Aufgaben:Exercise 2.1Z: About the Equivalent Bitrate - Revision history

Guenter at 14:54, 3 June 2022

2022-06-03T14:54:10Z

Hwang at 14:29, 23 May 2022

2022-05-23T14:29:22Z

Guenter at 16:05, 13 May 2022

2022-05-13T16:05:55Z

Guenter at 16:00, 13 May 2022

2022-05-13T16:00:22Z

Hwang at 15:41, 7 April 2022

2022-04-07T15:41:57Z

Guenter at 12:49, 4 April 2022

2022-04-04T12:49:21Z

Guenter: Guenter moved page Aufgaben:Aufgabe 2.1Z: Zur äquivalenten Bitrate to Aufgaben:Exercise 2.1Z: About the Equivalent Bitrate

2022-04-04T12:42:27Z

Guenter moved page Aufgabe 2.1Z: Zur äquivalenten Bitrate to Exercise 2.1Z: About the Equivalent Bitrate

Javier: Text replacement - "Category:Aufgaben zu Digitalsignalübertragung" to "Category:Digital Signal Transmission: Exercises"

2021-03-23T12:47:28Z

Text replacement - "Category:Aufgaben zu Digitalsignalübertragung" to "Category:Digital Signal Transmission: Exercises"

Javier: Text replacement - "[[Digitalsignalübertragung" to "[[Digital_Signal_Transmission"

2020-07-09T12:59:29Z

Text replacement - "[[Digitalsignalübertragung" to "[[Digital_Signal_Transmission"

Guenter at 10:48, 11 February 2019

2019-02-11T10:48:16Z

@@ Line 9: / Line 9: @@
 *This binary signal is coded symbol-by-symbol and results in the encoder signal &nbsp;$c(t)$ drawn below.
-*All possible code '''KORREKTUR: encoder''' symbols occur in the signal section of duration &nbsp;$6 \ \rm &micro; s$&nbsp; shown.
+*All possible encoder symbols occur in the signal section of duration &nbsp;$6 \ \rm &micro; s$&nbsp; shown.
 *The level number &nbsp;$M_{c}$&nbsp; and the symbol duration &nbsp;$T_{c}$&nbsp; can be used to specify the equivalent bit rate of the encoder signal:
 :$$R_c = \frac{{\rm log_2} (M_c)}{T_c} \hspace{0.05cm}.$$

@@ Line 9: / Line 9: @@
 *This binary signal is coded symbol-by-symbol and results in the encoder signal &nbsp;$c(t)$ drawn below.
-*All possible code symbols occur in the signal section of duration &nbsp;$6 \ \rm &micro; s$&nbsp; shown.
+*All possible code '''KORREKTUR: encoder''' symbols occur in the signal section of duration &nbsp;$6 \ \rm &micro; s$&nbsp; shown.
 *The level number &nbsp;$M_{c}$&nbsp; and the symbol duration &nbsp;$T_{c}$&nbsp; can be used to specify the equivalent bit rate of the encoder signal:
 :$$R_c = \frac{{\rm log_2} (M_c)}{T_c} \hspace{0.05cm}.$$

