Applets:Physical Signal & Equivalent Lowpass Signal - Revision history

Guenter at 15:04, 13 April 2023

2023-04-13T15:04:56Z

Guenter at 15:03, 13 April 2023

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Guenter at 14:11, 13 April 2023

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Guenter at 15:44, 10 April 2023

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Noah at 22:35, 26 March 2023

2023-03-26T22:35:45Z

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Hwang at 16:07, 23 January 2023

2023-01-23T16:07:52Z

Guenter at 14:38, 13 January 2023

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Hwang at 06:32, 18 September 2022

2022-09-18T06:32:10Z

Javier: Text replacement - "”" to """

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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:EN_Sig_T_4_2_S1b.png|right|frame|spectral functions $X(f)$, $X_+(f)$ and $X_{\rm TP}(f)$|class=fit]]
+[[File:EN_Sig_T_4_2_S1c.png|right|frame|spectral functions $X(f)$, $X_+(f)$ and $X_{\rm TP}(f)$|class=fit]]
 :$$X_+(f)=\big[1+{\rm sign}(f)\big] \cdot X(f) = \left\{ {2 \cdot
 X(f) \; \hspace{0.2cm}\rm for\hspace{0.2cm} {\it f} > 0, \atop {\,\,\,\, \rm 0 \; \hspace{0.9cm}\rm for\hspace{0.2cm} {\it f} < 0.} }\right.$$

@@ Line 129: / Line 129: @@
 The graph is intended to illustrate this relationship, assuming $A_{\rm U} > A_{\rm O}$ &nbsp; &rArr; &nbsp;  the green pointer (for the lower sideband) is longer than the blue pointer (upper sideband). This is a snapshot at time $t_0$:
-[[File:Ortskurve_3_neu.png|center|frame|band-pass spectrum $X(f)$ '''Korrektur'''|class=fit]]
+[[File:EN_Sig_T_4_2_ortskurve.png|center|frame|band-pass spectrum $X(f)$|class=fit]]
 *For these system parameters, the top of the pointer cluster $x_{\rm TP}(t)$ &ndash; that is, the geometric sum of red, blue and green pointers &ndash; on an ellipse.

@@ Line 57: / Line 57: @@
 The '''analytic signal''' $x_+(t)$ belonging to the physical signal $x(t)$ is the time function whose spectrum fulfills the following property:
-[[File:Ortskurve_2.png|right|frame|spectral functions $X(f)$, $X_+(f)$ and $X_{\rm TP}(f)$ '''Korrektur'''|class=fit]]
+[[File:EN_Sig_T_4_2_S1b.png|right|frame|spectral functions $X(f)$, $X_+(f)$ and $X_{\rm TP}(f)$|class=fit]]
 :$$X_+(f)=\big[1+{\rm sign}(f)\big] \cdot X(f) = \left\{ {2 \cdot
 X(f) \; \hspace{0.2cm}\rm for\hspace{0.2cm} {\it f} > 0, \atop {\,\,\,\, \rm 0 \; \hspace{0.9cm}\rm for\hspace{0.2cm} {\it f} < 0.} }\right.$$

@@ Line 57: / Line 57: @@
 The '''analytic signal''' $x_+(t)$ belonging to the physical signal $x(t)$ is the time function whose spectrum fulfills the following property:
-[[File:Ortskurve_2.png|right|frame|spectral functions $X(f)$, $X_+(f)$ and $X_{\rm TP}(f)$ |class=fit]]
+[[File:Ortskurve_2.png|right|frame|spectral functions $X(f)$, $X_+(f)$ and $X_{\rm TP}(f)$ '''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 129: / Line 129: @@
 The graph is intended to illustrate this relationship, assuming $A_{\rm U} > A_{\rm O}$ &nbsp; &rArr; &nbsp;  the green pointer (for the lower sideband) is longer than the blue pointer (upper sideband). This is a snapshot at time $t_0$:
-[[File:Ortskurve_3_neu.png|center|frame|band-pass spectrum $X(f)$ |class=fit]]
+[[File:Ortskurve_3_neu.png|center|frame|band-pass spectrum $X(f)$ '''Korrektur'''|class=fit]]
 *For these system parameters, the top of the pointer cluster $x_{\rm TP}(t)$ &ndash; that is, the geometric sum of red, blue and green pointers &ndash; on an ellipse.

@@ Line 51: / Line 51: @@
 Beside 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 applet [[Applets:Physical_Signal_%26_Analytic_Signal|Physical Signal & Analytic Signal]],
-*the equivalent lowpass signal $x_{\rm TP}(t)\ \circ\!\!-\!\!\!-\!\!\!-\!\!\bullet\, \ X_{\rm TP}(f)$, see next page
+*the equivalent lowpass signal $x_{\rm TP}(t)\ \circ\!\!-\!\!\!-\!\!\!-\!\!\bullet\, \ X_{\rm TP}(f)$, see next section
 <br><br>

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-{{LntAppletLinkEn|physAnLPSignal_en}}
+{{LntAppletLink|physAnSignal_en}}  &nbsp; &nbsp; &nbsp; &nbsp; [https://www.lntwww.de/Applets:Physikalisches_Signal_%26_%C3%84quivalentes_TP-Signal '''English Applet with German WIKI description''']
 ==Applet Description==
 <br>
@@ Line 255: / Line 254: @@
 ==Once again: Open Applet in new Tab==
-{{LntAppletLinkEn|physAnLPSignal_en}}
+{{LntAppletLink|physAnSignal_en}}  &nbsp; &nbsp; &nbsp; &nbsp; [https://www.lntwww.de/Applets:Physikalisches_Signal_%26_%C3%84quivalentes_TP-Signal '''English Applet with German WIKI description''']

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 The reason for this is that a bandpass signal $x(t)$ is usually described by the equivalent lowpass signal $x_{\rm TP}(t)$ that the functions $a(t)$ and $\phi(t)$ are interpretable in both representations:
-*The amount $a(t)$ of the equivalent lowpass signal $x_{\rm TP}(t)$ indicates the (time-dependent) envelope of $x(t)$.
+*The magnitude $a(t)$ of the equivalent lowpass signal $x_{\rm TP}(t)$ indicates the (time-dependent) envelope of $x(t)$.
 *The phase $\phi(t)$ of $x_{\rm TP}(t)$ denotes the location of the zero crossings of $x(t)$, where:
 :&ndash; &nbsp; For $\phi(t)>0$ the zero crossing is earlier than its nominal position &nbsp; &rArr; &nbsp; the signal is leading here.
@@ Line 133: / Line 133: @@
 *For these system parameters, the top of the pointer cluster $x_{\rm TP}(t)$ &ndash; that is, the geometric sum of red, blue and green pointers &ndash; on an ellipse.
-* The amount $a(t_0) = \vert x_{\rm TP}(t_0) \vert$ is drawn in black in the left-hand diagram and the phase value $\phi(t_0) = \text{arc }x_{\rm TP}(t_0) > 0$ is indicated in brown color.
+* The magnitude $a(t_0) = \vert x_{\rm TP}(t_0) \vert$ is drawn in black in the left-hand diagram and the phase value $\phi(t_0) = \text{arc }x_{\rm TP}(t_0) > 0$ is indicated in brown color.
-*In the graph on the right, the amount $a(t_0) = \vert x_{\rm TP}(t_0) \vert$ of the equivalent low-pass signal indicates the envelope of the physical signal $x(t)$.
+*In the graph on the right, the magnitude $a(t_0) = \vert x_{\rm TP}(t_0) \vert$ of the equivalent low-pass signal indicates the envelope of the physical signal $x(t)$.
 * At $\phi(t) \equiv 0$, all zero crossings of $x(t)$ would occur at equidistant intervals. Because of $\phi(t_0)  > 0$, the signal is leading at the time $t_0$, that is: the zero crossings come earlier than the grid dictates. }}
@@ Line 157: / Line 157: @@
 :Consider and interpret the equivalent lowpass signal $x_{\rm TP}(t)$ and the physical signal $x(t)$. Which period $T_0$ recognizable?}}
-::&nbsp;The equivalent lowpass signal $x_{\rm TP}(t)$ takes from $x_{\rm TP}(t=0)=1\ \text{V}$ on the real axis values between $0.2\ \text{V}$ and $1.8\ \text{V}$  &nbsp; &rArr; &nbsp; phase $\phi(t) \equiv 0$.<br>&nbsp;The amount $|x_{\rm TP}(t)|$ indicates the envelope $a(t)$ of the physical signal $x(t)$. It holds $A_{\rm N} = 0.8\ \text{V}$ and $f_{\rm N} = 20\ \text{kHz}$: &nbsp; $a(t) = A_{\rm T}+ A_{\rm N} \cdot \sin(2\pi\cdot f_{\rm N} \cdot t)$.<br>&nbsp;Both $x_{\rm TP}(t)$ and $x(t)$ are periodically with the period $T_0 = 1/f_{\rm N} = 50\ \rm &micro; s$.
+::&nbsp;The equivalent lowpass signal $x_{\rm TP}(t)$ takes from $x_{\rm TP}(t=0)=1\ \text{V}$ on the real axis values between $0.2\ \text{V}$ and $1.8\ \text{V}$  &nbsp; &rArr; &nbsp; phase $\phi(t) \equiv 0$.<br>&nbsp;The magnitude $|x_{\rm TP}(t)|$ indicates the envelope $a(t)$ of the physical signal $x(t)$. It holds $A_{\rm N} = 0.8\ \text{V}$ and $f_{\rm N} = 20\ \text{kHz}$: &nbsp; $a(t) = A_{\rm T}+ A_{\rm N} \cdot \sin(2\pi\cdot f_{\rm N} \cdot t)$.<br>&nbsp;Both $x_{\rm TP}(t)$ and $x(t)$ are periodically with the period $T_0 = 1/f_{\rm N} = 50\ \rm &micro; s$.
 {{BlaueBox|TEXT=

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 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 35: / Line 35: @@
-The temporal process of $x_{\rm TP}(t)$ is also referred to below as "locus&rdquo;. The relationship between $x_{\rm TP}(t)$ and the physical bandpass signal $x(t)$ is given in the section and the associated analytic signal is $x_+(t)$ :
+The temporal process of $x_{\rm TP}(t)$ is also referred to below as "locus". The relationship between $x_{\rm TP}(t)$ and the physical bandpass signal $x(t)$ is given in the section and the associated analytic signal is $x_+(t)$ :
 :$$x_{\rm TP}(t) = x_{\rm +}(t)\cdot {\rm e}^{-{\rm j} \hspace{0.05cm}\cdot \hspace{0.05cm}2 \pi \cdot f_{\rm T}\cdot \hspace{0.05cm}t},$$
@@ Line 89: / Line 89: @@
 :$$x(t) = x_{\rm T}(t) + x_{\rm O}(t) + x_{\rm U}(t) = A_{\rm T}\cdot \cos\left(2\pi f_{\rm T}\cdot t- \varphi_{\rm T}\right)+A_{\rm O}\cdot \cos\left(2\pi f_{\rm O}\cdot t- \varphi_{\rm O}\right) + A_{\rm U}\cdot \cos\left(2\pi f_{\rm U}\cdot t- \varphi_{\rm U}\right). $$
 * 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 modulation method [[Modulation_Methods/Zweiseitenband-Amplitudenmodulation|double sideband amplitude modulation]]. "T&rdquo; stands for "carrier&rdquo;, "U&rdquo; for "lower sideband&rdquo; and "O&rdquo; for "upper Sideband&rdquo;. Similarly, $f_{\rm U} < f_{\rm T}$ and $f_{\rm O} > f_{\rm T}$. There are no restrictions for the amplitudes and phases.
+*The indices are based on the modulation method [[Modulation_Methods/Zweiseitenband-Amplitudenmodulation|double sideband amplitude modulation]]. "T" stands for "carrier", "U" for "lower sideband" and "O" for "upper Sideband". Similarly, $f_{\rm U} < f_{\rm T}$ and $f_{\rm O} > f_{\rm T}$. There are no restrictions for the amplitudes and phases.
@@ Line 142: / Line 142: @@
 *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 the further explanation of the applet.
+The number "0" will reset the program and output a text with the further explanation of the applet.
@@ Line 172: / Line 172: @@
 '''(4)''' &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;  $\text{Green:} \hspace{0.15cm} A_{\rm U} = 0.4 \text{V}, \ f_{\rm U} = 80 \ \text{kHz}, \  \varphi_{\rm U} = 0^\circ$,  &nbsp;   $\text{Blue:} \hspace{0.15cm} A_{\rm O} = 0.4\ \text{V}, \ f_{\rm O} = 120 \ \text{kHz}, \ \varphi_{\rm O} = 0^\circ$.
-:What are the characteristics of this system "DSB&ndash;AM, where the message signal and carrier are respectively cosinusoidal&rdquo;? What is the degree of modulation $m$?}}
+:What are the characteristics of this system "DSB&ndash;AM, where the message signal and carrier are respectively cosinusoidal"? What is the degree of modulation $m$?}}
 ::&nbsp;The equivalent lowpass signal $x_{\rm TP}(t)$ takes from $x_{\rm TP}(t=0)=1.8\ \text{V}$ on the real axis values between $0.2\ \text{V}$ and $1.8\ \text{V}$ &nbsp; &rArr; &nbsp; phase $\phi(t) \equiv 0$.<br>&nbsp;Except for the start state $x_{\rm TP}(t=0)$ same behavior as at the setting '''(1)'''. The degree of modulation is $m = 0.8$.
@@ Line 215: / Line 215: @@
 &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 oder 3
+&nbsp; &nbsp; '''(E)''' &nbsp; &nbsp; Speed of animation: &nbsp; "Speed" &nbsp; &rArr; &nbsp; Values: 1, 2 oder 3
-&nbsp; &nbsp; '''(F)''' &nbsp; &nbsp; "Trace&rdquo; &nbsp; &rArr; &nbsp;  On or Off, trace of equivalent lowpass signal &nbsp; $x_{\rm TP}(t)$
+&nbsp; &nbsp; '''(F)''' &nbsp; &nbsp; "Trace" &nbsp; &rArr; &nbsp;  On or Off, trace of equivalent lowpass signal &nbsp; $x_{\rm TP}(t)$
 &nbsp; &nbsp; '''(G)''' &nbsp; &nbsp; Numerical output: &nbsp; time $t$, the signal values &nbsp;${\rm Re}[x_{\rm TP}(t)]$ &nbsp;and&nbsp; ${\rm Im}[x_{\rm TP}(t)]$,
@@ Line 225: / Line 225: @@
 &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; "$\rightarrow$&rdquo;
+$\hspace{1.5cm}$Move with "$\leftarrow$" (Section to the left, ordinate to the right),  "$\uparrow$" "$\downarrow$" "$\rightarrow$"
 &nbsp; &nbsp; '''(I)''' &nbsp; &nbsp; Experiment section: &nbsp; Task selection and task
@@ Line 248: / Line 248: @@
 ==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]]).