Digital Signal Transmission/Parameters of Digital Channel Models - Revision history

Maintenance script: Join split $$ formula lines for correct rendering

2026-03-16T13:46:50Z

Join split $$ formula lines for correct rendering

← Older revision		Revision as of 15:46, 16 March 2026
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	:$$H_{\rm K}(f) = 1\hspace{0.05cm},$$		:$$H_{\rm K}(f) = 1\hspace{0.05cm},$$
	:$${f}_{n}(n) = \frac{1}{\sqrt{2 \pi} \cdot \sigma} \cdot {\rm		:$${f}_{n}(n) = \frac{1}{\sqrt{2 \pi} \cdot \sigma} \cdot {\rm e}^{-n^2\hspace{-0.05cm}/(2 \sigma^2)}\hspace{0.05cm},$$
	e}^{-n^2\hspace{-0.05cm}/(2 \sigma^2)}\hspace{0.05cm},$$
	:$${\it \Phi}_{n}(f) = {\rm const.}\hspace{0.05cm}.$$		:$${\it \Phi}_{n}(f) = {\rm const.}\hspace{0.05cm}.$$

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	To take  '''time-variant characteristics'''  into account,  one must use other models,  which are described in the book  "Mobile communications"  such as		To take  '''time-variant characteristics'''  into account,  one must use other models,  which are described in the book  "Mobile communications"  such as
	*[[Mobile_Communications/Probability_Density_of_Rayleigh_Fading\|"Rayleigh fading"]],		*[[Mobile_Communications/Probability_Density_of_Rayleigh_Fading\|"Rayleigh fading"]],
	*[[Mobile_Communications/Non-~~Frequency_Selective_Fading_With_Direct_Component~~#Example_of_signal_behaviour_with_Rice_fading\|"Rice fading"]],  and		*[[Mobile_Communications/Non-Frequency-Selective_Fading_With_Direct_Component#Example_of_signal_behaviour_with_Rice_fading\|"Rice fading"]],  and
	*[[Mobile_Communications/Distance_Dependent_Attenuation_and_Shading#Lognormal_channel_model\|"Lognormal fading"]].<br>		*[[Mobile_Communications/Distance_Dependent_Attenuation_and_Shading#Lognormal_channel_model\|"Lognormal fading"]].<br>

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	*In particular:		*In particular:
	:$$V_a(k = 1) = 1 \hspace{0.05cm},\hspace{0.5cm} \lim_{k \rightarrow \infty}V_a(k ) =		:$$V_a(k = 1) = 1 \hspace{0.05cm},\hspace{0.5cm} \lim_{k \rightarrow \infty}V_a(k ) =0 \hspace{0.05cm}.$$}}
	0 \hspace{0.05cm}.$$}}

Maintenance script: Add German interlanguage link

2026-03-16T12:26:40Z

Add German interlanguage link

← Older revision		Revision as of 14:26, 16 March 2026
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	{{Display}}		{{Display}}
			[[de:Digitalsignalübertragung/Beschreibungsgrößen_digitaler_Kanalmodelle]]

Guenter at 12:01, 19 October 2022

2022-10-19T12:01:34Z

← Older revision		Revision as of 14:01, 19 October 2022
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	<br>		<br>
	Digital channel models are preferably used for cascaded transmission,  as shown in the graph.  You can see from this diagram:		Digital channel models are preferably used for cascaded transmission,  as shown in the graph.  You can see from this diagram:
	[[File:EN_Dig_T_5_1_S3_neu2.png\|right\|frame\|Model of a transmission system with encoder/decoder ~~'''KORREKTUR: Komparator'''~~\|class=fit]]		[[File:EN_Dig_T_5_1_S3_neu2.png\|right\|frame\|Model of a transmission system with encoder/decoder \|class=fit]]
	*The inner transmission system – consisting of modulator, analog channel, noise, demodulator, receiver filter, decision, clock recovery – is summarized in the block  "Digital channel"  marked in blue.<br>		*The inner transmission system – consisting of modulator, analog channel, noise, demodulator, receiver filter, decision, clock recovery – is summarized in the block  "Digital channel"  marked in blue.<br>

Guenter at 16:05, 17 October 2022

2022-10-17T16:05:01Z

← Older revision		Revision as of 18:05, 17 October 2022
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	<br>		<br>
	Digital channel models are preferably used for cascaded transmission,  as shown in the graph.  You can see from this diagram:		Digital channel models are preferably used for cascaded transmission,  as shown in the graph.  You can see from this diagram:
	[[File:~~EN_Dig_T_5_1_S3_neu~~.png\|right\|frame\|Model of a transmission system with encoder/decoder '''KORREKTUR: Komparator'''\|class=fit]]		[[File:EN_Dig_T_5_1_S3_neu2.png\|right\|frame\|Model of a transmission system with encoder/decoder '''KORREKTUR: Komparator'''\|class=fit]]
	*The inner transmission system – consisting of modulator, analog channel, noise, demodulator, receiver filter, decision, clock recovery – is summarized in the block  "Digital channel"  marked in blue.<br>		*The inner transmission system – consisting of modulator, analog channel, noise, demodulator, receiver filter, decision, clock recovery – is summarized in the block  "Digital channel"  marked in blue.<br>

Guenter at 13:11, 1 October 2022

2022-10-01T13:11:59Z

← Older revision		Revision as of 15:11, 1 October 2022
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	Such channel models are mainly used for  »cascaded transmission systems«  for the inner block,  if the performance of the outer system components  $($e.g. ~~coder '''KORREKTUR:~~ encoder~~'''~~ and decoder$)$  is to be determined by simulation.		Such channel models are mainly used for  »cascaded transmission systems«  for the inner block,  if the performance of the outer system components  $($e.g. encoder and decoder$)$  is to be determined by simulation.

	The following are dealt with in detail:		The following are dealt with in detail:

Hwang at 02:56, 11 September 2022

2022-09-11T02:56:55Z

← Older revision		Revision as of 04:56, 11 September 2022
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	{{GraueBox\|TEXT=		{{GraueBox\|TEXT=
	$\text{Example 5:}$  The graph shows in the left sketch an arbitrary discrete error distance density function  $f_a(a)$  and the ~~resultingintegrated~~ functions.		$\text{Example 5:}$  The graph shows in the left sketch an arbitrary discrete error distance density function  $f_a(a)$  and the resulting integrated functions.
	[[File:P ID1826 Dig T 5 1 S5b version1.png\|right\|frame\|Discrete probability density function  $f_a(a)$ and the functions  $F_a(k )$  and  $V_a(k )$ \|class=fit]]		[[File:P ID1826 Dig T 5 1 S5b version1.png\|right\|frame\|Discrete probability density function  $f_a(a)$ and the functions  $F_a(k )$  and  $V_a(k )$ \|class=fit]]

Hwang at 02:45, 11 September 2022

2022-09-11T02:45:13Z

← Older revision		Revision as of 04:45, 11 September 2022
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	<br>		<br>
	Digital channel models are preferably used for cascaded transmission,  as shown in the graph.  You can see from this diagram:		Digital channel models are preferably used for cascaded transmission,  as shown in the graph.  You can see from this diagram:
	[[File:EN_Dig_T_5_1_S3_neu.png\|right\|frame\|Model of a transmission system with encoder/decoder\|class=fit]]		[[File:EN_Dig_T_5_1_S3_neu.png\|right\|frame\|Model of a transmission system with encoder/decoder '''KORREKTUR: Komparator'''\|class=fit]]
	*The inner transmission system – consisting of modulator, analog channel, noise, demodulator, receiver filter, decision, clock recovery – is summarized in the block  "Digital channel"  marked in blue.<br>		*The inner transmission system – consisting of modulator, analog channel, noise, demodulator, receiver filter, decision, clock recovery – is summarized in the block  "Digital channel"  marked in blue.<br>

Hwang at 02:33, 11 September 2022

2022-09-11T02:33:53Z

← Older revision		Revision as of 04:33, 11 September 2022
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	Such channel models are mainly used for  »cascaded transmission systems«  for the inner block,  if the performance of the outer system components  $($e.g. coder and decoder$)$  is to be determined by simulation.		Such channel models are mainly used for  »cascaded transmission systems«  for the inner block,  if the performance of the outer system components  $($e.g. coder '''KORREKTUR: encoder''' and decoder$)$  is to be determined by simulation.

	The following are dealt with in detail:		The following are dealt with in detail:

Guenter at 15:22, 6 September 2022

2022-09-06T15:22:13Z

← Older revision		Revision as of 17:22, 6 September 2022
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	{{GraueBox\|TEXT=		{{GraueBox\|TEXT=
	$\text{Example 2:}$  In the graph,  we see in the center the BMP image  "White"  with $300 × 200$ pixels.		$\text{Example 2:}$  In the graph,  we see in the center the BMP image  "White"  with $300 × 200$ pixels.
	[[File:~~EN_Dig_T_5_1_S2b~~.png\|right\|frame\|BMP image  "White"  with independent errors  $($left$)$  and burst errors  $($right) \|class=fit]]		[[File:EN_Dig_T_5_1_S2b_neu.png\|right\|frame\|BMP image  "White"  with independent errors  $($left$)$  and burst errors  $($right) \|class=fit]]
	*The left image shows the falsification with statistically independent errors   ⇒   [[Digital_Signal_Transmission/Binary_Symmetric_Channel_(BSC)\|"BSC model"]].		*The left image shows the falsification with statistically independent errors   ⇒   [[Digital_Signal_Transmission/Binary_Symmetric_Channel_(BSC)\|"BSC model"]].

