Aufgaben:Exercise 1.1Z: Non-redundant Binary Source - Revision history

Guenter at 11:45, 29 April 2022

2022-04-29T11:45:28Z

Guenter at 11:39, 29 April 2022

2022-04-29T11:39:38Z

Hwang at 12:31, 2 March 2022

2022-03-02T12:31:13Z

Hwang at 16:37, 10 February 2022

2022-02-10T16:37:04Z

Guenter: Guenter moved page Aufgaben:Exercise 1.1Z: Nonredundant Binary Source to Aufgaben:Exercise 1.1Z: Non-redundant Binary Source

2022-02-09T15:38:50Z

Guenter moved page Exercise 1.1Z: Nonredundant Binary Source to Exercise 1.1Z: Non-redundant Binary Source

Guenter at 15:17, 2 February 2022

2022-02-02T15:17:06Z

Guenter: Guenter moved page Aufgaben:Aufgabe 1.1Z: Redundanzfreie Binärquelle to Aufgaben:Exercise 1.1Z: Nonredundant Binary Source

2022-02-02T15:14:42Z

Guenter moved page Aufgabe 1.1Z: Redundanzfreie Binärquelle to Exercise 1.1Z: Nonredundant Binary Source

Javier: Text replacement - "„" to """

2021-05-28T14:28:15Z

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Javier: Text replacement - "”" to """

2021-05-28T14:22:41Z

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

2021-03-23T12:53:01Z

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

@@ Line 58: / Line 58: @@
 ===Solution===
 {{ML-Kopf}}
-'''(1)'''&nbsp; According to the diagram, the distance between two symbols is $\underline{T = 2\ \rm &micro; s}$.
+'''(1)'''&nbsp; According to the diagram,&nbsp; the distance between two symbols is&nbsp; $\underline{T = 2\ \rm &micro; s}$.
@@ Line 64: / Line 64: @@
-'''(3)'''&nbsp; The possible amplitude coefficients are $\pm 1$. Therefore, the given symbol sequence is <u>bipolar</u>.
+'''(3)'''&nbsp; The possible amplitude coefficients are $\pm 1$.&nbsp; Therefore,&nbsp; the given symbol sequence is&nbsp; <u>bipolar</u>.
-'''(4)'''&nbsp; The amplitude coefficient $a_2$ can be read at $2T = 4 \ \rm &micro; s$.
+'''(4)'''&nbsp; The amplitude coefficient&nbsp; $a_2$&nbsp; can be read at&nbsp; $2T = 4 \ \rm &micro; s$.&nbsp; With bipolar mapping,&nbsp; it follows that&nbsp; $a_2 = -1$&nbsp; for symbol&nbsp; $q_2 \hspace{0.15cm}\underline {=\rm L}$.
-'''(5)'''&nbsp; Even if the diagram suggests otherwise for the short time interval shown here:
+'''(5)'''&nbsp; Even if the diagram suggests otherwise for the short time interval shown here:&nbsp; For a redundancy-free binary source,&nbsp; in addition to the statistical independence of the symbols,&nbsp; $p_{\rm H} = p_{\rm L}\hspace{0.15cm}\underline{ = 0.5}$&nbsp; (equally probable symbols)&nbsp; must also hold.
 {{ML-Fuß}}

@@ Line 2: / Line 2: @@
 {{quiz-Header|Buchseite=Digital_Signal_Transmission/System_Components_of_a_Baseband_Transmission_System
 }}
 [[File:P_ID1257__Dig_Z_1_1.png|right|frame|Dirac-shaped source signal]]
 Any digital source can be completely described by its source symbol sequence
-:$$\langle q_\nu \rangle = \langle \hspace{0.05cm}q_0 \hspace{0.05cm}, q_1 \hspace{0.05cm}, q_2 \hspace{0.05cm}, ... \hspace{0.05cm} \rangle$$
+:$$\langle q_\nu \rangle = \langle \hspace{0.05cm}q_0 \hspace{0.05cm}, q_1 \hspace{0.05cm}, q_2 \hspace{0.05cm}, ... \hspace{0.05cm} \rangle.$$
-Contrary to the theory part, here the control variable &nbsp;$\nu$&nbsp; starts with zero. If each individual symbol &nbsp;$q_\nu$&nbsp; originates from the symbol set &nbsp;$\{\rm L, \ H\}$, it is called a binary source.
+Contrary to the theory part,&nbsp; here the control variable &nbsp;$\nu$&nbsp; starts with zero.&nbsp; If each individual symbol &nbsp;$q_\nu$&nbsp; originates from the symbol set &nbsp;$\{\rm L, \ H\}$,&nbsp; it is called a binary source.
 Using the symbol spacing &nbsp;$T$,&nbsp; one can also characterize the source symbol sequence &nbsp;$\langle q_\nu \rangle$&nbsp; in an equivalent way by the Dirac-shaped source signal
-:$$q(t) = \sum_{(\nu)} a_\nu \cdot {\rm \delta} ( t - \nu \cdot T)$$
+:$$q(t) = \sum_{(\nu)} a_\nu \cdot {\rm \delta} ( t - \nu \cdot T),$$
-which rather corresponds to a system-theoretic approach. Here, we denote &nbsp;$a_\nu$&nbsp; as the amplitude coefficients.
+which rather corresponds to a system-theoretic approach.&nbsp; Here, we denote &nbsp;$a_\nu$&nbsp; as the amplitude coefficients.
-*In the case of a binary unipolar digital signal transmission, holds:
+*In the case of a binary unipolar digital signal transmission holds:
 :$$a_\nu = \left\{ \begin{array}{c} 1 \\ 0 \\ \end{array} \right.\quad \begin{array}{*{1}c} {\rm{for}} \\ {\rm{for}} \\ \end{array}\begin{array}{*{20}c} q_\nu = \mathbf{H} \hspace{0.05cm}, \\ q_\nu = \mathbf{L} \hspace{0.05cm}. \\ \end{array}$$
-*Correspondingly, in the case of a bipolar system:
+*Correspondingly,&nbsp; in the case of a bipolar system:
 :$$a_\nu = \left\{ \begin{array}{c} +1 \\ -1 \\ \end{array} \right.\quad \begin{array}{*{1}c} {\rm{for}} \\ {\rm{for}} \\ \end{array}\begin{array}{*{20}c} q_\nu = \mathbf{H} \hspace{0.05cm}, \\ q_\nu = \mathbf{L} \hspace{0.05cm}. \\ \end{array}$$
-The diagram shows the Dirac-shaped source signal &nbsp;$q(t)$&nbsp; of a binary source. It is known from this source that it is redundancy-free. This statement is quite relevant for solving the problems.
+The diagram shows the Dirac-shaped source signal &nbsp;$q(t)$&nbsp; of a binary source.&nbsp; It is known from this source that it is redundancy-free.&nbsp; This statement is quite relevant for solving the problems.
@@ Line 24: / Line 22: @@
-''Notes:''
+Notes:
-*The exercise belongs to the chapter&nbsp; [[Digital_Signal_Transmission/System_Components_of_a_Baseband_Transmission_System|System Components of a Baseband Transmission System]].
+*The exercise belongs to the chapter&nbsp; [[Digital_Signal_Transmission/System_Components_of_a_Baseband_Transmission_System|"System Components of a Baseband Transmission System"]].
-*Reference is made in particular to the section&nbsp; [[Digital_Signal_Transmission/System_Components_of_a_Baseband_Transmission_System#Descriptive_variables_of_the_digital_source|Descriptive variables of the digital source]].
+*Reference is made in particular to the section&nbsp; [[Digital_Signal_Transmission/System_Components_of_a_Baseband_Transmission_System#Descriptive_variables_of_the_digital_source|"Descriptive variables of the digital source"]].
+*In the literature,&nbsp; the two possible binary symbols are usually designated as &nbsp;$\rm L$&nbsp; and &nbsp;$\rm 0$.&nbsp;
 *To avoid the somewhat confusing mapping &nbsp;$a_\nu = 1$&nbsp; for &nbsp;$q_\nu =\rm 0$&nbsp; and &nbsp;$a_\nu = 0$&nbsp; for &nbsp;$q_\nu =\rm L$,&nbsp; we use the symbols &nbsp;$\rm L$&nbsp; ("Low") and &nbsp;$\rm H$&nbsp; ("High") in our learning tutorial.

@@ Line 13: / Line 13: @@
 which rather corresponds to a system-theoretic approach. Here, we denote &nbsp;$a_\nu$&nbsp; as the amplitude coefficients.
 *In the case of a binary unipolar digital signal transmission, holds:
-:$$a_\nu = \left\{ \begin{array}{c} 1 \\ 0 \\ \end{array} \right.\quad \begin{array}{*{1}c} {\rm{f\ddot{u}r}} \\ {\rm{f\ddot{u}r}} \\ \end{array}\begin{array}{*{20}c} q_\nu = \mathbf{H} \hspace{0.05cm}, \\ q_\nu = \mathbf{L} \hspace{0.05cm}. \\ \end{array}$$
+:$$a_\nu = \left\{ \begin{array}{c} 1 \\ 0 \\ \end{array} \right.\quad \begin{array}{*{1}c} {\rm{for}} \\ {\rm{for}} \\ \end{array}\begin{array}{*{20}c} q_\nu = \mathbf{H} \hspace{0.05cm}, \\ q_\nu = \mathbf{L} \hspace{0.05cm}. \\ \end{array}$$
 *Correspondingly, in the case of a bipolar system:
-:$$a_\nu = \left\{ \begin{array}{c} +1 \\ -1 \\ \end{array} \right.\quad \begin{array}{*{1}c} {\rm{f\ddot{u}r}} \\ {\rm{f\ddot{u}r}} \\ \end{array}\begin{array}{*{20}c} q_\nu = \mathbf{H} \hspace{0.05cm}, \\ q_\nu = \mathbf{L} \hspace{0.05cm}. \\ \end{array}$$
+:$$a_\nu = \left\{ \begin{array}{c} +1 \\ -1 \\ \end{array} \right.\quad \begin{array}{*{1}c} {\rm{for}} \\ {\rm{for}} \\ \end{array}\begin{array}{*{20}c} q_\nu = \mathbf{H} \hspace{0.05cm}, \\ q_\nu = \mathbf{L} \hspace{0.05cm}. \\ \end{array}$$
 The diagram shows the Dirac-shaped source signal &nbsp;$q(t)$&nbsp; of a binary source. It is known from this source that it is redundancy-free. This statement is quite relevant for solving the problems.

@@ Line 1: / Line 1: @@
-{{quiz-Header|Buchseite=Digitalsignalübertragung/Systemkomponenten eines Basisbandübertragungssystems
+{{quiz-Header|Buchseite=Digital_Signal_Transmission/System_Components_of_a_Baseband_Transmission_System
 }}
-[[File:P_ID1257__Dig_Z_1_1.png|right|frame|Diracförmiges Quellensignal]]
+[[File:P_ID1257__Dig_Z_1_1.png|right|frame|Dirac-shaped source signal]]
-Eine jede digitale Quelle kann durch ihre Quellensymbolfolge
+Any digital source can be completely described by its source symbol sequence
 :$$\langle q_\nu \rangle = \langle \hspace{0.05cm}q_0 \hspace{0.05cm}, q_1 \hspace{0.05cm}, q_2 \hspace{0.05cm}, ... \hspace{0.05cm} \rangle$$
-vollständig beschrieben werden, wobei hier entgegen dem Theorieteil die Laufvariable &nbsp;$\nu$&nbsp; mit Null beginnt. Entstammt jedes einzelne Symbol &nbsp;$q_\nu$&nbsp; dem Symbolvorrat &nbsp;$\{\rm L, \ H\}$, so spricht man von einer Binärquelle.
+Contrary to the theory part, here the control variable &nbsp;$\nu$&nbsp; starts with zero. If each individual symbol &nbsp;$q_\nu$&nbsp; originates from the symbol set &nbsp;$\{\rm L, \ H\}$, it is called a binary source.
-Unter Verwendung des Symbolabstandes &nbsp;$T$&nbsp; kann man die Quellensymbolfolge &nbsp;$\langle q_\nu \rangle$&nbsp; in äquivalenter Weise auch durch das diracförmige Quellensignal
+Using the symbol spacing &nbsp;$T$,&nbsp; one can also characterize the source symbol sequence &nbsp;$\langle q_\nu \rangle$&nbsp; in an equivalent way by the Dirac-shaped source signal
 :$$q(t) = \sum_{(\nu)} a_\nu \cdot {\rm \delta} ( t - \nu \cdot T)$$
-kennzeichnen, was eher einer systemtheoretischen Betrachtungsweise entspricht. Hierbei bezeichnet man &nbsp;$a_\nu$&nbsp; als die Amplitudenkoeffizienten.
+which rather corresponds to a system-theoretic approach. Here, we denote &nbsp;$a_\nu$&nbsp; as the amplitude coefficients.
-*Im Falle einer binären unipolaren Digitalsignalübertragung gilt:
+*In the case of a binary unipolar digital signal transmission, holds:
 :$$a_\nu = \left\{ \begin{array}{c} 1 \\ 0 \\ \end{array} \right.\quad \begin{array}{*{1}c} {\rm{f\ddot{u}r}} \\ {\rm{f\ddot{u}r}} \\ \end{array}\begin{array}{*{20}c} q_\nu = \mathbf{H} \hspace{0.05cm}, \\ q_\nu = \mathbf{L} \hspace{0.05cm}. \\ \end{array}$$
-*Entsprechend gilt bei einem bipolaren System:
+*Correspondingly, in the case of a bipolar system:
 :$$a_\nu = \left\{ \begin{array}{c} +1 \\ -1 \\ \end{array} \right.\quad \begin{array}{*{1}c} {\rm{f\ddot{u}r}} \\ {\rm{f\ddot{u}r}} \\ \end{array}\begin{array}{*{20}c} q_\nu = \mathbf{H} \hspace{0.05cm}, \\ q_\nu = \mathbf{L} \hspace{0.05cm}. \\ \end{array}$$
-In der Grafik ist das diracförmige Quellensignal &nbsp;$q(t)$&nbsp; einer Binärquelle dargestellt. Von dieser ist bekannt, dass sie redundanzfrei ist. Diese Aussage ist für die Lösung der Aufgabe durchaus relevant.
+The diagram shows the Dirac-shaped source signal &nbsp;$q(t)$&nbsp; of a binary source. It is known from this source that it is redundancy-free. This statement is quite relevant for solving the problems.
@@ Line 24: / Line 24: @@
-''Hinweise:''
+''Notes:''
-*Die Aufgabe gehört zum  Kapitel&nbsp; [[Digital_Signal_Transmission/Systemkomponenten_eines_Basisbandübertragungssystems|Systemkomponenten eines Basisbandübertragungssystems]].
+*The exercise belongs to the chapter&nbsp; [[Digital_Signal_Transmission/System_Components_of_a_Baseband_Transmission_System|System Components of a Baseband Transmission System]].
-*Bezug genommen wird insbesondere auf den Abschnitt&nbsp; [[Digital_Signal_Transmission/Systemkomponenten_eines_Basisbandübertragungssystems#Beschreibungsgr.C3.B6.C3.9Fen_der_digitalen_Quelle|Kenngrößen der digitalen Quelle]].
