Applets:Sampling of Analog Signals and Signal Reconstruction - Revision history

Noah at 17:10, 26 April 2023

2023-04-26T17:10:51Z

Noah at 17:10, 26 April 2023

2023-04-26T17:10:29Z

Noah at 17:05, 26 April 2023

2023-04-26T17:05:42Z

Guenter at 15:26, 21 April 2023

2023-04-21T15:26:00Z

Guenter at 14:26, 21 April 2023

2023-04-21T14:26:08Z

Guenter at 16:02, 20 April 2023

2023-04-20T16:02:33Z

Noah at 14:30, 15 April 2023

2023-04-15T14:30:57Z

Guenter at 12:40, 14 April 2023

2023-04-14T12:40:26Z

Guenter at 16:12, 10 April 2023

2023-04-10T16:12:09Z

Noah at 22:40, 26 March 2023

2023-03-26T22:40:04Z

@@ Line 319: / Line 319: @@
 ::*Sampled signal&nbsp; $x_{\rm A}(t)$ &nbsp; &rArr; &nbsp; blue,
 ::*Reconstructed signal&nbsp; $y(t)$ &nbsp; &rArr; &nbsp; green,
-::*Differential signal&nbsp; $\varepsilon(t)=y(t) - x(t)$ &nbsp; &rArr; &nbsp; purple,
+::*Differential signal&nbsp; $\varepsilon(t)=y(t) - x(t)$ &nbsp; &rArr; &nbsp; purple
 &nbsp; &nbsp; '''(F)''' &nbsp; &nbsp; Graphical output area for frequency domain:
@@ Line 325: / Line 325: @@
 ::*$X_{\rm A}(f)$ &nbsp; &rArr; &nbsp; blue,
 ::*$Y(f)$ &nbsp; &rArr; &nbsp; green,
-::*$E(f)=Y(f) - X(f)$ &nbsp; &rArr; &nbsp; purple.
+::*$E(f)=Y(f) - X(f)$ &nbsp; &rArr; &nbsp; purple
 &nbsp; &nbsp; '''(G)''' &nbsp; &nbsp; Exercise selection

@@ Line 327: / Line 327: @@
 ::*$E(f)=Y(f) - X(f)$ &nbsp; &rArr; &nbsp; purple.
-&nbsp; &nbsp; '''(G)''' &nbsp; &nbsp; Exercise selection.
+&nbsp; &nbsp; '''(G)''' &nbsp; &nbsp; Exercise selection
 &nbsp; &nbsp; '''(H)''' &nbsp; &nbsp; Questions and solutions

