Applets:Physical Signal & Analytic Signal - Revision history

Guenter at 13:54, 13 April 2023

2023-04-13T13:54:40Z

Guenter at 15:41, 10 April 2023

2023-04-10T15:41:22Z

Noah at 22:25, 26 March 2023

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Hwang at 16:08, 23 January 2023

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Guenter at 14:33, 13 January 2023

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Tasnad at 14:10, 1 April 2021

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Guenter at 09:51, 1 April 2021

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Guenter at 09:48, 1 April 2021

2021-04-01T09:48:34Z

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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:
-[[File:Zeigerdiagramm_3a.png|right|frame|Construction of the spectral function $X_+(f)$ '''Korrektur'''|class=fit]]
+[[File:EN_Sig_T_4_2_S1a.png|right|frame|Construction of the spectral function $X_+(f)$|class=fit]]
 :$$X_+(f)=\big[1+{\rm sign}(f)\big] \cdot X(f) = \left\{ {2 \cdot
 X(f) \; \hspace{0.2cm}\rm for\hspace{0.2cm} {\it f} > 0, \atop {\,\,\,\, \rm 0 \; \hspace{0.9cm}\rm for\hspace{0.2cm} {\it f} < 0.} }\right.$$

@@ Line 55: / Line 55: @@
 The '''analytic signal''' $x_+(t)$ belonging to the physical signal $x(t)$ is the time function whose spectrum fulfills the following property:
-[[File:Zeigerdiagramm_3a.png|right|frame|Construction of the spectral function $X_+(f)$ |class=fit]]
+[[File:Zeigerdiagramm_3a.png|right|frame|Construction of the spectral function $X_+(f)$ '''Korrektur'''|class=fit]]
 :$$X_+(f)=\big[1+{\rm sign}(f)\big] \cdot X(f) = \left\{ {2 \cdot
 X(f) \; \hspace{0.2cm}\rm for\hspace{0.2cm} {\it f} > 0, \atop {\,\,\,\, \rm 0 \; \hspace{0.9cm}\rm for\hspace{0.2cm} {\it f} < 0.} }\right.$$

