Digital Signal Transmission/Intersymbol Interference for Multi-Level Transmission - Revision history

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	In contrast to the  [[Digital_Signal_Transmission/Berücksichtigung_von_Kanalverzerrungen_und_Entzerrung\| last chapter]],  the still redundancy-free transmitted signal  $s(t)$  is now no longer binary, but of  $M$–level,  which only has an effect in the set of of the amplitude coefficients:		In contrast to the  [[Digital_Signal_Transmission/Berücksichtigung_von_Kanalverzerrungen_und_Entzerrung\| last chapter]],  the still redundancy-free transmitted signal  $s(t)$  is now no longer binary, but of  $M$–level,  which only has an effect in the set of of the amplitude coefficients:
	:$$s(t) = \sum_{\nu = -\infty}^{+\infty} a_\nu \cdot g_s ( t - \nu \cdot T)\hspace{0.3cm}{\rm with}\hspace{0.3cm}		:$$s(t) = \sum_{\nu = -\infty}^{+\infty} a_\nu \cdot g_s ( t - \nu \cdot T)\hspace{0.3cm}{\rm with}\hspace{0.3cm}a_\nu \in \{ a_1,\ \text{ ...} \ , a_\mu , \ \text{ ...} \ , a_{M}\}\hspace{0.05cm}.$$
	a_\nu \in \{ a_1,\ \text{ ...} \ , a_\mu , \ \text{ ...} \ , a_{M}\}\hspace{0.05cm}.$$

	Accordingly,  the decision unit now has not only one,  but  $M-1$  decision thresholds and in the eye diagram  $M-1$  eye openings are visible when the eye is open.<br>		Accordingly,  the decision unit now has not only one,  but  $M-1$  decision thresholds and in the eye diagram  $M-1$  eye openings are visible when the eye is open.<br>
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	*In the multi-level systems,  the eye opening is per se smaller by a factor of  $1/(M-1)$.  Thus,  the eye opening is reduced  (relatively speaking)  more by the  ISI causing pulse values  $g_1$  and  $g_{-1}=g_1$  than in the binary system.  One obtains with the same basic detection pulse values for		*In the multi-level systems,  the eye opening is per se smaller by a factor of  $1/(M-1)$.  Thus,  the eye opening is reduced  (relatively speaking)  more by the  ISI causing pulse values  $g_1$  and  $g_{-1}=g_1$  than in the binary system.  One obtains with the same basic detection pulse values for
	:$$M = 3\text{:} \hspace{0.2cm}{\ddot{o}(T_{\rm D})} = 2 \cdot (g_0/2 - 2 \cdot g_1) \approx 0.6 \cdot s_0		:$$M = 3\text{:} \hspace{0.2cm}{\ddot{o}(T_{\rm D})} = 2 \cdot (g_0/2 - 2 \cdot g_1) \approx 0.6 \cdot s_0\hspace{0.05cm},$$
	\hspace{0.05cm},$$		:$$M = 4\text{:} \hspace{0.2cm}{\ddot{o}(T_{\rm D})} = 2 \cdot (g_0/3 - 2 \cdot g_1) \approx 0.3 \cdot s_0\hspace{0.05cm}.$$
	:$$M = 4\text{:} \hspace{0.2cm}{\ddot{o}(T_{\rm D})} = 2 \cdot (g_0/3 - 2 \cdot g_1) \approx 0.3 \cdot s_0
	\hspace{0.05cm}.$$