@@ Line 51: / Line 51: @@
 ===Solution===
 {{ML-Kopf}}
-'''(1)'''&nbsp; The bit duration $T_{q} = \underline{0.5\ \rm &micro; s}$ can be taken from the graphic.
+'''(1)'''&nbsp; The bit duration&nbsp; $T_{q} = \underline{0.5\ \rm &micro; s}$&nbsp; can be taken from the graphic.
-*Since the source is binary and redundancy-free, the following applies to the bit rate of the source: $R_{q}= 1/T_{q}\ \underline{= 2\ \rm Mbit/s}$.
+*Since the source is binary and redundancy-free,&nbsp; the following applies to the bit rate of the source:
-'''(2)'''&nbsp; For symbol-wise coding, $T_{c} = T_{q}$ always applies.
+'''(2)'''&nbsp; For symbol-wise coding,&nbsp; $T_{c} = T_{q}$&nbsp; always applies.
-*Thus, in the present example, $T_{c}\ \underline{ = 0.5\ \rm &micro; s}$ is also valid.
+*Thus,&nbsp; in the present example,&nbsp; $T_{c}\ \underline{ = 0.5\ \rm &micro; s}$ is valid.
-*The number of steps $M_{c}\ \underline{ = 3}$ can be read from the sketch below.
+*The level number&nbsp; $M_{c}\ \underline{ = 3}$&nbsp; can be read from the sketch below.
-'''(3)'''&nbsp; The symbol rate of the encoder signal is $2 \cdot 10^{6}$ ternary symbols per second.
+'''(3)'''&nbsp; The symbol rate of the encoder signal is&nbsp; $2 \cdot 10^{6}$&nbsp; ternary symbols per second.
-*For the equivalent bit rate, the following applies:
+*For the equivalent bit rate,&nbsp; the following applies:
 :$$R_c = \frac{{\rm log_2} (M_c)}{T_c} = \frac{{\rm log_2}(3)}{0.5\,\,{\rm \mu s}} = \frac{{\rm lg} (3)}{{\rm lg} (2) \cdot 0.5\,\,{\rm \mu s}}= \frac{1.585\,\,{\rm (bit)}}{0.5\,\,{\rm \mu s}}\hspace{0.15cm} \underline {\approx 3.17\,\,{\rm Mbit/s}} \hspace{0.05cm}.$$
-'''(4)'''&nbsp; For relative code redundancy, when the source is redundancy-free, the general rule is:
+'''(4)'''&nbsp; For relative code redundancy,&nbsp; when the source is redundancy-free,&nbsp; the general rule is:
 :$$ r_c = \frac{R_c - R_q}{R_c} = 1- \frac{R_q}{R_c}= 1- \frac{T_c}{T_q \cdot {\rm log_2} (M_c)}\hspace{0.05cm}.$$
-*In the case of the second order biploar code considered here, with parameters $T_{c} = T_{q}$ and $M_{c} = 3$, the following holds further:
+*In the case of the second order biploar code considered here,&nbsp; with parameters&nbsp; $T_{c} = T_{q}$&nbsp; and&nbsp; $M_{c} = 3$,&nbsp; the following holds:
 :$$r_c = 1- \frac{1}{{\rm log_2} (3)}\hspace{0.15cm}\underline {\approx 36.9 \% }\hspace{0.05cm}.$$

@@ Line 8: / Line 8: @@
 The upper diagram shows the source signal &nbsp;$q(t)$&nbsp; of a redundancy-free binary source with bit duration &nbsp;$T_{q}$&nbsp; and &nbsp;bit rate $R_{q}$. The two signal parameters &nbsp;$T_{q}$&nbsp; and &nbsp;$R_{q}$&nbsp; can be taken from the sketch.
-*This binary signal is coded symbol by symbol and results in the encoder signal &nbsp;$c(t)$ drawn below.
+*This binary signal is coded symbol-by-symbol and results in the encoder signal &nbsp;$c(t)$ drawn below.
-*All possible code symbols occur in the signal section of duration &nbsp;$6 \ \rm &micro; s$ shown.
+*All possible code symbols occur in the signal section of duration &nbsp;$6 \ \rm &micro; s$&nbsp; shown.
-*The number of steps &nbsp;$M_{c}$&nbsp; and the symbol duration &nbsp;$T_{c}$&nbsp; can be used to specify the equivalent bit rate of the encoder signal:
+*The level number &nbsp;$M_{c}$&nbsp; and the symbol duration &nbsp;$T_{c}$&nbsp; can be used to specify the equivalent bit rate of the encoder signal:
 :$$R_c = \frac{{\rm log_2} (M_c)}{T_c} \hspace{0.05cm}.$$
-From this, one obtains the relative redundancy of the code if one assumes, as here, that the source itself is redundancy-free:
+From this,&nbsp; one obtains the relative redundancy of the code if one assumes,&nbsp; as here,&nbsp; that the source itself is redundancy-free:
 :$$r_c = \frac{R_c - R_q}{R_c}\hspace{0.05cm}.$$
 Notes:
+*The exercise belongs to the chapter&nbsp;  [[Digital_Signal_Transmission/Basics_of_Coded_Transmission|"Basics of Coded Transmission"]].
-*The transmission code considered here is the second order bipolar code, but this is not important for the solution of this exercise.
+*The transmission code considered here is the second order bipolar code,&nbsp; but this is not important for the solution of this exercise.
@@ Line 32: / Line 28: @@
 <quiz display=simple>
-{Specify bit duration &nbsp;$(T_{q})$&nbsp; and bit rate &nbsp;$(R_{q})$&nbsp; of the source
+{Specify bit duration &nbsp;$(T_{q})$&nbsp; and bit rate &nbsp;$(R_{q})$&nbsp; of the source.
 |type="{}"}
 $T_{q}  \ = \ $ { 0.5 3% } $\ \rm &micro; s $
 $R_{q}  \ = \ $ { 2 3% } $\ \rm Mbit/s $
-{What are the symbol duration &nbsp;$(T_{c})$&nbsp; and number of steps &nbsp;$(M_{c})$&nbsp; of the encoder signal?
+{What are the symbol duration &nbsp;$(T_{c})$&nbsp; and level number &nbsp;$(M_{c})$&nbsp; of the encoder signal?
 |type="{}"}
 $T_{c} \ = \ $ { 0.5 3% } $\ \rm &micro; s $