@@ Line 2: / Line 2: @@
 ==Applet Description==
 <br>
-This applet shows the relationship between the physical bandpass signal $x(t)$ and the associated analytic signal $x_+(t)$. It is assumed that the bandpass signal $x(t)$ has a frequency-discrete spectrum $X(f)$:
+This applet shows the relationship between the physical band-pass signal $x(t)$ and the associated analytic signal $x_+(t)$. It is assumed that the band-pass signal $x(t)$ has a frequency-discrete spectrum $X(f)$:
 :$$x(t) = x_{\rm U}(t) + x_{\rm T}(t) + x_{\rm O}(t) = A_{\rm U}\cdot \cos\left(2\pi f_{\rm U}\cdot t- \varphi_{\rm U}\right)+A_{\rm T}\cdot \cos\left(2\pi f_{\rm T}\cdot t- \varphi_{\rm T}\right)+A_{\rm O}\cdot \cos\left(2\pi f_{\rm O}\cdot t- \varphi_{\rm O}\right). $$
 The physical signal $x(t)$ is thus composed of three harmonic oscillations, a constellation that can be found, for example, in the ''Double-sideband Amplitude Modulation''
@@ Line 30: / Line 30: @@
-The time trace of $x_+(t)$ is also referred to below as ''Pointer Diagram''. The relationship between the physical bandpass signal $x(t)$ and the associated analytic signal $x_+(t)$ is:
+The time trace of $x_+(t)$ is also referred to below as ''Pointer Diagram''. The relationship between the physical band-pass signal $x(t)$ and the associated analytic signal $x_+(t)$ is:
 :$$x(t) = {\rm Re}\big [x_+(t)\big ].$$
-''Note:'' &nbsp; In the figure $\varphi_{\rm O} = +30^\circ$. This leads to the angle with respect to the coordinate system at $t=0$: &nbsp; $\phi_{\rm O}=-\varphi_{\rm O}=-30^\circ$. Similarly, the null phase angle $\varphi_{\rm U}=-30^\circ$ of the lower sideband leads to the phase angle to be considered in the complex plane: &nbsp; $\phi_{\rm U}=+30^\circ$.
+''Note:'' &nbsp; In the figure $\varphi_{\rm O} = +30^\circ$. This leads to the angle with respect to the coordinate system at $t=0$: &nbsp; $\phi_{\rm O}=-\varphi_{\rm O}=-30^\circ$. Similarly, the zero phase angle $\varphi_{\rm U}=-30^\circ$ of the lower sideband leads to the phase angle to be considered in the complex plane: &nbsp; $\phi_{\rm U}=+30^\circ$.
@@ Line 40: / Line 40: @@
 ==Theoretical Background==
 <br>
-===Description of Bandpass Signals===
+===Description of Band-pass Signals===
-[[File:Zeigerdiagramm_1a.png|right|frame|Bandpass spectrum $X(f)$ |class=fit]]
+[[File:Zeigerdiagramm_1a.png|right|frame|Band-pass spectrum $X(f)$ |class=fit]]
-We consider '''bandpass signals''' $x(t)$ with the property that their spectra $X(f)$ are not in the range around the frequency $f=0$, but around a carrier frequency $f_{\rm T}$. In most cases it can also be assumed that the bandwidth is $B \ll f_{\rm T}$.
+We consider '''band-pass signals''' $x(t)$ with the property that their spectra $X(f)$ are not in the range around the frequency $f=0$, but around a carrier frequency $f_{\rm T}$. In most cases it can also be assumed that the bandwidth is $B \ll f_{\rm T}$.
-The figure shows such a bandpass spectrum $X(f)$. Assuming that the associated $x(t)$ is a physical signal and thus real, the spectral function $X(f)$ has a symmetry with respect to the frequency $f = 0$, if $x(t)$ is an even function &nbsp; &rArr; &nbsp; $x(-t)=x(t)$, $X(f)$ is real and even.
+The figure shows such a band-pass spectrum $X(f)$. Assuming that the associated $x(t)$ is a physical signal and thus real, the spectral function $X(f)$ has a symmetry with respect to the frequency $f = 0$, if $x(t)$ is an even function &nbsp; &rArr; &nbsp; $x(-t)=x(t)$, $X(f)$ is real and even.
-Besides the physical signal $x(t)\ \circ\!\!-\!\!\!-\!\!\!-\!\!\bullet\, \ X(f)$, one can also use the following descriptions of bandpass signals:
+Besides the physical signal $x(t)\ \circ\!\!-\!\!\!-\!\!\!-\!\!\bullet\, \ X(f)$, one can also use the following descriptions of band-pass signals:
 *the analytic signal $x_+(t)\ \circ\!\!-\!\!\!-\!\!\!-\!\!\bullet\, \ X_+(f)$, see next section,
-*the equivalent lowpass signal &nbsp; (in German: &nbsp; äquivalentes '''T'''ief '''P'''ass&ndash;Signal) $x_{\rm TP}(t)\ \circ\!\!-\!\!\!-\!\!\!-\!\!\bullet\, \ X_{\rm TP}(f)$, <br>see Applet [[Applets:Physical_Signal_%26_Equivalent_Low-pass_Signal|Physical Signal & Equivalent Lowpass signal]].
+*the equivalent low-pass signal &nbsp; (in German: &nbsp; äquivalentes '''T'''ief '''P'''ass&ndash;Signal) $x_{\rm TP}(t)\ \circ\!\!-\!\!\!-\!\!\!-\!\!\bullet\, \ X_{\rm TP}(f)$, <br>see Applet [[Applets:Physical_Signal_%26_Equivalent_Low-pass_Signal|"Physical Signal & Equivalent Low-pass signal"]].