	*But when comparing the systems,  it should be noted that the larger level number  $M$  also increases the information flow.  That is,  the multi-level systems are better than these graphs indicate.  More about this in the next section.}}<br>		*But when comparing the systems,  it should be noted that the larger level number  $M$  also increases the information flow.  That is,  the multi-level systems are better than these graphs indicate.  More about this in the next section.}}<br>
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	The graph shows the half eye opening  $($normalized to  $s_0)$  as a function of the quotient  $f_{\rm G}/R_{\rm B}$  of the Gaussian receiver filter.  In  [[Aufgaben:Exercise_3.4Z:_Eye_Opening_and_Level_Number\|Exercise 3.4Z]],  this is calculated in analytical form as follows:		The graph shows the half eye opening  $($normalized to  $s_0)$  as a function of the quotient  $f_{\rm G}/R_{\rm B}$  of the Gaussian receiver filter.  In  [[Aufgaben:Exercise_3.4Z:_Eye_Opening_and_Level_Number\|Exercise 3.4Z]],  this is calculated in analytical form as follows:
	:$$\ddot{o}_{\rm norm} = \frac{\ddot{o}(T_{\rm D})}{ 2 \cdot s_0} = \frac{M}{ M-1}\cdot \frac{g_0}{		:$$\ddot{o}_{\rm norm} = \frac{\ddot{o}(T_{\rm D})}{ 2 \cdot s_0} = \frac{M}{ M-1}\cdot \frac{g_0}{s_0} -1 = \frac{1}{ M-1}\cdot \big [1- 2 \cdot M \cdot {\rm Q} \left(\sqrt{2\pi} \cdot {\log_2}\hspace{0.1cm}(M) \cdot {f_{\rm G}}/{R_{\rm B}}\right)\big]\hspace{0.05cm}.$$
	s_0} -1 = \frac{1}{ M-1}\cdot \big [1- 2 \cdot M \cdot {\rm Q} \left(
	\sqrt{2\pi} \cdot {\log_2}\hspace{0.1cm}(M) \cdot {f_{\rm
	G}}/{R_{\rm B}}
	\right)\big]
	\hspace{0.05cm}.$$
	[[File:P ID3140 Dig T 3 4 S2 version1.png\|right\|frame\|Half normalized eye opening for  $M = 2$,  $M = 3$  and  $M = 4$\|class=fit]]		[[File:P ID3140 Dig T 3 4 S2 version1.png\|right\|frame\|Half normalized eye opening for  $M = 2$,  $M = 3$  and  $M = 4$\|class=fit]]
	One can see from the graph:		One can see from the graph:
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	The right graph shows the  '''signal-to-noise ratio gain'''  of the quaternary system over the binary system,		The right graph shows the  '''signal-to-noise ratio gain'''  of the quaternary system over the binary system,
	:$$G_{_{M=4}} = 10 \cdot {\rm lg}\hspace{0.1cm}\rho_{_{{\rm U},\hspace{0.05cm}		:$$G_{_{M=4}} = 10 \cdot {\rm lg}\hspace{0.1cm}\rho_{_{{\rm U},\hspace{0.05cm}M=4}} - 10 \cdot {\rm lg}\hspace{0.1cm}\rho_{_{{\rm U}, \hspace{0.05cm}M=2}},$$
	M=4}} - 10 \cdot {\rm lg}\hspace{0.1cm}\rho_{_{{\rm U}, \hspace{0.05cm}M=2}},$$

	when the cutoff frequencies are chosen optimally in each case according to the left graph.  Accordingly:		when the cutoff frequencies are chosen optimally in each case according to the left graph.  Accordingly:
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	Thus,  for the redundancy-free binary system (middle graph),  due to the intersymbol interference, we obtain for the eye opening		Thus,  for the redundancy-free binary system (middle graph),  due to the intersymbol interference, we obtain for the eye opening
	:$${\ddot{o}(T_{\rm D})}= 2 \cdot (g_0 - 2 \cdot g_1 ) = 0.72$$		:$${\ddot{o}(T_{\rm D})}= 2 \cdot (g_0 - 2 \cdot g_1 ) = 0.72$$
	:$$\Rightarrow \hspace{0.3cm}		:$$\Rightarrow \hspace{0.3cm}\ddot{o}_{\rm norm} = \frac{\ddot{o}(T_{\rm D})}{ 2 \cdot s_0} = 36\%$$
	\ddot{o}_{\rm norm} = \frac{\ddot{o}(T_{\rm D})}{ 2 \cdot s_0} = 36\%$$