+*Reference is made in particular to the section&nbsp; [[Digital_Signal_Transmission/System_Components_of_a_Baseband_Transmission_System#Descriptive_variables_of_the_digital_source|Descriptive variables of the digital source]].
-*In der Literatur werden die beiden möglichen Binärsymbole meist mit &nbsp;$\rm L$&nbsp; und &nbsp;$\rm 0$&nbsp; bezeichnet.
+*In the literature, the two possible binary symbols are usually designated as &nbsp;$\rm L$&nbsp; and &nbsp;$\rm 0$.&nbsp;
-*Um die etwas verwirrende Zuordnung &nbsp;$a_\nu = 1$&nbsp; für &nbsp;$q_\nu =\rm 0$&nbsp; und &nbsp;$a_\nu = 0$&nbsp; für &nbsp;$q_\nu =\rm L$&nbsp; zu vermeiden, werden in unserem Lerntutorial die Symbole &nbsp;$\rm L$&nbsp; ("Low") und &nbsp;$\rm H$&nbsp; ("High") verwendet.
+*To avoid the somewhat confusing mapping &nbsp;$a_\nu = 1$&nbsp; for &nbsp;$q_\nu =\rm 0$&nbsp; and &nbsp;$a_\nu = 0$&nbsp; for &nbsp;$q_\nu =\rm L$,&nbsp; we use the symbols &nbsp;$\rm L$&nbsp; ("Low") and &nbsp;$\rm H$&nbsp; ("High") in our learning tutorial.
-===Fragebogen===
+===Questions===
 <quiz display=simple>
-{Wie groß ist der Symbolabstand &nbsp;$T$?
+{What is the symbol distance &nbsp;$T$?
 |type="{}"}
 $T \ = \ $  { 2 3% } $\ \rm &micro; s$
-{Wie groß ist die von der Quelle abgegebene Bitrate &nbsp;$R$?
+{What is the bit rate &nbsp;$R$ output by the source?
 |type="{}"}
 $R \ = \ $  { 500 3% } $\ \rm kbit/s$
-{Handelt es sich hierbei um die unipolare oder bipolare Repräsentation?
+{Is this representation unipolar or bipolar?
 |type="()"}
-- Die Symbolfolge ist unipolar.
+- The symbol sequence is unipolar.
-+ Die Symbolfolge ist bipolar.
++ The symbol sequence is bipolar.
-{Wie lautet das Quellensymbol &nbsp;$q_2$?
+{What is the source symbol &nbsp;$q_2$?
 |type="()"}
 + $q_2 = \rm L$,
 - $q_2 = \rm H$.
-{Wie groß ist die Symbolwahrscheinlichkeit &nbsp;$p_{\rm H} = {\rm Pr}(q_\nu = \rm H$)?
+{What is the symbol probability &nbsp;$p_{\rm H} = {\rm Pr}(q_\nu = \rm H$)?
 |type="{}"}
 $p_{\rm H} \ = \ $ { 0.5 3% }
@@ Line 59: / Line 59: @@
 </quiz>
-===Musterlösung===
+===Solution===
 {{ML-Kopf}}
-'''(1)'''&nbsp; Entsprechend der Grafik beträgt der Abstand zweier Symbole $\underline{T = 2\ \rm &micro; s}$.
+'''(1)'''&nbsp; According to the diagram, the distance between two symbols is $\underline{T = 2\ \rm &micro; s}$.
-'''(2)'''&nbsp; Bei dieser redundanzfreien Binärquelle &ndash; und nur bei einer solchen &ndash; ist die Bitrate $R = 1/T\hspace{0.15cm}\underline{=500 \ \rm kbit/s}$.
+'''(2)'''&nbsp; With this redundancy-free binary source &ndash; and only with such a source &ndash; the bit rate is $R = 1/T\hspace{0.15cm}\underline{=500 \ \rm kbit/s}$.
-'''(3)'''&nbsp; Die möglichen Amplitudenkoeffizienten sind $\pm 1$. Deshalb ist die gegebene Symbolfolge <u>bipolar</u>.
+'''(3)'''&nbsp; The possible amplitude coefficients are $\pm 1$. Therefore, the given symbol sequence is <u>bipolar</u>.
-'''(4)'''&nbsp; Der Amplitudenkoeffizient $a_2$ kann bei $2T = 4 \ \rm &micro; s$ abgelesen werden.
+'''(4)'''&nbsp; The amplitude coefficient $a_2$ can be read at $2T = 4 \ \rm &micro; s$.
-*Bei bipolarer Zuordnung folgt aus $a_2 = -1$ für das Symbol $q_2 \hspace{0.15cm}\underline {=\rm L}$.
+*With bipolar mapping, it follows that $a_2 = -1$ for symbol $q_2 \hspace{0.15cm}\underline {=\rm L}$.
-'''(5)'''&nbsp; Auch wenn die Grafik für den hier dargestellten kurzen Zeitabschnitt etwas anderes suggeriert:
+'''(5)'''&nbsp; Even if the diagram suggests otherwise for the short time interval shown here:
-*Bei einer redundanzfreien Binärquelle muss neben der statistischen Unabhängigkeit der Symbole auch  $p_{\rm H} = p_{\rm L}\hspace{0.15cm}\underline{ = 0.5}$ (gleichwahrscheinliche Symbole) gelten.
+*For a redundancy-free binary source, in addition to the statistical independence of the symbols, $p_{\rm H} = p_{\rm L}\hspace{0.15cm}\underline{ = 0.5}$ (equally probable symbols) must also hold.
 {{ML-Fuß}}