 <br><br>
@@ Line 66: / Line 66: @@
 From the graph you can see the calculation rule for $X_+(f)$:
-The actual bandpass spectrum $X(f)$ becomes
+The actual band-pass spectrum $X(f)$ becomes
 * doubled at the positive frequencies, and
 * set to zero at the negative frequencies.
@@ Line 85: / Line 85: @@
 \tau} }\hspace{0.15cm} {\rm d}\tau.$$
-This particular integral is not solvable in a simple, conventional way, but must be evaluated using the [https://en.wikipedia.org/wiki/Cauchy_principal_value Cauchy principal value theorem].
+This particular integral is not solvable in a simple, conventional way, but must be evaluated using the [https://en.wikipedia.org/wiki/Cauchy_principal_value "Cauchy principal value theorem"].
 Accordingly, in the frequency domain:
@@ Line 92: / Line 92: @@
 The above result can be summarized with this definition as follows:
-* The analytic signal $x_+(t)$ is obtained from the physical bandpass signal $x(t)$ by adding an imaginary part to $x(t)$ according to the Hilbert transform:
+* The analytic signal $x_+(t)$ is obtained from the physical band-pass signal $x(t)$ by adding an imaginary part to $x(t)$ according to the Hilbert transform:
 :$$x_+(t) = x(t)+{\rm j} \cdot {\rm H}\left\{x(t)\right\} .$$
@@ Line 99: / Line 99: @@
-* From the analytic signal $x_+(t)$, the physical bandpass signal can be easily determined by the following operation:
+* From the analytic signal $x_+(t)$, the physical band-pass signal can be easily determined by the following operation:
 :$$x(t) = {\rm Re}\big[x_+(t)\big] .$$
@@ Line 115: / Line 115: @@
 ===Representation of the Harmonic Oscillation as an Analytic Signal===
-The spectral function $X(f)$ of a harmonic oscillation $x(t) = A\cdot\text{cos}(2\pi f_{\rm T}\cdot t - \varphi)$ is known to consist of two Dirac functions at the frequencies
+The spectral function $X(f)$ of a harmonic oscillation $x(t) = A\cdot\text{cos}(2\pi f_{\rm T}\cdot t - \varphi)$ is known to consist of two Dirac delta functions at the frequencies
 * $+f_{\rm T}$ with the complex weight $A/2 \cdot \text{e}^{-\text{j}\hspace{0.05cm}\varphi}$,
 * $-f_{\rm T}$ with the complex weight $A/2 \cdot \text{e}^{+\text{j}\hspace{0.05cm}\varphi}$.
-Thus, the spectrum of the analytic signal (that is, without the Dirac function at the frequency $f =-f_{\rm T}$, but doubling at $f =+f_{\rm T}$):
+Thus, the spectrum of the analytic signal (that is, without the Dirac delta function at the frequency $f =-f_{\rm T}$, but doubling at $f =+f_{\rm T}$):
 :$$X_+(f) = A \cdot {\rm e}^{-{\rm j} \hspace{0.05cm}\varphi}\cdot\delta (f - f_{\rm
@@ Line 161: / Line 161: @@
 {{GraueBox|TEXT=
 $\text{Example 3:}$&nbsp;
-Shown the constellation arises i.e. in the [https://en.wikipedia.org/wiki/Sideband Double-sideband Amplitude Modulation] (with carrier) 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.
+Shown the constellation arises i.e. in the [https://en.wikipedia.org/wiki/Sideband "Double-sideband Amplitude Modulation"] (with carrier) 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.
@@ Line 245: / Line 245: @@
 '''(8)''' &nbsp; Now&nbsp; $\text{Red:} \hspace{0.05cm} A_{\rm T} = 1\ \text{V}, \ f_{\rm T} = 100 \ \text{kHz}, \ \varphi_{\rm T} = 0^\circ$, &nbsp;  $\text{Green:} \hspace{0.05cm} A_{\rm U} = 0.4\ \text{V}, \ f_{\rm U} = 80 \ \text{kHz}, \ \varphi_{\rm U} = -90^\circ$,  &nbsp;   $\text{Blue:} \hspace{0.05cm} A_{\rm O} = 0.2\ \text{V}, \ f_{\rm O} = 120 \ \text{kHz}, \ \varphi_{\rm O} = +90^\circ$.
-:Which constellation could be described here? Which shape results for the equivalent lowpass signal $x_{\rm TP}(t)$?}}
+:Which constellation could be described here? Which shape results for the equivalent low-pass signal $x_{\rm TP}(t)$?}}
-::It could be a DSB&ndash;AM of a sinusoidal signal with cosinusoidal carrier and modulation degree $m=0.8$, in which the upper sideband is attenuated by a factor of 2. The equivalent lowpass signal $x_{\rm TP}(t)$ has an elliptical trace in the complex plane.
+::It could be a DSB&ndash;AM of a sinusoidal signal with cosinusoidal carrier and modulation degree $m=0.8$, in which the upper sideband is attenuated by a factor of 2. The equivalent low-pass signal $x_{\rm TP}(t)$ has an elliptical trace in the complex plane.
 ==Applet Manual==

@@ Line 48: / Line 48: @@
 Besides the physical signal $x(t)\ \circ\!\!-\!\!\!-\!\!\!-\!\!\bullet\, \ X(f)$, one can also use the following descriptions of bandpass signals:
-*the analytic signal $x_+(t)\ \circ\!\!-\!\!\!-\!\!\!-\!\!\bullet\, \ X_+(f)$, see next page,
+*the analytic signal $x_+(t)\ \circ\!\!-\!\!\!-\!\!\!-\!\!\bullet\, \ X_+(f)$, see next section,
 *the equivalent lowpass signal &nbsp; (in German: &nbsp; äquivalentes '''T'''ief '''P'''ass&ndash;Signal) $x_{\rm TP}(t)\ \circ\!\!-\!\!\!-\!\!\!-\!\!\bullet\, \ X_{\rm TP}(f)$, <br>see Applet [[Applets:Physical_Signal_%26_Equivalent_Low-pass_Signal|Physical Signal & Equivalent Lowpass signal]].
 <br><br>

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-{{LntAppletLinkEn|physAnSignal_en}}
+{{LntAppletLink|physAnSignal_en}}  &nbsp; &nbsp; &nbsp; &nbsp; [https://www.lntwww.de/Applets:Physikalisches_Signal_%26_Analytisches_Signal '''English Applet with German WIKI description''']
 ==Applet Description==
 <br>
@@ Line 300: / Line 299: @@
 ==Once again:&nbsp; Open Applet in new Tab==
-{{LntAppletLinkEn|physAnSignal_en}}
+{{LntAppletLink|physAnSignal_en}}  &nbsp; &nbsp; &nbsp; &nbsp; [https://www.lntwww.de/Applets:Physikalisches_Signal_%26_Analytisches_Signal '''English Applet with German WIKI description''']

@@ Line 11: / Line 11: @@
 The nomenclature is also adapted to this case:
-* $x_{\rm O}(t)$ denotes the "upper sideband&rdquo; &nbsp; (in German: &nbsp; '''O'''beres Seitenband) with the amplitude $A_{\rm O}= A_{\rm N}/2$, the frequency $f_{\rm O} = f_{\rm T} + f_{\rm N}$ and the phase $\varphi_{\rm O} = \varphi_{\rm T} + \varphi_{\rm N}$.
+* $x_{\rm O}(t)$ denotes the "upper sideband" &nbsp; (in German: &nbsp; '''O'''beres Seitenband) with the amplitude $A_{\rm O}= A_{\rm N}/2$, the frequency $f_{\rm O} = f_{\rm T} + f_{\rm N}$ and the phase $\varphi_{\rm O} = \varphi_{\rm T} + \varphi_{\rm N}$.
-*Similarly, for the "lower sideband&rdquo; &nbsp; (in German: &nbsp; '''U'''nteres Seitenband) $x_{\rm U}(t)$ with $f_{\rm U} = f_{\rm T} - f_{\rm N}$, $A_{\rm U}= A_{\rm O}$ and $\varphi_{\rm U} = -\varphi_{\rm O}$.
+*Similarly, for the "lower sideband" &nbsp; (in German: &nbsp; '''U'''nteres Seitenband) $x_{\rm U}(t)$ with $f_{\rm U} = f_{\rm T} - f_{\rm N}$, $A_{\rm U}= A_{\rm O}$ and $\varphi_{\rm U} = -\varphi_{\rm O}$.
@@ Line 151: / Line 151: @@
 :$$x(t) = x_{\rm U}(t) + x_{\rm T}(t) + x_{\rm O}(t) = A_{\rm U}\cdot \cos\left(2\pi f_{\rm U}\cdot t- \varphi_{\rm U}\right)+A_{\rm T}\cdot \cos\left(2\pi f_{\rm T}\cdot t- \varphi_{\rm T}\right)+A_{\rm O}\cdot \cos\left(2\pi f_{\rm O}\cdot t- \varphi_{\rm O}\right). $$
 * Each of the three harmonic oscillations $x_{\rm T}(t)$, $x_{\rm U}(t)$ and $x_{\rm O}(t)$ is represented by an amplitude $(A)$, a frequency $(f)$ and a phase value $(\varphi)$.
-*The indices are based on the ''Double-sideband Amplitude Modulation'' method. "T&rdquo; stands for "carrier&rdquo;, "U&rdquo; for "lower sideband&rdquo; and "O&rdquo; for "upper Sideband&rdquo;.
+*The indices are based on the ''Double-sideband Amplitude Modulation'' method. "T" stands for "carrier", "U" for "lower sideband" and "O" for "upper Sideband".
 *Accordingly, $f_{\rm U} < f_{\rm T}$ and $f_{\rm O} > f_{\rm T}$. There are no restrictions for the amplitudes and phases.
@@ Line 178: / Line 178: @@
 *A task description is displayed.
 *Parameter values are adjusted.
-*Solution after pressing "Hide solition&rdquo;.
+*Solution after pressing "Hide solition".
-The number "0&rdquo; will reset the program and output a text with further explanation of the applet.
+The number "0" will reset the program and output a text with further explanation of the applet.
 <br clear=all>
 In the following, $\rm Green$ denotes the lower sideband &nbsp; &rArr; &nbsp; $\big (A_{\rm U}, f_{\rm U}, \varphi_{\rm U}\big )$, &nbsp;
@@ Line 235: / Line 235: @@
 '''(7)''' &nbsp; &nbsp; Now let &nbsp; $\text{Red:} \hspace{0.15cm} A_{\rm T} = 1\ \text{V}, \ f_{\rm T} = 100 \ \text{kHz}, \ \varphi_{\rm T} = 0^\circ$, &nbsp;  $\text{Green:} \hspace{0.15cm} A_{\rm U} = 0$, &nbsp;   $\text{Blue:} \hspace{0.15cm} A_{\rm O} = 0.8\ \text{V}, \ f_{\rm O} = 120 \ \text{kHz}, \ \varphi_{\rm O} = 90^\circ$.
-:Which constellation is described here? Which figure is given for the equivalent low-pass signal $x_{\rm TP}(t)$? &nbsp; &rArr; &nbsp; "locus&rdquo;? <br>What changes with $A_{\rm U} = 0.8\ \text{V}$ and $A_{\rm O} = 0$?}}
+:Which constellation is described here? Which figure is given for the equivalent low-pass signal $x_{\rm TP}(t)$? &nbsp; &rArr; &nbsp; "locus"? <br>What changes with $A_{\rm U} = 0.8\ \text{V}$ and $A_{\rm O} = 0$?}}
 ::In both cases, it is a [https://en.wikipedia.org/wiki/Single-sideband_modulation Single-sideband Amplitude Modulation] (SSB&ndash;AM) with the modulation degree $\mu = 0.8$ (in SSB we denote the degree of modulation with $\mu$ instead of $m$). The carrier signal is cosinusoidal and the message signal is sinusoidal. The equivalent low-pass signal $x_{\rm TP}(t)$ has a circular course in the complex plane.
@@ Line 270: / Line 270: @@
 &nbsp; &nbsp; '''(D)''' &nbsp; &nbsp; Control elements: &nbsp; Start &ndash; Step &ndash; Pause/Continue &ndash; Reset
-&nbsp; &nbsp; '''(E)''' &nbsp; &nbsp; Speed of animation: &nbsp; "Speed&rdquo; &nbsp; &rArr; &nbsp; Values: 1, 2, 3
+&nbsp; &nbsp; '''(E)''' &nbsp; &nbsp; Speed of animation: &nbsp; "Speed" &nbsp; &rArr; &nbsp; Values: 1, 2, 3
-&nbsp; &nbsp; '''(F)''' &nbsp; &nbsp; "Trace&rdquo; &nbsp; &rArr; &nbsp;  On or Off, trace of complex signal values $x_{\rm +}(t)$
+&nbsp; &nbsp; '''(F)''' &nbsp; &nbsp; "Trace" &nbsp; &rArr; &nbsp;  On or Off, trace of complex signal values $x_{\rm +}(t)$
 &nbsp; &nbsp; '''(G)''' &nbsp; &nbsp; Numerical output of the time $t$ and the signal values &nbsp;${\rm Re}[x_{\rm +}(t)] = x(t)$&nbsp; and &nbsp;${\rm Im}[x_{\rm +}(t)]$
@@ Line 278: / Line 278: @@
 &nbsp; &nbsp; '''(H)''' &nbsp; &nbsp; Variations for the graphical representation
-$\hspace{1.5cm}$Zoom&ndash;Functions "$+$&rdquo; (Enlarge), "$-$&rdquo; (Decrease) and $\rm o$ (Reset to default)
+$\hspace{1.5cm}$Zoom&ndash;Functions "$+$" (Enlarge), "$-$" (Decrease) and $\rm o$ (Reset to default)
-$\hspace{1.5cm}$Move with "$\leftarrow$&rdquo; (Section to the left, ordinate to the right),  "$\uparrow$&rdquo; "$\downarrow$&rdquo; and "$\rightarrow$&rdquo;
+$\hspace{1.5cm}$Move with "$\leftarrow$" (Section to the left, ordinate to the right),  "$\uparrow$" "$\downarrow$" and "$\rightarrow$"
 &nbsp; &nbsp; '''(I)''' &nbsp; &nbsp; Experiment section:&nbsp; Task selection and task
@@ Line 295: / Line 295: @@
 ==About the Authors==
 This interactive calculation was designed and realized at the&nbsp;  [https://www.ei.tum.de/en/lnt/home//startseite Institute for Communications Engineering]&nbsp; of the&nbsp;  [https://www.tum.de/ Technical University of Munich] .
-*The original version was created in 2005 by&nbsp; [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Ji_Li_.28Bachelorarbeit_EI_2003.2C_Diplomarbeit_EI_2005.29|Ji Li]]&nbsp; as part of her Diploma thesis using  "FlashMX&ndash;Actionscript&rdquo;&nbsp; (Supervisor:&nbsp; [[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]]).
+*The original version was created in 2005 by&nbsp; [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Ji_Li_.28Bachelorarbeit_EI_2003.2C_Diplomarbeit_EI_2005.29|Ji Li]]&nbsp; as part of her Diploma thesis using  "FlashMX&ndash;Actionscript"&nbsp; (Supervisor:&nbsp; [[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 2018 this Applet was redesigned and updated to "HTML5&rdquo; by&nbsp; [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Xiaohan_Liu_.28Bachelorarbeit_2018.29|Xiaohan Liu]]&nbsp; as part of her Bachelor's thesis (Supervisor: [[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]]).
+*In 2018 this Applet was redesigned and updated to "HTML5" by&nbsp; [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Xiaohan_Liu_.28Bachelorarbeit_2018.29|Xiaohan Liu]]&nbsp; as part of her Bachelor's thesis (Supervisor: [[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]]).
 ==Once again:&nbsp; Open Applet in new Tab==
 {{LntAppletLinkEn|physAnSignal_en}}