@@ Line 300: / Line 300: @@
 [[File:Exercise_Abtast_v2.png|right|600px|frame|Screenshot]]
-&nbsp; &nbsp; '''(A)''' &nbsp; &nbsp; Auswahl eines der vier vorgegebenen Quellensignale, <br>  &nbsp; &nbsp; &nbsp;  &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  Einstellung von Amplituden, Frequenzen und Phasen
+&nbsp; &nbsp; '''(A)''' &nbsp; &nbsp; Selection of one of the four given source signals, <br> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; Adjustment of amplitudes, frequencies and phases.
-&nbsp; &nbsp; '''(B)''' &nbsp; &nbsp; Ausgabe aller eingestellten Parameter des Quellensignals:
+&nbsp; &nbsp; '''(B)''' &nbsp; &nbsp; Output of all set parameters of the source signal:
-&nbsp; &nbsp; '''(C)''' &nbsp; &nbsp; Parameter für Abtastung & Signalrekonstrukion:
+&nbsp; &nbsp; '''(C)''' &nbsp; &nbsp; Sampling & signal reconstruction parameters:
-::*Abtastfrequenz&nbsp; $f_{\rm A}$,&nbsp;
+::*Sampling frequency&nbsp; $f_{\rm A}$,&nbsp;
-::*Grenzfrequenz des Empfangsfilters&nbsp; $f_{\rm G}$,
+::*Limit frequency of the receiving filter&nbsp; $f_{\rm G}$,
-::*Rolloff-Faktors des Empfangsfilters&nbsp; $r$,
+::*Rolloff factor of the receiving filter&nbsp; $r$,
-:::&rArr; &nbsp; Trapez&ndash;Eckfrequenzen:&nbsp; $f_{1,\ 2} = f_{\rm G}\cdot (1\mp r)$
+:::&rArr; &nbsp; Trapezoidal&ndash;corner frequencies:&nbsp; $f_{1,\ 2} = f_{\rm G}\cdot (1\mp r)$
-&nbsp; &nbsp; '''(D)''' &nbsp; &nbsp; Numerische Ergebnisausgabe:
+&nbsp; &nbsp; '''(D)''' &nbsp; &nbsp; Numerical result output:
-::*Signalleistung&nbsp; $P_{x}$
+::*Signal power&nbsp; $P_{x}$
-::*Verzerrungsleistung&nbsp; $P_{\varepsilon}$
+::*Distortion power&nbsp; $P_{\varepsilon}$
-::*Signal-zu-Verzerrung-Verhältnis&nbsp; $10 \cdot \lg \ P_{x}/P_{\varepsilon}$
+::*Signal to distortion ratio&nbsp; $10 \cdot \lg \ P_{x}/P_{\varepsilon}$
-&nbsp; &nbsp; '''(E)''' &nbsp; &nbsp; Grafischer Ausgabebereich für den Zeitbereich:
+&nbsp; &nbsp; '''(E)''' &nbsp; &nbsp; Graphical output range for time domain:
-::*Quellensignal&nbsp; $x(t)$ &nbsp; &rArr; &nbsp; blau,
+::*Source signal&nbsp; $x(t)$ &nbsp; &rArr; &nbsp; blue,
-::*abgetastetes Signal&nbsp; $x_{\rm A}(t)$ &nbsp; &rArr; &nbsp; blau,
+::*Sampled signal&nbsp; $x_{\rm A}(t)$ &nbsp; &rArr; &nbsp; blue,
-::*rekonstruiertes Signal&nbsp; $y(t)$ &nbsp; &rArr; &nbsp; grün,
+::*Reconstructed signal&nbsp; $y(t)$ &nbsp; &rArr; &nbsp; green,
-::*Differenzsignal&nbsp; $\varepsilon(t)=y(t) - x(t)$ &nbsp; &rArr; &nbsp; violett,
+::*Differential signal&nbsp; $\varepsilon(t)=y(t) - x(t)$ &nbsp; &rArr; &nbsp; purple,
-&nbsp; &nbsp; '''(F)''' &nbsp; &nbsp; Grafischer Ausgabebereich für den Frequenzbereich:
+&nbsp; &nbsp; '''(F)''' &nbsp; &nbsp; Graphical output area for frequency domain:
-::*$X(f)$ &nbsp; &rArr; &nbsp; blau,
+::*$X(f)$ &nbsp; &rArr; &nbsp; blue,
-::*$X_{\rm A}(f)$ &nbsp; &rArr; &nbsp; blau,
+::*$X_{\rm A}(f)$ &nbsp; &rArr; &nbsp; blue,
-::*$Y(f)$ &nbsp; &rArr; &nbsp; grün,
+::*$Y(f)$ &nbsp; &rArr; &nbsp; green,
-::*$E(f)=Y(f) - X(f)$ &nbsp; &rArr; &nbsp; violett.
+::*$E(f)=Y(f) - X(f)$ &nbsp; &rArr; &nbsp; purple.
-&nbsp; &nbsp; '''(G)''' &nbsp; &nbsp; Aufgabenauswahl
+&nbsp; &nbsp; '''(G)''' &nbsp; &nbsp; Exercise selection.
-&nbsp; &nbsp; '''(H)''' &nbsp; &nbsp; Fragen und Lösungen
+&nbsp; &nbsp; '''(H)''' &nbsp; &nbsp; Questions and solutions
 <br clear=all>
 ==About the Authors==

@@ Line 298: / Line 298: @@
 ==Applet Manual==
-[[File:Exercise_Abtast_v2.png|right|600px|frame|Screenshot '''Korrektur''']]&nbsp; &nbsp; '''(A)''' &nbsp; &nbsp; Auswahl:
+[[File:Exercise_Abtast_v2.png|right|600px|frame|Screenshot]]
-::*Kohärent,
+&nbsp; &nbsp; '''(A)''' &nbsp; &nbsp; Auswahl eines der vier vorgegebenen Quellensignale, <br>  &nbsp; &nbsp; &nbsp;  &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;  Einstellung von Amplituden, Frequenzen und Phasen
-&nbsp; &nbsp; '''(B)''' &nbsp; &nbsp; Parametereingabe:&nbsp;
+&nbsp; &nbsp; '''(B)''' &nbsp; &nbsp; Ausgabe aller eingestellten Parameter des Quellensignals:
-::*$\sigma_{\rm AWGN}$,&nbsp;
-::*$s_0$,&nbsp;
+&nbsp; &nbsp; '''(C)''' &nbsp; &nbsp; Parameter für Abtastung & Signalrekonstrukion:
-::*$E_{\rm S}/N_0$,&nbsp;
+::*Abtastfrequenz&nbsp; $f_{\rm A}$,&nbsp;
-::*$G_{\rm opt}$
+::*Grenzfrequenz des Empfangsfilters&nbsp; $f_{\rm G}$,
-&nbsp; &nbsp; '''(C)''' &nbsp; &nbsp; Numerischer Ausgabebereich der Wahrscheinlichkeiten
+&nbsp; &nbsp; '''(D)''' &nbsp; &nbsp; Numerische Ergebnisausgabe:
-&nbsp; &nbsp; '''(D)''' &nbsp; &nbsp; Grafischer Ausgabebereich der WDF-Anteile
+&nbsp; &nbsp; '''(H)''' &nbsp; &nbsp; Fragen und Lösungen
 <br clear=all>
 ==About the Authors==