	compared to  $\ddot{o}(T_{\rm D}) = 2$  or  $\ddot{o}_{\rm norm} = 100\%$  for the binary Nyquist system.<br>		compared to  $\ddot{o}(T_{\rm D}) = 2$  or  $\ddot{o}_{\rm norm} = 100\%$  for the binary Nyquist system.<br>
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	*The lower boundary line  $d_{\rm bottom} = g_1$  goes back to the symbol sequence  "$\text{...} 0,\hspace{0.05cm} {\it 0},\hspace{0.05cm} +\hspace{-0.05cm}\hspace{-0.05cm}1 \text{...}$"  and to the sequence  "$\text{...} +\hspace{-0.05cm}\hspace{-0.05cm}1,\hspace{0.05cm} {\it 0},\hspace{0.05cm} 0\hspace{0.05cm} \text{...}$",  respectively.		*The lower boundary line  $d_{\rm bottom} = g_1$  goes back to the symbol sequence  "$\text{...} 0,\hspace{0.05cm} {\it 0},\hspace{0.05cm} +\hspace{-0.05cm}\hspace{-0.05cm}1 \text{...}$"  and to the sequence  "$\text{...} +\hspace{-0.05cm}\hspace{-0.05cm}1,\hspace{0.05cm} {\it 0},\hspace{0.05cm} 0\hspace{0.05cm} \text{...}$",  respectively.
	*Here it is considered that the sequence  "$\text{...} +\hspace{-0.05cm}\hspace{-0.05cm}1,\hspace{0.05cm} {\it 0},\hspace{0.05cm} +\hspace{-0.05cm}\hspace{-0.05cm}1\hspace{0.05cm} \text{...}$"  is excluded by the AMI coding rule.  Thus,  the eye opening of the AMI code is:		*Here it is considered that the sequence  "$\text{...} +\hspace{-0.05cm}\hspace{-0.05cm}1,\hspace{0.05cm} {\it 0},\hspace{0.05cm} +\hspace{-0.05cm}\hspace{-0.05cm}1\hspace{0.05cm} \text{...}$"  is excluded by the AMI coding rule.  Thus,  the eye opening of the AMI code is:
	:$${\ddot{o}(T_{\rm D})}= d_{\rm top} - d_{\rm bottom} =g_0 - 3 \cdot g_1 = 0.20		:$${\ddot{o}(T_{\rm D})}= d_{\rm top} - d_{\rm bottom} =g_0 - 3 \cdot g_1 = 0.20\hspace{0.3cm}\Rightarrow \hspace{0.3cm}\ddot{o}_{\rm norm} = \frac{\ddot{o}(T_{\rm D})}{ 2 \cdot s_0} = 10\, \%.$$
	\hspace{0.3cm}\Rightarrow \hspace{0.3cm}
	\ddot{o}_{\rm norm} = \frac{\ddot{o}(T_{\rm D})}{ 2 \cdot s_0} = 10\, \%.$$
	*The upper decision threshold  $E_2$  as well as the lower decision threshold  $E_1$  are at		*The upper decision threshold  $E_2$  as well as the lower decision threshold  $E_1$  are at
	:$$E_2 = {1}/{2} \cdot (d_{\rm top} + d_{\rm bottom}) = {1}/{2} \cdot (g_0 - g_1) = 0.27 \hspace{0.05cm}, \hspace{0.2cm}E_1 = - 0.27 \hspace{0.05cm}.$$		:$$E_2 = {1}/{2} \cdot (d_{\rm top} + d_{\rm bottom}) = {1}/{2} \cdot (g_0 - g_1) = 0.27 \hspace{0.05cm}, \hspace{0.2cm}E_1 = - 0.27 \hspace{0.05cm}.$$
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	In the  '''duobinary code'''  (right graph),  the particularly unfavorable alternating symbol sequence does not occur and one obtains for the eye opening as well as the decision thresholds:		In the  '''duobinary code'''  (right graph),  the particularly unfavorable alternating symbol sequence does not occur and one obtains for the eye opening as well as the decision thresholds:
	:$$d_{\rm top}= g_0, \hspace{0.2cm} d_{\rm bottom} = g_1 \hspace{0.3cm}\Rightarrow		:$$d_{\rm top}= g_0, \hspace{0.2cm} d_{\rm bottom} = g_1 \hspace{0.3cm}\Rightarrow\hspace{0.3cm}{\ddot{o}(T_{\rm D})} = g_0 - g_1 = 0.52\hspace{0.3cm}\Rightarrow \hspace{0.3cm}\ddot{o}_{\rm norm} = 26\, \%\hspace{0.05cm}, \hspace{0.3cm} E_2 = {1}/{2} \cdot (g_0 + g_1) = 0.42 \hspace{0.05cm}, \hspace{0.2cm}E_1 = - 0.42 \hspace{0.05cm}.$$
	\hspace{0.3cm}{\ddot{o}(T_{\rm D})} = g_0 - g_1 = 0.52
	\hspace{0.3cm}\Rightarrow \hspace{0.3cm}
	\ddot{o}_{\rm norm} = 26\, \%
	\hspace{0.05cm}, \hspace{0.3cm} E_2 = {1}/{2} \cdot (g_0 + g_1) = 0.42 \hspace{0.05cm}, \hspace{0.2cm}E_1 = - 0.42 \hspace{0.05cm}.$$

Maintenance script: Add German interlanguage link

2026-03-16T12:26:45Z

Add German interlanguage link

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	{{Display}}		{{Display}}
			[[de:Digitalsignalübertragung/Impulsinterferenzen_bei_mehrstufiger_Übertragung]]

Hwang at 14:14, 23 January 2023

2023-01-23T14:14:23Z

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	{{BlaueBox\|TEXT=		{{BlaueBox\|TEXT=
	$\text{However, it has to be taken into account:}$  All results in this chapter are valid under the condition  $H_{\rm K}(f=0) = 1$.		$\text{However, it has to be taken into account:}$  All results in this chapter are valid under the condition  $H_{\rm K}(f=0) = 1$.
	#If a redundancy-free signal or the duobinary-~~coded~~ signal is to be transmitted over a DC-impermeable channel,  a complex DC recovery is required,  which is always associated with a degradation of the S/N ratio as well  [TS87]<ref>Tröndle, K.; Söder, G.:  Optimization of Digital Transmission Systems.  Boston – London: Artech House, 1987,  ISBN:  0-89006-225-0.</ref>.<br><br>		#If a redundancy-free signal or the duobinary-encoded signal is to be transmitted over a DC-impermeable channel,  a complex DC recovery is required,  which is always associated with a degradation of the S/N ratio as well  [TS87]<ref>Tröndle, K.; