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

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	[[File:P_ID1669__Mod_A_5_10.png\|right\|frame\|Bandwidth organization for   $\rm DSL$]]		[[File:P_ID1669__Mod_A_5_10.png\|right\|frame\|Bandwidth organization for   $\rm DSL$]]
	In this exercise we consider a  $\rm DSL$ System  ("Digital Subscriber Line"),  where for modulation		In this exercise we consider a  $\rm DSL$ System  ("Digital Subscriber Line"),  where for modulation
	*[[Examples_of_Communication_Systems/~~xDSL_als_Übertragungstechnik~~#~~Grundlagen_von_DMT_.E2.80.93_Discrete_Multitone_Transmission~~\|$\rm DMT$]]  ("Discrete Multitone Transmission")		*[[Examples_of_Communication_Systems/xDSL_as_Transmission_Technology#Basics_of_Discrete_Multitone_Transmission\|$\rm DMT$]]  ("Discrete Multitone Transmission")
	* with  $N = 512$  grid points		* with  $N = 512$  grid points

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	[[Category:Modulation Methods: Exercises\|^5.8 Further OFDM Applications^]]		[[Category:Modulation Methods: Exercises\|^5.8 Further OFDM Applications^]]
	[[de:Aufgaben:5.~~10_DMT–Verfahren_bei_DSL~~]]		[[de:Aufgaben:Aufgabe 5.10: DMT–Verfahren bei DSL]]

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	:$$S\big[(N - \mu ) \cdot f_0 \big ] = S^*(\mu \cdot f_0).$$		:$$S\big[(N - \mu ) \cdot f_0 \big ] = S^*(\mu \cdot f_0).$$
	*Thus,  with  $N = 512$  and  $S(198 · f_0) = 1 + 3 · {\rm j}$  holds:		*Thus,  with  $N = 512$  and  $S(198 · f_0) = 1 + 3 · {\rm j}$  holds:
	:$$S(314 \cdot f_0) = 1 - 3 \cdot {\rm j}\hspace{0.3cm}\Rightarrow\hspace{0.3cm}\text{Re}[S(314 · f_0)]\hspace{0.15cm}\underline {= 1},		:$$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}.$$
	\hspace{0.3cm}\text{Im}[S(314 · f_0)]\hspace{0.15cm}\underline {= -3}.$$

	{{ML-Fuß}}		{{ML-Fuß}}

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	[[Category:Modulation Methods: Exercises\|^5.8 Further OFDM Applications^]]		[[Category:Modulation Methods: Exercises\|^5.8 Further OFDM Applications^]]
			[[de:Aufgaben:5.10_DMT–Verfahren_bei_DSL]]

Guenter at 12:02, 25 January 2022

2022-01-25T12:02:24Z

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	===Solution===		===Solution===
	{{ML-Kopf}}		{{ML-Kopf}}
	'''(1)'''  <u>Solution 2</u> is correct:		'''(1)'''  <u>Solution 2</u>  is correct:
	*DSL is a baseband system.		*DSL is a baseband system.
	*In contrast, mobile radio systems are bandpass systems which are operated in correspondingly high frequency ranges.		*In contrast,  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.		*In order to be able to consider them in the usual way, a (equivalent) lowpass transformation is necessary.



	'''(2)'''  <u>Solution 1</u> is correct:		'''(2)'''  <u>Solution 1</u>  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,  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.  The time signal thus becomes complex.		*This property is lost in bandpass systems,  which must be transformed to the equivalent baseband,  by cutting off the negative frequencies.  The time signal thus becomes complex.


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	'''(4)'''  The core symbol duration is the reciprocal of the ~~fundamental~~ frequency:		'''(4)'''  The core symbol duration is the reciprocal of the basic frequency:
	:$$T = \frac{1} {f_0}= \frac{1} {{4.3125\,\,{\rm kHz}}} \hspace{0.15cm}\underline {\approx 232 \,\,{\rm µ s}}.$$		:$$T = \frac{1} {f_0}= \frac{1} {{4.3125\,\,{\rm kHz}}} \hspace{0.15cm}\underline {\approx 232 \,\,{\rm µ s}}.$$



	'''(5)'''  From this, the duration of the guard interval is:		'''(5)'''  From this,  the duration of the guard interval is:
	:$$T_{\rm G} = \frac{N_{\rm G}} {N} \cdot T = \frac{32} {512} \cdot 232 \,\,{\rm µ s} \hspace{0.15cm}\underline {\approx 14 \,\,{\rm µ s}}.$$		:$$T_{\rm G} = \frac{N_{\rm G}} {N} \cdot T = \frac{32} {512} \cdot 232 \,\,{\rm µ s} \hspace{0.15cm}\underline {\approx 14 \,\,{\rm µ s}}.$$


	'''(6)'''  A frame is composed of core symbol and cyclic prefix:		'''(6)'''  A frame is composed of the core symbol and the cyclic prefix:
	:$$T_{\rm R} = T + T_{\rm G}\hspace{0.15cm}\underline { ≈ 246 \ \rm µs}.$$		:$$T_{\rm R} = T + T_{\rm G}\hspace{0.15cm}\underline { ≈ 246 \ \rm µs}.$$