← Older revision		Revision as of 15:17, 2 February 2022
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−	[[Category:Digital Signal Transmission: Exercises\|^1.1 ~~Basisband-Systemkomponenten~~^]]	+	[[Category:Digital Signal Transmission: Exercises\|^1.1 Baseband System Components^]]

← Older revision	Revision as of 15:38, 9 February 2022
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← Older revision		Revision as of 14:28, 28 May 2021
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	*In der Literatur werden die beiden möglichen Binärsymbole meist mit  $\rm L$  und  $\rm 0$  bezeichnet.		*In der Literatur werden die beiden möglichen Binärsymbole meist mit  $\rm L$  und  $\rm 0$  bezeichnet.
−	*Um die etwas verwirrende Zuordnung  $a_\nu = 1$  für  $q_\nu =\rm 0$  und  $a_\nu = 0$  für  $q_\nu =\rm L$  zu vermeiden, werden in unserem Lerntutorial die Symbole  $\rm L$  (~~&bdquo;~~Low") und  $\rm H$  (~~&bdquo;~~High") verwendet.	+	*Um die etwas verwirrende Zuordnung  $a_\nu = 1$  für  $q_\nu =\rm 0$  und  $a_\nu = 0$  für  $q_\nu =\rm L$  zu vermeiden, werden in unserem Lerntutorial die Symbole  $\rm L$  ("Low") und  $\rm H$  ("High") verwendet.

← Older revision		Revision as of 14:22, 28 May 2021
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	*In der Literatur werden die beiden möglichen Binärsymbole meist mit  $\rm L$  und  $\rm 0$  bezeichnet.		*In der Literatur werden die beiden möglichen Binärsymbole meist mit  $\rm L$  und  $\rm 0$  bezeichnet.
−	*Um die etwas verwirrende Zuordnung  $a_\nu = 1$  für  $q_\nu =\rm 0$  und  $a_\nu = 0$  für  $q_\nu =\rm L$  zu vermeiden, werden in unserem Lerntutorial die Symbole  $\rm L$  (&bdquo;Low~~”~~) und  $\rm H$  (&bdquo;High~~”~~) verwendet.	+	*Um die etwas verwirrende Zuordnung  $a_\nu = 1$  für  $q_\nu =\rm 0$  und  $a_\nu = 0$  für  $q_\nu =\rm L$  zu vermeiden, werden in unserem Lerntutorial die Symbole  $\rm L$  (&bdquo;Low") und  $\rm H$  (&bdquo;High") verwendet.

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−	[[Category:~~Aufgaben zu Digitalsignalübertragung~~\|^1.1 Basisband-Systemkomponenten^]]	+	[[Category:Digital Signal Transmission: Exercises\|^1.1 Basisband-Systemkomponenten^]]