cm} A_{\rm O}\cdot {\rm e}^{-{\rm j} \varphi_{\rm O} } \cdot {\rm e}^{ {\rm j}\hspace{0.05cm}\cdot \hspace{0.05cm}2\pi \hspace{0.05cm}\cdot \hspace{0.05cm}f_{\rm O}\hspace{0.01cm}'\hspace{0.05cm}\cdot \hspace{0.05cm}t}\hspace{0.1cm}+ \hspace{0.1cm}A_{\rm U}\cdot {\rm e}^{-{\rm j} \varphi_{\rm U} } \cdot {\rm e}^{ {\rm j}\hspace{0.05cm}\cdot \hspace{0.05cm}2\pi \hspace{0.05cm}\cdot \hspace{0.05cm}f_{\rm U}\hspace{0.01cm}'\hspace{0.05cm}\cdot \hspace{0.05cm}t} . $$
	A_{\rm U}\cdot {\rm e}^{-{\rm j} \varphi_{\rm U} } \cdot {\rm e}^{ {\rm j}\hspace{0.05cm}\cdot \hspace{0.05cm}2\pi \hspace{0.05cm}\cdot \hspace{0.05cm}f_{\rm U}\hspace{0.01cm}'\hspace{0.05cm}\cdot \hspace{0.05cm}t} . $$

	{{GraueBox\|TEXT=		{{GraueBox\|TEXT=

Höfler: 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“

2025-02-24T09:43:33Z

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“

← Nächstältere Version		Version vom 24. Februar 2025, 11:43 Uhr
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	==About the Authors==		==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] .		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–Actionscript” (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–Actionscript” (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” 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” 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]]).

Höfler am 26. Oktober 2023 um 09:38 Uhr

2023-10-26T09:38:58Z

← Nächstältere Version		Version vom 26. Oktober 2023, 11:38 Uhr
Zeile 257:		Zeile 257:
	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] .		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–Actionscript” (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–Actionscript” (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” 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” 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: Open Applet in new Tab==		==Once again: Open Applet in new Tab==

	{{LntAppletLinkEn\|physAnLPSignal_en}}		{{LntAppletLinkEn\|physAnLPSignal_en}}

Tasnad am 1. April 2021 um 14:10 Uhr

2021-04-01T14:10:25Z

← Nächstältere Version		Version vom 1. April 2021, 16:10 Uhr
Zeile 262:		Zeile 262:

	{{LntAppletLinkEn\|physAnLPSignal_en}}		{{LntAppletLinkEn\|physAnLPSignal_en}}

	~~[[Category:Applets\|^Verzerrungen^]]~~

Tasnad am 9. Juni 2020 um 20:04 Uhr

2020-06-09T20:04:48Z

← Nächstältere Version		Version vom 9. Juni 2020, 22:04 Uhr
Zeile 1:		Zeile 1:
	{{LntAppletLinkEn\|~~physAnTPSignal~~}}		{{LntAppletLinkEn\|physAnLPSignal_en}}

	==Applet Description==		==Applet Description==
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	==Once again: Open Applet in new Tab==		==Once again: Open Applet in new Tab==

	{{LntAppletLinkEn\|~~physAnTPSignal~~}}		{{LntAppletLinkEn\|physAnLPSignal_en}}

	[[Category:Applets\|^Verzerrungen^]]		[[Category:Applets\|^Verzerrungen^]]

Tasnad am 9. Juni 2020 um 19:57 Uhr

2020-06-09T19:57:17Z

← Nächstältere Version		Version vom 9. Juni 2020, 21:57 Uhr
Zeile 1:		Zeile 1:
	{{LntAppletLinkEn\|~~analPhysSignal~~}}		{{LntAppletLinkEn\|physAnTPSignal}}

	==Applet Description==		==Applet Description==
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	==Once again: Open Applet in new Tab==		==Once again: Open Applet in new Tab==

	{{LntAppletLinkEn\|~~physAnSignal~~}}		{{LntAppletLinkEn\|physAnTPSignal}}

	[[Category:Applets\|^Verzerrungen^]]		[[Category:Applets\|^Verzerrungen^]]

Guenter am 29. August 2018 um 13:46 Uhr

2018-08-29T13:46:45Z

← Nächstältere Version		Version vom 29. August 2018, 15:46 Uhr
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	The constellation given here results, for example, in the [[Modulationsverfahren/Zweiseitenband-Amplitudenmodulation#AM-Signale_und_-Spektren_bei_harmonischem_Eingangssignal\|double sideband amplitude modulation]] of the message signal $x_{\rm N}(t) = A_{\rm N}\cdot \cos\left(2\pi f_{\rm N}\cdot t- \varphi_{\rm N}\right)$ with the carrier signal $x_{\rm T}(t) = A_{\rm T}\cdot \cos\left(2\pi f_{\rm T}\cdot t - \varphi_{\rm T}\right)$. This is discussed frequently in the exercises.		The constellation given here results, for example, in the [[Modulationsverfahren/Zweiseitenband-Amplitudenmodulation#AM-Signale_und_-Spektren_bei_harmonischem_Eingangssignal\|double sideband amplitude modulation]] of the message signal $x_{\rm N}(t) = A_{\rm N}\cdot \cos\left(2\pi f_{\rm N}\cdot t- \varphi_{\rm N}\right)$ with the carrier signal $x_{\rm T}(t) = A_{\rm T}\cdot \cos\left(2\pi f_{\rm T}\cdot t - \varphi_{\rm T}\right)$. This is discussed frequently in the exercises.

	[[Datei:~~Zeigerdiagramm_abzug4~~.png\|center\|frame\|Spectrum $X_{\rm TP}(f)$ of the equivalent low–pass signal for different phase constellations \|class=fit]]		[[Datei:Ortskurve_5.png\|center\|frame\|Spectrum $X_{\rm TP}(f)$ of the equivalent low–pass signal for different phase constellations \|class=fit]]

	There are some limitations to the program parameters in this approach:		There are some limitations to the program parameters in this approach:

Guenter am 29. August 2018 um 10:47 Uhr

2018-08-29T10:47:44Z

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