@@ Line 300: / Line 300: @@
 <br>
-[[File:Exercise_Abtast_v2.png|right|600px|frame|Screenshot '''Korrektur''']]
+[[File:Exercise_Abtast_v2.png|right|600px|frame|Screenshot '''Korrektur''']]&nbsp; &nbsp; '''(A)''' &nbsp; &nbsp; Auswahl:
 &nbsp; &nbsp; '''(A)''' &nbsp; &nbsp; Selection: &nbsp; Encoding<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;(binary,&nbsp; quaternary,&nbsp; AMI&ndash;code,&nbsp; duobinary code).

@@ Line 301: / Line 301: @@
 '''Korrektur'''
 [[File:Anleitung_abtast.png|right|600px]]
-&nbsp; &nbsp; '''(A)''' &nbsp; &nbsp; Auswahl: &nbsp; Codierung <br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;(binär,&nbsp; quaternär,&nbsp; AMI&ndash;Code,&nbsp; Duobinärcode)
+&nbsp; &nbsp; '''(A)''' &nbsp; &nbsp; Selection: &nbsp; Encoding<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;(binary,&nbsp; quaternary,&nbsp; AMI&ndash;code,&nbsp; duobinary code).
-&nbsp; &nbsp; '''(B)''' &nbsp; &nbsp; Auswahl: &nbsp; Detektionsgrundimpuls<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (nach Gauß&ndash;TP,&nbsp; CRO&ndash;Nyquist,&nbsp; nach Spalt&ndash;TP}
+&nbsp; &nbsp; '''(B)''' &nbsp; &nbsp; Selection: &nbsp; Detection base pulse<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (by Gaussian&ndash;LP,&nbsp; CRO&ndash;Nyquist,&nbsp; by slit&ndash;LP}
-&nbsp; &nbsp; '''(C)''' &nbsp; &nbsp; Prametereingabe zu&nbsp; '''(B)'''<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;(Grenzfrequenz,&nbsp; Rolloff&ndash;Faktor,&nbsp; Rechteckdauer)
+&nbsp; &nbsp; '''(C)''' &nbsp; &nbsp; Parameter input to&nbsp; '''(B)'''<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;(cutoff frequency,&nbsp; rolloff&ndash;factor,&nbsp; rectangular wave duration)
-&nbsp; &nbsp; '''(D)''' &nbsp; &nbsp; Steuerung der Augendiagrammdarstellung<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;(Start,&nbsp; Pause/Weiter,&nbsp; Einzelschritt,&nbsp; Gesamt,&nbsp; Reset)
+&nbsp; &nbsp; '''(D)''' &nbsp; &nbsp; Eye diagram display control<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;(start,&nbsp; pause/continue,&nbsp; single step,&nbsp; total,&nbsp; reset).
-&nbsp; &nbsp; '''(E)''' &nbsp; &nbsp; Geschwindigkeit der Augendiagrammdarstellung
+&nbsp; &nbsp; '''(E)''' &nbsp; &nbsp; Velocity of the eye diagram representation.
-&nbsp; &nbsp; '''(F)''' &nbsp; &nbsp; Darstellung:&nbsp; Detektionsgrundimpuls &nbsp;$g_d(t)$
+&nbsp; &nbsp; '''(F)''' &nbsp; &nbsp; Representation:&nbsp; Detection ground momentum &nbsp;$g_d(t)$
-&nbsp; &nbsp; '''(G)''' &nbsp; &nbsp; Darstellung:&nbsp; Detektionsnutzsignal &nbsp;$d_{\rm S}(t - \nu \cdot T)$
+&nbsp; &nbsp; '''(G)''' &nbsp; &nbsp; Representation:&nbsp; detection useful signal &nbsp;$d_{\rm S}(t - \nu \cdot T)$
-&nbsp; &nbsp; '''(H)''' &nbsp; &nbsp; Darstellung:&nbsp; Augendiagramm im Bereich &nbsp;$\pm T$
