Applets:Pulses and Spectra - Revision history

Guenter at 12:10, 21 April 2023

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Guenter at 12:09, 21 April 2023

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Guenter at 16:32, 20 April 2023

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Guenter at 12:36, 14 April 2023

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Noah at 18:20, 25 March 2023

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Noah at 17:44, 25 March 2023

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Noah at 16:48, 25 March 2023

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Noah at 19:31, 24 March 2023

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Noah at 18:48, 24 March 2023

2023-03-24T18:48:40Z

@@ Line 197: / Line 197: @@
 ==Applet Manual==
-<br>
 [[File:EN_Impulse_Man_neu.png|right|frame|Screenshot]]
 &nbsp; &nbsp; '''(A)''' &nbsp; &nbsp; Theme (changeable graphical user interface design)
 :* Dark: &nbsp; dark background&nbsp; (recommended by the authors)

@@ Line 198: / Line 198: @@
 ==Applet Manual==
 <br>
-[[File:EN_Impulse_Man_neu.png|right|frame|Screenshot '''Korrektur''' Pulses]]
+[[File:EN_Impulse_Man_neu.png|right|frame|Screenshot]]
 &nbsp; &nbsp; '''(A)''' &nbsp; &nbsp; Theme (changeable graphical user interface design)
 :* Dark: &nbsp; dark background&nbsp; (recommended by the authors)
@@ Line 205: / Line 205: @@
 :*  Protanopia: &nbsp; for users with pronounced red visual impairment
-&nbsp; &nbsp; '''(B)''' &nbsp; &nbsp; Preselection for pulse shape&nbsp; $x_1(t)$&nbsp; (red curve)
+&nbsp; &nbsp; '''(B)''' &nbsp; &nbsp; Preselection for pulse shape&nbsp; $x_1(t)$ &nbsp; &rArr; &nbsp; red curve
 &nbsp; &nbsp; '''(C)''' &nbsp; &nbsp; Parameter definition for&nbsp; $x_1(t)$&nbsp;
@@ Line 211: / Line 211: @@
 &nbsp; &nbsp; '''(D)''' &nbsp; &nbsp; Numeric output for&nbsp; $x_1(t_*)$&nbsp; and&nbsp; $X_1(f_*)$
-&nbsp; &nbsp; '''(E)''' &nbsp; &nbsp; Preselection for pulse shape&nbsp; $x_2(t)$&nbsp; (blue curve)
+&nbsp; &nbsp; '''(E)''' &nbsp; &nbsp; Preselection for pulse shape&nbsp; $x_2(t)$&nbsp; &rArr; &nbsp; blue curve
 &nbsp; &nbsp; '''(F)''' &nbsp; &nbsp; Parameter definition for&nbsp; $x_2(t)$&nbsp;
@@ Line 230: / Line 230: @@
 &nbsp; &nbsp; '''(N)''' &nbsp; &nbsp; Show and hide sample solution
+<br clear=all>
 ==About the Authors==

@@ Line 198: / Line 198: @@
 ==Applet Manual==
 <br>
-[[File:Exercise_impuls_v2.png|right|frame|Screenshot '''Korrektur''' Pulses]]
+[[File:EN_Impulse_Man_neu.png|right|frame|Screenshot '''Korrektur''' Pulses]]
 &nbsp; &nbsp; '''(A)''' &nbsp; &nbsp; Theme (changeable graphical user interface design)
 :* Dark: &nbsp; dark background&nbsp; (recommended by the authors)

@@ Line 198: / Line 198: @@
 ==Applet Manual==
 <br>
-[[File:Exercise_impuls.png |right|frame|Screenshot '''Korrektur''' Pulses]]
+[[File:Exercise_impuls_v2.png|right|frame|Screenshot '''Korrektur''' Pulses]]
 &nbsp; &nbsp; '''(A)''' &nbsp; &nbsp; Theme (changeable graphical user interface design)
 :* Dark: &nbsp; dark background&nbsp; (recommended by the authors)

@@ Line 198: / Line 198: @@
 ==Applet Manual==
 <br>
-[[File:Exercise_impuls.png |right|frame|Screenshot]]
+[[File:Exercise_impuls.png |right|frame|Screenshot '''Korrektur''' Pulses]]
 &nbsp; &nbsp; '''(A)''' &nbsp; &nbsp; Theme (changeable graphical user interface design)
 :* Dark: &nbsp; dark background&nbsp; (recommended by the authors)

@@ Line 83: / Line 83: @@
 *From this follows:&nbsp; $X(f)$&nbsp; contains instead of the&nbsp; ${\rm si}$-function the&nbsp; ${\rm si}^2$-function.
 *$X(f)$&nbsp; thus also has zeros at equidistant intervals&nbsp; $1/\rm f$&nbsp;.
-*The asymptotic decay of&nbsp; $X(f)$&nbsp; occurs here with&nbsp; $1/f^2$, while for comparison the rectangular momentum decays with&nbsp; $1/f$&nbsp;.
+*The asymptotic decay of&nbsp; $X(f)$&nbsp; occurs here with&nbsp; $1/f^2$, while for comparison the rectangular pulse decays with&nbsp; $1/f$&nbsp;.

@@ Line 26: / Line 26: @@
 *The relationship between the time function&nbsp; $x(t)$&nbsp; and the spectrum&nbsp; $X(f)$&nbsp; is given by the&nbsp; [[Signal_Representation/The_Fourier_Transform_and_its_Inverse#The_first_Fourier_integral|"first Fourier integral"]]&nbsp;:
 :$$X(f)={\rm FT} [x(t)] = \int_{-\infty}^{+\infty}x(t)\cdot {\rm e}^{-{\rm j}2\pi f t}\hspace{0.15cm} {\rm d}t\hspace{1cm}
-\rm FT\hspace{-0.1cm}: \ Fouriertransformation.$$
+\rm FT\hspace{-0.1cm}: \ Fourier \ transform.$$
-*Um aus der Spektralfunktion&nbsp; $X(f)$&nbsp; die Zeitfunktion&nbsp; $x(t)$&nbsp; berechnen zu können, benötigt man das&nbsp; [[Signal_Representation/The_Fourier_Transform_and_its_Inverse#The_second_Fourier_integral|"zweite Fourierintegral"]]:
+*In order to calculate the time function&nbsp; $x(f)$&nbsp; from the spectral function&nbsp; $x(t)$&nbsp; one needs the&nbsp; [[Signal_Representation/The_Fourier_Transform_and_its_Inverse#The_second_Fourier_integral|"second Fourier integral"]]:
 :$$x(t)={\rm IFT} [X(f)] = \int_{-\infty}^{+\infty}X(f)\cdot {\rm e}^{+{\rm j}2\pi f t}\hspace{0.15cm} {\rm d}f\hspace{1cm}
-{\rm IFT}\hspace{-0.1cm}: \rm  Inverse \ Fouriertransformation.$$
+{\rm IFT}\hspace{-0.1cm}: \rm  Inverse \ Fourier \ transform.$$
-*In allen Beispielen verwenden wir reelle und gerade Funktionen.&nbsp; Somit gilt:
+*In all examples we use real and even functions.&nbsp; Thus:
 :$$x(t)=\int_{-\infty}^{+\infty}X(f)\cdot \cos(2\pi ft) \hspace{0.15cm} {\rm d}f \ \ \circ\!\!-\!\!\!-\!\!\!-\!\!\bullet\ \ \ X(f)=\int_{-\infty}^{+\infty}x(t)\cdot \cos(2\pi ft) \hspace{0.15cm} {\rm d}t .$$
-*$x(t)$&nbsp; und&nbsp; $X(f)$&nbsp; haben unterschiedliche Einheiten, beispielsweise&nbsp; $x(t)$&nbsp; in&nbsp; $\rm V$,&nbsp; $X(f)$&nbsp; in&nbsp; $\rm V/Hz$.
+*$x(t)$&nbsp; and&nbsp; $X(f)$&nbsp; have different units, for example&nbsp; $x(t)$&nbsp; in&nbsp; $\rm V$,&nbsp; $X(f)$&nbsp; in&nbsp; $\rm V/Hz$.
