Aufgaben:Exercise 5.10: DMT Process for DSL - Revision history

Guenter at 12:02, 25 January 2022

2022-01-25T12:02:24Z

Guenter at 11:34, 25 January 2022

2022-01-25T11:34:43Z

Guenter at 11:33, 25 January 2022

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Hwang at 10:56, 5 January 2022

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Guenter at 16:03, 14 December 2021

2021-12-14T16:03:31Z

Guenter: Guenter moved page Aufgaben:Aufgabe 5.10: DMT–Verfahren bei DSL to Aufgaben:Exercise 5.10: DMT Process for DSL

2021-12-14T16:02:30Z

Guenter moved page Aufgabe 5.10: DMT–Verfahren bei DSL to Exercise 5.10: DMT Process for DSL

Javier: Text replacement - "„" to """

2021-05-28T14:44:33Z

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2021-05-28T14:38:32Z

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Javier: Text replacement - "Category:Aufgaben zu Modulationsverfahren" to "Category:Modulation Methods: Exercises"

2021-03-23T12:46:45Z

Text replacement - "Category:Aufgaben zu Modulationsverfahren" to "Category:Modulation Methods: Exercises"

Javier: Text replacement - "[[Beispiele_von_Nachrichtensystemen" to "[[Examples_of_Communication_Systems"

2020-07-09T12:58:32Z

Text replacement - "[[Beispiele_von_Nachrichtensystemen" to "[[Examples_of_Communication_Systems"

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 ===Solution===
 {{ML-Kopf}}
-'''(1)'''&nbsp;   <u>Solution 2</u> is correct:
+'''(1)'''&nbsp;   <u>Solution 2</u>&nbsp; is correct:
 *DSL is a baseband system.
-*In contrast, mobile radio systems are bandpass systems which are operated in correspondingly high frequency ranges.
+*In contrast,&nbsp; mobile radio systems are bandpass systems which are operated in correspondingly high frequency ranges.
 *In order to be able to consider them in the usual way, a (equivalent) lowpass transformation is necessary.
-'''(2)'''&nbsp;   <u>Solution 1</u> is correct:
+'''(2)'''&nbsp;   <u>Solution 1</u>&nbsp; is correct:
-*The time signal is purely real, since the real part of the spectrum is even and the imaginary part is odd.
+*The time signal is purely real,&nbsp; since the real part of the spectrum is even and the imaginary part is odd.
-*This property is lost in bandpass systems, which must be transformed to the equivalent baseband, by cutting off the negative frequencies.&nbsp; The time signal thus becomes complex.
+*This property is lost in bandpass systems,&nbsp; which must be transformed to the equivalent baseband,&nbsp; by cutting off the negative frequencies.&nbsp; The time signal thus becomes complex.
@@ Line 96: / Line 96: @@
-'''(4)'''&nbsp;   The core symbol duration is the reciprocal of the fundamental frequency:
+'''(4)'''&nbsp;   The core symbol duration is the reciprocal of the basic frequency:
 :$$T = \frac{1} {f_0}= \frac{1} {{4.3125\,\,{\rm kHz}}} \hspace{0.15cm}\underline {\approx 232 \,\,{\rm &micro; s}}.$$
-'''(5)'''&nbsp;   From this, the duration of the guard interval is:
+'''(5)'''&nbsp;   From this,&nbsp; the duration of the guard interval is:
 :$$T_{\rm G} = \frac{N_{\rm G}} {N} \cdot T = \frac{32} {512} \cdot 232 \,\,{\rm &micro; s} \hspace{0.15cm}\underline {\approx 14 \,\,{\rm &micro; s}}.$$
-'''(6)'''&nbsp;   A frame is composed of core symbol and cyclic prefix:
+'''(6)'''&nbsp;   A frame is composed of the core symbol and the cyclic prefix:
 :$$T_{\rm R} = T + T_{\rm G}\hspace{0.15cm}\underline { ≈ 246 \ \rm &micro;s}.$$
@@ Line 116: / Line 116: @@
-'''(8)'''&nbsp;   For the DMT spectrum, in general:
+'''(8)'''&nbsp;   For the DMT spectrum,&nbsp; in general:
 :$$S\big[(N - \mu ) \cdot f_0 \big ] = S^*(\mu \cdot f_0).$$
-*Thus, with&nbsp; $N = 512$&nbsp; and&nbsp; $S(198 · f_0) = 1 + 3 · {\rm j}$&nbsp; holds:
+*Thus,&nbsp; with&nbsp; $N = 512$&nbsp; and&nbsp; $S(198 · f_0) = 1 + 3 · {\rm j}$&nbsp; holds:
 :$$S(314 \cdot f_0) = 1 - 3 \cdot {\rm j}\hspace{0.3cm}\Rightarrow\hspace{0.3cm}\text{Re}[S(314 · f_0)]\hspace{0.15cm}\underline {= 1},
 \hspace{0.3cm}\text{Im}[S(314 · f_0)]\hspace{0.15cm}\underline {= -3}.$$