+&nbsp; &nbsp; '''(H)''' &nbsp; &nbsp; Representation:&nbsp; Eye diagram in the range &nbsp;$\pm T$
-&nbsp; &nbsp; '''( I )''' &nbsp; &nbsp; Numerikausgabe:&nbsp; $ö_{\rm norm}$&nbsp; (normierte Augenöffnung)
+&nbsp; &nbsp; '''( I )'''' &nbsp; &nbsp; Numerical output:&nbsp; $ö_{\rm norm}$&nbsp; (normalized eye opening).
-&nbsp; &nbsp; '''(J)''' &nbsp; &nbsp; Prametereingabe &nbsp;$10 \cdot \lg \ E_{\rm B}/N_0$&nbsp; für&nbsp; '''(K)'''
+&nbsp; &nbsp; '''(J)'''' &nbsp; &nbsp; Parameter input &nbsp;$10 \cdot \lg \ E_{\rm B}/N_0$&nbsp; for&nbsp; '''(K)'''
-&nbsp; &nbsp; '''(K)''' &nbsp; &nbsp; Numerikausgabe:&nbsp; $\sigma_{\rm norm}$&nbsp; (normierter Rauscheffektivwert)
+&nbsp; &nbsp; '''(K)'''' &nbsp; &nbsp; Numeric output:&nbsp; $\sigma_{\rm norm}$&nbsp; (normalized noise rms).
-&nbsp; &nbsp; '''(L)''' &nbsp; &nbsp; Numerikausgabe:&nbsp; $p_{\rm U}$&nbsp; (ungünstigste Fehlerwahrscheinlichkeit)
+&nbsp; &nbsp; '''(L)'''' &nbsp; &nbsp; Numeric output:&nbsp; $p_{\rm U}$&nbsp; (worst case error probability)
-&nbsp; &nbsp; '''(M)''' &nbsp; &nbsp; Bereich für die Versuchsdurchführung: &nbsp;  Aufgabenauswahl
+&nbsp; &nbsp; '''(M)'''' &nbsp; &nbsp; Range for experimental performance: &nbsp; Task selection.
-&nbsp; &nbsp; '''(N)''' &nbsp; &nbsp; Bereich für die Versuchsdurchführung: &nbsp;  Aufgabenstellung
+&nbsp; &nbsp; '''(N)'''' &nbsp; &nbsp; Range for the execution of experiments: &nbsp; Task selection
-&nbsp; &nbsp; '''(O)''' &nbsp; &nbsp; Bereich für die Versuchsdurchführung: &nbsp;  Musterlösung einblenden
+&nbsp; &nbsp; '''(O)'''' &nbsp; &nbsp; Range for carrying out the experiment: &nbsp; Show sample solution
 <br clear=all>
 ==About the Authors==

@@ Line 147: / Line 147: @@
 ===Signal reconstruction===
-[[File:P_ID1123__Sig_T_5_1_S5a_neu.png|right|frame|Joint model of "signal sampling" and "signal reconstruction"]]
+[[File:EN_Sig_T_5_1_S2_v2.png|right|frame|Joint model of "signal sampling" and "signal reconstruction"]]
 Signal sampling is not an end in itself in a digital transmission system, but it must be reversed at some point&nbsp; For example, consider the following system:
 *The analog signal&nbsp; $x(t)$&nbsp; with bandwidth&nbsp; $B_{\rm NF}$&nbsp; is sampled as described above.

@@ Line 142: / Line 142: @@
 Sampling the signal at the sampling rate&nbsp; $f_{\rm A}\,\text{ = 20 kHz}$, i.e., at the respective spacing&nbsp; $T_{\rm A}\, = {\rm 50 \, &micro;s}$&nbsp; yields the periodic spectrum&nbsp; $X_{\rm A}(f)$ sketched below.
 *Since the Dirac delta functions are infinitely narrow, the sampled signal&nbsp; $x_{\rm A}(t)$&nbsp; also contains arbitrary high frequency components.
-*Correspondingly, the spectral function&nbsp; $X_{\rm A}(f)$&nbsp; of the sampled signal is extended to infinity}}.
+*Correspondingly, the spectral function&nbsp; $X_{\rm A}(f)$&nbsp; of the sampled signal is extended to infinity.}}