← Older revision		Revision as of 14:10, 1 April 2021
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	==Once again:  Open Applet in new Tab==		==Once again:  Open Applet in new Tab==

−	{{LntAppletLinkEn\|physAnSignal_en}}	+	{{LntAppletLinkEn\|physAnSignal_en}}
−
−	~~[[Category:Applets\|^Verzerrungen^]]~~

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 ==About the Authors==
-This interactive calculation was designed and realized at the&nbsp;  [http://www.lnt.ei.tum.de/startseite Lehrstuhl für Nachrichtentechnik]&nbsp; of the&nbsp;  [https://www.tum.de/ Technical University of Munich] .
+This interactive calculation was designed and realized at the&nbsp;  [https://www.ei.tum.de/en/lnt/home//startseite Institute for Communications Engineering]&nbsp; of the&nbsp;  [https://www.tum.de/ Technical University of Munich] .
 *The original version was created in 2005 by&nbsp; [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Ji_Li_.28Bachelorarbeit_EI_2003.2C_Diplomarbeit_EI_2005.29|Ji Li]]&nbsp; as part of her Diploma thesis using  &bdquo;FlashMX&ndash;Actionscript&rdquo;&nbsp; (Supervisor:&nbsp; [[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 2018 this Applet was redesigned and updated to &bdquo;HTML5&rdquo; by&nbsp; [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Xiaohan_Liu_.28Bachelorarbeit_2018.29|Xiaohan Liu]]&nbsp; as part of her Bachelor's thesis (Supervisor: [[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]]).