@@ Line 28: / Line 28: @@
 *The exercise belongs to the chapter&nbsp; [[Modulation_Methods/Weitere_OFDM–Anwendungen|Further OFDM Applications]].
 *Reference is made in particular to the sections &nbsp;  [[Modulation_Methods/Further_OFDM_Applications#A_brief_description_of_DSL_-_Digital_Subscriber_Line|A brief description of DSL]] &nbsp; and &nbsp; [[Modulation_Methods/Further_OFDM_Applications#Differences_between_DMT_and_the_described_OFDM|Differences between DMT and the described OFDM]].
-* For more information on the topic,&nbsp; refer to the second chapter: &nbsp; $\rm DSL$&nbsp; &ndash; "Digital Subscriber Line"&nbsp; of the LNTwww book [[Examples_of_Communication_Systems]].
+* For more information on the topic,&nbsp; refer to the second chapter: &nbsp; $\rm DSL$&nbsp; &ndash; "Digital Subscriber Line"&nbsp; of the LNTwww book&nbsp; [[Examples_of_Communication_Systems]].

@@ Line 4: / Line 4: @@
 [[File:P_ID1669__Mod_A_5_10.png|right|frame|Bandwidth organization for &nbsp; $\rm DSL$]]
-In this exercise we consider a&nbsp; $\rm DSL$ System&nbsp; (''Digital Subscriber Line''), where for modulation
+In this exercise we consider a&nbsp; $\rm DSL$ System&nbsp; ("Digital Subscriber Line"),&nbsp; where for modulation
-*[[Examples_of_Communication_Systems/xDSL_als_Übertragungstechnik#Grundlagen_von_DMT_.E2.80.93_Discrete_Multitone_Transmission|$\rm DMT$]]&nbsp; (''Discrete Multitone Transmission'')
+*[[Examples_of_Communication_Systems/xDSL_als_Übertragungstechnik#Grundlagen_von_DMT_.E2.80.93_Discrete_Multitone_Transmission|$\rm DMT$]]&nbsp; ("Discrete Multitone Transmission")
 * with&nbsp; $N = 512$&nbsp; grid points
-is used. In this context, the carriers are also referred to as "bins".
+is used.&nbsp; In this context,&nbsp; the carriers are also referred to as&nbsp; "bins".
 For DSL is specified:
 * The carrier spacing is &nbsp;$f_0 = 4.3125\ \rm  kHz$.
-* The signal is free of equal parts: &nbsp;$S(f = 0) = 0$.
+* For the spectrum holds: &nbsp;$S(f = 0) = 0$.
-* The so-called&nbsp; ''Nyquist tone''&nbsp; is also set to zero: &nbsp; $S(256 · f_0) = 0$.
+* The so-called&nbsp; "Nyquist tone"&nbsp; is also set to zero: &nbsp; $S(256 · f_0) = 0$.
 The diagram shows the bandwidth organization of the considered system for positive frequencies:
-*A transmission frame of&nbsp; $\rm DMT$&nbsp; is composed of the core symbol duration &nbsp;$T$&nbsp; and the duration &nbsp;$T_{\rm G}$&nbsp; of the cyclic prefix, as in OFDM.&nbsp; This consists of &nbsp;$N_{\rm G} = 32$&nbsp; samples.
+*A transmission frame of&nbsp; $\rm DMT$&nbsp; is composed of the core symbol duration &nbsp;$T$&nbsp; and the duration &nbsp;$T_{\rm G}$&nbsp; of the cyclic prefix,&nbsp; as in OFDM.&nbsp; This consists of &nbsp;$N_{\rm G} = 32$&nbsp; samples.
-*For synchronization between transmitter and receiver, a synchronization frame is sent after every &nbsp;$68$&nbsp; frames, which does not contain any user data.
+*For synchronization between transmitter and receiver,&nbsp; a synchronization frame is sent after every &nbsp;$68$&nbsp; frames,&nbsp; which does not contain any user data.
@@ Line 25: / Line 25: @@
 Notes:
 *The exercise belongs to the chapter&nbsp; [[Modulation_Methods/Weitere_OFDM–Anwendungen|Further OFDM Applications]].
-*Reference is made in particular to the pages&nbsp;  [[Modulation_Methods/Further_OFDM_Applications#A_brief_description_of_DSL_-_Digital_Subscriber_Line|A brief description of DSL]]&nbsp; and &nbsp;[[Modulation_Methods/Further_OFDM_Applications#Differences_between_DMT_and_the_described_OFDM|Differences between DMT and the described OFDM
+*Reference is made in particular to the sections &nbsp;  [[Modulation_Methods/Further_OFDM_Applications#A_brief_description_of_DSL_-_Digital_Subscriber_Line|A brief description of DSL]] &nbsp; and &nbsp; [[Modulation_Methods/Further_OFDM_Applications#Differences_between_DMT_and_the_described_OFDM|Differences between DMT and the described OFDM]].
-]].
+* For more information on the topic,&nbsp; refer to the second chapter: &nbsp; $\rm DSL$&nbsp; &ndash; "Digital Subscriber Line"&nbsp; of the LNTwww book [[Examples_of_Communication_Systems]].

← Older revision		Revision as of 16:03, 14 December 2021
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−	[[Category:Modulation Methods: Exercises\|^5.8 ~~Weitere OFDM–Anwendungen~~^]]	+	[[Category:Modulation Methods: Exercises\|^5.8 Further OFDM Applications^]]

@@ Line 32: / Line 32: @@
 *Die Aufgabe gehört zum  Kapitel&nbsp; [[Modulation_Methods/Weitere_OFDM–Anwendungen|Weitere OFDM–Anwendungen]].
 *Bezug genommen wird insbesondere auf die Seiten&nbsp;  [[Modulation_Methods/Weitere_OFDM–Anwendungen#Eine_Kurzbeschreibung_von_DSL_.E2.80.93_Digital_Subscriber_Line|Eine Kurzbeschreibung von DSL]]&nbsp; sowie &nbsp;[[Modulation_Methods/Weitere_OFDM–Anwendungen#Unterschiede_zwischen_DMT_und_dem_beschriebenen_OFDM|Unterschiede zwischen DMT und dem beschriebenen OFDM]].
-* Weitere Informationen zum Thema finden Sie im zweiten Kapitel: &nbsp; $\rm DSL$&nbsp; &ndash; &bdquo;Digital Subscriber Line" des LNTwww&ndash;Buchs [[Examples_of_Communication_Systems]].
+* Weitere Informationen zum Thema finden Sie im zweiten Kapitel: &nbsp; $\rm DSL$&nbsp; &ndash; "Digital Subscriber Line" des LNTwww&ndash;Buchs [[Examples_of_Communication_Systems]].

← Older revision	Revision as of 16:02, 14 December 2021
(No difference)

← Older revision		Revision as of 12:46, 23 March 2021
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−	[[Category:~~Aufgaben zu Modulationsverfahren~~\|^5.8 Weitere OFDM–Anwendungen^]]	+	[[Category:Modulation Methods: Exercises\|^5.8 Weitere OFDM–Anwendungen^]]

@@ Line 5: / Line 5: @@
 [[File:P_ID1669__Mod_A_5_10.png|right|frame|Bandbreitenorganisation bei&nbsp; $\rm DSL$]]
 Wir betrachten in dieser Aufgabe ein&nbsp; $\rm DSL$–System&nbsp; (''Digital Subscriber Line''), wobei zur Modulation
-*[[Beispiele_von_Nachrichtensystemen/xDSL_als_Übertragungstechnik#Grundlagen_von_DMT_.E2.80.93_Discrete_Multitone_Transmission|$\rm DMT$]]&nbsp; (''Discrete Multitone Transmission'')
+*[[Examples_of_Communication_Systems/xDSL_als_Übertragungstechnik#Grundlagen_von_DMT_.E2.80.93_Discrete_Multitone_Transmission|$\rm DMT$]]&nbsp; (''Discrete Multitone Transmission'')
 * mit&nbsp; $N = 512$&nbsp; Stützstellen
@@ Line 32: / Line 32: @@
 *Die Aufgabe gehört zum  Kapitel&nbsp; [[Modulation_Methods/Weitere_OFDM–Anwendungen|Weitere OFDM–Anwendungen]].
 *Bezug genommen wird insbesondere auf die Seiten&nbsp;  [[Modulation_Methods/Weitere_OFDM–Anwendungen#Eine_Kurzbeschreibung_von_DSL_.E2.80.93_Digital_Subscriber_Line|Eine Kurzbeschreibung von DSL]]&nbsp; sowie &nbsp;[[Modulation_Methods/Weitere_OFDM–Anwendungen#Unterschiede_zwischen_DMT_und_dem_beschriebenen_OFDM|Unterschiede zwischen DMT und dem beschriebenen OFDM]].
-* Weitere Informationen zum Thema finden Sie im zweiten Kapitel: &nbsp; $\rm DSL$&nbsp; &ndash; &bdquo;Digital Subscriber Line&rdquo; des LNTwww&ndash;Buchs [[Beispiele_von_Nachrichtensystemen]].
+* Weitere Informationen zum Thema finden Sie im zweiten Kapitel: &nbsp; $\rm DSL$&nbsp; &ndash; &bdquo;Digital Subscriber Line&rdquo; des LNTwww&ndash;Buchs [[Examples_of_Communication_Systems]].