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	'''(8)'''  For the DMT spectrum, in general:		'''(8)'''  For the DMT spectrum,  in general:
	:$$S\big[(N - \mu ) \cdot f_0 \big ] = S^*(\mu \cdot f_0).$$		:$$S\big[(N - \mu ) \cdot f_0 \big ] = S^*(\mu \cdot f_0).$$
	*Thus, with  $N = 512$  and  $S(198 · f_0) = 1 + 3 · {\rm j}$  holds:		*Thus,  with  $N = 512$  and  $S(198 · f_0) = 1 + 3 · {\rm j}$  holds:
	:$$S(314 \cdot f_0) = 1 - 3 \cdot {\rm j}\hspace{0.3cm}\Rightarrow\hspace{0.3cm}\text{Re}[S(314 · f_0)]\hspace{0.15cm}\underline {= 1},		:$$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}.$$		\hspace{0.3cm}\text{Im}[S(314 · f_0)]\hspace{0.15cm}\underline {= -3}.$$

Guenter at 11:34, 25 January 2022

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

Guenter at 11:33, 25 January 2022

2022-01-25T11:33:39Z

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	[[File:P_ID1669__Mod_A_5_10.png\|right\|frame\|Bandwidth organization for   $\rm DSL$]]		[[File:P_ID1669__Mod_A_5_10.png\|right\|frame\|Bandwidth organization for   $\rm DSL$]]
	In this exercise we consider a  $\rm DSL$ System  (''Digital Subscriber Line''), where for modulation		In this exercise we consider a  $\rm DSL$ System  ("Digital Subscriber Line"),  where for modulation
	*[[Examples_of_Communication_Systems/xDSL_als_Übertragungstechnik#Grundlagen_von_DMT_.E2.80.93_Discrete_Multitone_Transmission\|$\rm DMT$]]  (''Discrete Multitone Transmission'')		*[[Examples_of_Communication_Systems/xDSL_als_Übertragungstechnik#Grundlagen_von_DMT_.E2.80.93_Discrete_Multitone_Transmission\|$\rm DMT$]]  ("Discrete Multitone Transmission")
	* with  $N = 512$  grid points		* with  $N = 512$  grid points


	is used. In this context, the carriers are also referred to as "bins".		is used.  In this context,  the carriers are also referred to as  "bins".

	For DSL is specified:		For DSL is specified:
	* The carrier spacing is  $f_0 = 4.3125\ \rm kHz$.		* The carrier spacing is  $f_0 = 4.3125\ \rm kHz$.
	* ~~The signal is free of equal parts~~:  $S(f = 0) = 0$.		* For the spectrum holds:  $S(f = 0) = 0$.
	* The so-called  ''Nyquist tone''  is also set to zero:   $S(256 · f_0) = 0$.		* The so-called  "Nyquist tone"  is also set to zero:   $S(256 · f_0) = 0$.


	The diagram shows the bandwidth organization of the considered system for positive frequencies:		The diagram shows the bandwidth organization of the considered system for positive frequencies:
	*A transmission frame of  $\rm DMT$  is composed of the core symbol duration  $T$  and the duration  $T_{\rm G}$  of the cyclic prefix, as in OFDM.  This consists of  $N_{\rm G} = 32$  samples.		*A transmission frame of  $\rm DMT$  is composed of the core symbol duration  $T$  and the duration  $T_{\rm G}$  of the cyclic prefix,  as in OFDM.  This consists of  $N_{\rm G} = 32$  samples.
	*For synchronization between transmitter and receiver, a synchronization frame is sent after every  $68$  frames, which does not contain any user data.		*For synchronization between transmitter and receiver,  a synchronization frame is sent after every  $68$  frames,  which does not contain any user data.


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			Notes:



	''Notes:''
	*The exercise belongs to the chapter  [[Modulation_Methods/Weitere_OFDM–Anwendungen\|Further OFDM Applications]].		*The exercise belongs to the chapter  [[Modulation_Methods/Weitere_OFDM–Anwendungen\|Further OFDM Applications]].
	*Reference is made in particular to the ~~pages~~  [[Modulation_Methods/Further_OFDM_Applications#A_brief_description_of_DSL_-_Digital_Subscriber_Line\|A brief description of DSL]]  and  [[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   [[Modulation_Methods/Further_OFDM_Applications#A_brief_description_of_DSL_-_Digital_Subscriber_Line\|A brief description of DSL]]   and   [[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,  refer to the second chapter:   $\rm DSL$  – "Digital Subscriber Line"  of the LNTwww book [[Examples_of_Communication_Systems]].
	* For more information on the topic, refer to the second chapter:   $\rm DSL$  – "Digital Subscriber Line" of the ~~LNTww~~ book [[Examples_of_Communication_Systems]].

Hwang at 10:56, 5 January 2022

2022-01-05T10:56:11Z

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Guenter at 16:03, 14 December 2021

2021-12-14T16:03:31Z

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	[[Category:Modulation Methods: Exercises\|^5.8 ~~Weitere OFDM–Anwendungen~~^]]		[[Category:Modulation Methods: Exercises\|^5.8 Further OFDM Applications^]]

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

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