-*Der Zusammenhang zwischen diesem Modul und dem ähnlich aufgebauten Applet&nbsp; [[Applets:Frequenzgang_und_Impulsantwort|"Frequenzgang & Impulsantwort"]]&nbsp; basiert auf dem&nbsp; [[Signal_Representation/The_Fourier_Transform_Theorems#Duality_Theorem|"Duality Theorem"]].
+*The relationship between this module and the similarly constructed applet&nbsp; [[Applets:Frequenzgang_und_Impulsantwort|"Frequency response & Impulse response"]]&nbsp; is based on the&nbsp; [[Signal_Representation/The_Fourier_Transform_Theorems#Duality_Theorem|"Duality Theorem"]].
-*Alle Zeiten sind auf eine Zeit&nbsp; $T$&nbsp; normiert und alle Frequenzen auf&nbsp; $1/T$ &nbsp; &rArr; &nbsp; die Spektralwerte&nbsp; $X(f)$&nbsp; müssen noch mit der Normierungszeit&nbsp; $T$&nbsp; multipliziert werden.
+*All times are normalized to a time&nbsp; $T$&nbsp; and all frequencies are normalized to&nbsp; $1/T$ &nbsp; &rArr; &nbsp; the spectral values&nbsp; $X(f)$&nbsp; still have to be multiplied by the normalization time&nbsp; $T$&nbsp;.
 {{GraueBox|TEXT=
-$\text{Beispiel:}$ &nbsp; Stellt man einen Rechteckimpuls mit Amplitude&nbsp; $A_1 = 1$&nbsp; und äquivalenter Impulsdauer&nbsp; $\Delta t_1 = 1$&nbsp; ein, so ist&nbsp; $x_1(t)$&nbsp; im Bereich&nbsp; $-0.5 < t < +0.5$&nbsp; gleich Eins und außerhalb dieses Bereichs gleich Null.&nbsp; Die Spektralfunktion&nbsp; $X_1(f)$&nbsp; verläuft&nbsp; $\rm si$&ndash;förmig mit&nbsp; $X_1(f= 0) = 1$&nbsp; und der ersten Nullstelle bei&nbsp; $f=1$.
+$\text{Example:}$ &nbsp; If one sets a rectangular pulse with amplitude&nbsp; $A_1 = 1$&nbsp; and equivalent pulse duration&nbsp; $\Delta t_1 = 1$&nbsp; then&nbsp; $x_1(t)$&nbsp; in the range&nbsp; $-0.5 < t < +0. 5$&nbsp; equal to one and outside this range equal to zero.&nbsp; The spectral function&nbsp; $X_1(f)$&nbsp; proceeds&nbsp; $\rm si$&ndash;shaped with&nbsp; $X_1(f= 0) = 1$&nbsp; and the first zero at&nbsp; $f=1$.
-*Soll mit dieser Einstellung ein Rechteckimpuls mit&nbsp; $A = K = 3 \ \rm V$&nbsp; und&nbsp; $\Delta t = T = 2 \ \rm ms$&nbsp; nachgebildet werden, dann sind alle Signalwerte mit&nbsp; $K = 3 \ \rm V$&nbsp; und alle Spektralwerte mit&nbsp; $K \cdot T = 0.006 \ \rm V/Hz$&nbsp; zu multiplizieren.
+*If a rectangular pulse with&nbsp; $A = K = 3 \ \rm V$&nbsp; and&nbsp; $\delta t = T = 2 \ \rm ms$&nbsp; is to be simulated with this setting, then all signal values with&nbsp; $K = 3 \ \rm V$&nbsp; and all spectral values with&nbsp; $K \cdot T = 0. 006 \ \rm V/Hz$&nbsp; to be multiplied by.
-*Der maximale Spektralwert ist dann&nbsp; $X(f= 0) = 0.006 \ \rm V/Hz$&nbsp; und die erste Nullstelle liegt bei&nbsp; $f=1/T = 0.5 \ \rm kHz$.}}
+*The maximum spectral value is then&nbsp; $X(f= 0) = 0.006 \ \rm V/Hz$&nbsp; and the first zero is at&nbsp; $f=1/T = 0.5 \ \rm kHz$.}}