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	<br>		<br>
	Digital channel models are preferably used for cascaded transmission,  as shown in the graph.  You can see from this diagram:		Digital channel models are preferably used for cascaded transmission,  as shown in the graph.  You can see from this diagram:
	[[File:~~EN_Dig_T_5_1_S3~~.png\|right\|frame\|Model of a transmission system with encoder/decoder\|class=fit]]		[[File:EN_Dig_T_5_1_S3_neu.png\|right\|frame\|Model of a transmission system with encoder/decoder\|class=fit]]
	*The inner transmission system – consisting of modulator, analog channel, noise, demodulator, receiver filter, decision, clock recovery – is summarized in the block  "Digital channel"  marked in blue.<br>		*The inner transmission system – consisting of modulator, analog channel, noise, demodulator, receiver filter, decision, clock recovery – is summarized in the block  "Digital channel"  marked in blue.<br>

Guenter at 15:51, 3 September 2022

2022-09-03T15:51:04Z

← Older revision		Revision as of 17:51, 3 September 2022
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	#  The descriptive quantities  »error correlation function«  and  »error distance distribution«,		#  The descriptive quantities  »error correlation function«  and  »error distance distribution«,
	#  the  »BSC model«   ("Binary Symmetric Channel")   for the description of statistically independent errors,		#  the  »BSC model«   ("Binary Symmetric Channel")   for the description of statistically independent errors,
	#  the  »~~bundle~~ error channel models«  according to Gilbert-Elliott and McCullough,		#  the  »burst error channel models«  according to Gilbert-Elliott and McCullough,
	#  the  »Wilhelm channel model«  for the formulaic approximation of measured error curves,		#  the  »Wilhelm channel model«  for the formulaic approximation of measured error curves,
	#  some notes on the  »generation of error sequences«,  for example with respect to  »error distance simulation«,		#  some notes on the  »generation of error sequences«,  for example with respect to  »error distance simulation«,
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	$\text{Conclusion:}$  The  '''error sequence'''  $ \langle e_\nu \rangle$  allows statements about the error statistics,  for example whether the errors are so-called		$\text{Conclusion:}$  The  '''error sequence'''  $ \langle e_\nu \rangle$  allows statements about the error statistics,  for example whether the errors are so-called
	# "statistically independent errors",  or<br>		# "statistically independent errors",  or<br>
	# "~~bundle~~ errors".<br><br>		# "burst errors".<br><br>

	The following example is intended to illustrate these two error types.}}<br>		The following example is intended to illustrate these two error types.}}<br>
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	{{GraueBox\|TEXT=		{{GraueBox\|TEXT=
	$\text{Example 2:}$  In the graph,  we see in the center the BMP image  "White"  with $300 × 200$ pixels.		$\text{Example 2:}$  In the graph,  we see in the center the BMP image  "White"  with $300 × 200$ pixels.
	[[File:EN_Dig_T_5_1_S2b.png\|right\|frame\|BMP image  "White"  with independent errors  $($left$)$  and ~~bundle~~ errors  $($right) \|class=fit]]		[[File:EN_Dig_T_5_1_S2b.png\|right\|frame\|BMP image  "White"  with independent errors  $($left$)$  and burst errors  $($right) \|class=fit]]
	*The left image shows the falsification with statistically independent errors   ⇒   [[Digital_Signal_Transmission/Binary_Symmetric_Channel_(BSC)\|"BSC model"]].		*The left image shows the falsification with statistically independent errors   ⇒   [[Digital_Signal_Transmission/Binary_Symmetric_Channel_(BSC)\|"BSC model"]].

	* The right image illustrates a ~~bundle~~ error channel   ⇒   [[Digital_Signal_Transmission/Burst_Error_Channels#Channel_model_according_to_Gilbert-Elliott\|"Gilbert-Elliott model"]].  <br>		* The right image illustrates a burst error channel   ⇒   [[Digital_Signal_Transmission/Burst_Error_Channels#Channel_model_according_to_Gilbert-Elliott\|"Gilbert-Elliott model"]].  <br>


	<u>Notes:</u>		<u>Notes:</u>
	# A  [[Digital_Signal_Transmission/Applications_for_Multimedia_Files#Images_in_BMP_format\|"BMP graphics"]]  is always saved line by line,  which can be seen in the error ~~bundles~~ in the right image.		# A  [[Digital_Signal_Transmission/Applications_for_Multimedia_Files#Images_in_BMP_format\|"BMP graphics"]]  is always saved line by line,  which can be seen in the error bursts in the right image.
	# Mean error probability in both cases:  $2.5\%$;  on average every $40$th pixel is falsified  $($here:   white  ⇒  black$)$.}}<br>		# Mean error probability in both cases:  $2.5\%$;  on average every $40$th pixel is falsified  $($here:   white  ⇒  black$)$.}}<br>