@@ Line 1: / Line 1: @@
-{{quiz-Header|Buchseite=Digitalsignalübertragung/Grundlagen der codierten Übertragung
+{{quiz-Header|Buchseite=Digital_Signal_Transmission/Basics_of_Coded_Transmission
 }}
-[[File:P_ID1309__Dig_Z_2_1.png|right|frame|Quellensignal (oben) und Codersignal (unten)]]
+[[File:P_ID1309__Dig_Z_2_1.png|right|frame|Source signal (top) and encoder signal (bottom)]]
-Die obere Darstellung zeigt das Quellensignal &nbsp;$q(t)$&nbsp; einer redundanzfreien Binärquelle mit Bitdauer &nbsp;$T_{q}$&nbsp; und &nbsp;Bitrate $R_{q}$. Die beiden Signalparameter &nbsp;$T_{q}$&nbsp; und &nbsp;$R_{q}$&nbsp; können der Skizze entnommen werden.
+The upper diagram shows the source signal &nbsp;$q(t)$&nbsp; of a redundancy-free binary source with bit duration &nbsp;$T_{q}$&nbsp; and &nbsp;bit rate $R_{q}$. The two signal parameters &nbsp;$T_{q}$&nbsp; and &nbsp;$R_{q}$&nbsp; can be taken from the sketch.
-*Dieses Binärsignal wird symbolweise codiert und ergibt das unten gezeichnete Codersignal &nbsp;$c(t)$.
+*This binary signal is coded symbol by symbol and results in the encoder signal &nbsp;$c(t)$ drawn below.
-*Alle möglichen Codesymbole kommen in dem dargestellten Signalausschnitt der Dauer &nbsp;$6 \ \rm &micro; s$ vor.
+*All possible code symbols occur in the signal section of duration &nbsp;$6 \ \rm &micro; s$ shown.
-*Mit der Stufenzahl &nbsp;$M_{c}$&nbsp; und der Symboldauer &nbsp;$T_{c}$&nbsp; kann man die äquivalente Bitrate  des Codersignals angeben:
+*The number of steps &nbsp;$M_{c}$&nbsp; and the symbol duration &nbsp;$T_{c}$&nbsp; can be used to specify the equivalent bit rate of the encoder signal:
 :$$R_c = \frac{{\rm log_2} (M_c)}{T_c} \hspace{0.05cm}.$$
-Daraus erhält man die relative Redundanz des Codes, wenn man wie hier davon ausgeht, dass die Quelle selbst redundanzfrei ist:
+From this, one obtains the relative redundancy of the code if one assumes, as here, that the source itself is redundancy-free:
 :$$r_c = \frac{R_c - R_q}{R_c}\hspace{0.05cm}.$$
@@ Line 21: / Line 21: @@
-''Hinweise:''
+''Notes:''
-*Die Aufgabe gehört zum  Kapitel&nbsp;  [[Digital_Signal_Transmission/Grundlagen_der_codierten_Übertragung|Grundlagen der codierten Übertragung]].
+*The exercise belongs to the chapter&nbsp;  [[Digital_Signal_Transmission/Basics_of_Coded_Transmission|Basics of Coded Transmission]].
-*Bei dem hier betrachteten Übertragungscode handelt es sich um den Bipolarcode zweiter Ordnung, was jedoch für die Lösung dieser Aufgabe nicht von Bedeutung ist.
+*The transmission code considered here is the second order bipolar code, but this is not important for the solution of this exercise.
-===Fragebogen===
+===Questions===
 <quiz display=simple>
-{Geben Sie Bitdauer &nbsp;$(T_{q})$&nbsp; und Bitrate &nbsp;$(R_{q})$&nbsp; der Quelle an
+{Specify bit duration &nbsp;$(T_{q})$&nbsp; and bit rate &nbsp;$(R_{q})$&nbsp; of the source
 |type="{}"}
 $T_{q}  \ = \ $ { 0.5 3% } $\ \rm &micro; s $
 $R_{q}  \ = \ $ { 2 3% } $\ \rm Mbit/s $
-{Wie groß sind Symboldauer &nbsp;$(T_{c})$&nbsp; und Stufenzahl &nbsp;$(M_{c})$&nbsp; des Codersignals?
+{What are the symbol duration &nbsp;$(T_{c})$&nbsp; and number of steps &nbsp;$(M_{c})$&nbsp; of the encoder signal?
 |type="{}"}
 $T_{c} \ = \ $ { 0.5 3% } $\ \rm &micro; s $
 $M_{c} \ = \ $ { 3 3% }
-{Wie groß ist die äquivalente Bitrate &nbsp;$R_{c}$&nbsp; des Codersignals?
+{What is the equivalent bit rate &nbsp;$R_{c}$&nbsp; of the encoder signal?
 |type="{}"}
 $R_{c}  \ = \ $ { 3.17 3% } $\ \rm Mbit/s $
-{Geben Sie die relative Redundanz des Codes an.
+{Specify the relative redundancy of the code.
 |type="{}"}
 $r_{c} \ = \ $ { 36.9 3% } $\ \% $
@@ Line 53: / Line 53: @@
 </quiz>
-===Musterlösung===
+===Solution===
 {{ML-Kopf}}
-'''(1)'''&nbsp; Die Bitdauer $T_{q} = \underline{0.5\ \rm &micro; s}$ kann der Grafik entnommen werden.
+'''(1)'''&nbsp; The bit duration $T_{q} = \underline{0.5\ \rm &micro; s}$ can be taken from the graphic.
-*Da die Quelle binär und redundanzfrei ist, gilt für die Bitrate der Quelle: $R_{q}= 1/T_{q}\ \underline{= 2\ \rm Mbit/s}$.
+*Since the source is binary and redundancy-free, the following applies to the bit rate of the source: $R_{q}= 1/T_{q}\ \underline{= 2\ \rm Mbit/s}$.
-'''(2)'''&nbsp; Bei symbolweiser Codierung gilt stets $T_{c} = T_{q}$.
+'''(2)'''&nbsp; For symbol-wise coding, $T_{c} = T_{q}$ always applies.
-*Im vorliegenden Beispiel ist somit auch $T_{c}\ \underline{ = 0.5\ \rm &micro; s}$.
+*Thus, in the present example, $T_{c}\ \underline{ = 0.5\ \rm &micro; s}$ is also valid.
-*Die Stufenzahl $M_{c}\ \underline{ = 3}$ kann aus der unteren Skizze abgelesen werden.
+*The number of steps $M_{c}\ \underline{ = 3}$ can be read from the sketch below.
-'''(3)'''&nbsp; Die Symbolrate des Codersignals beträgt $2 \cdot 10^{6}$ Ternärsymbole pro Sekunde.
+'''(3)'''&nbsp; The symbol rate of the encoder signal is $2 \cdot 10^{6}$ ternary symbols per second.
-*Für die äquivalente Bitrate gilt:
+*For the equivalent bit rate, the following applies:
 :$$R_c = \frac{{\rm log_2} (M_c)}{T_c} = \frac{{\rm log_2}(3)}{0.5\,\,{\rm \mu s}} = \frac{{\rm lg} (3)}{{\rm lg} (2) \cdot 0.5\,\,{\rm \mu s}}= \frac{1.585\,\,{\rm (bit)}}{0.5\,\,{\rm \mu s}}\hspace{0.15cm} \underline {\approx 3.17\,\,{\rm Mbit/s}} \hspace{0.05cm}.$$
-'''(4)'''&nbsp; Für die relative Coderedundanz gilt bei redundanzfreier Quelle allgemein:
+'''(4)'''&nbsp; For relative code redundancy, when the source is redundancy-free, the general rule is:
 :$$ r_c = \frac{R_c - R_q}{R_c} = 1- \frac{R_q}{R_c}= 1- \frac{T_c}{T_q \cdot {\rm log_2} (M_c)}\hspace{0.05cm}.$$
-*Beim hier betrachteten Biploarcodes 2. Ordnung mit den Parametern $T_{c} = T_{q}$ und $M_{c} = 3$ gilt weiter:
+*In the case of the second order biploar code considered here, with parameters $T_{c} = T_{q}$ and $M_{c} = 3$, the following holds further:
 :$$r_c = 1- \frac{1}{{\rm log_2} (3)}\hspace{0.15cm}\underline {\approx 36.9 \% }\hspace{0.05cm}.$$

← Older revision		Revision as of 12:49, 4 April 2022
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−	[[Category:Digital Signal Transmission: Exercises\|^2.1 ~~Codierte Übertragung - Grundlagen~~^]]	+	[[Category:Digital Signal Transmission: Exercises\|^2.1 Basics of Coded Transmission^]]

← Older revision		Revision as of 12:47, 23 March 2021
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−	[[Category:~~Aufgaben zu Digitalsignalübertragung~~\|^2.1 Codierte Übertragung - Grundlagen^]]	+	[[Category:Digital Signal Transmission: Exercises\|^2.1 Codierte Übertragung - Grundlagen^]]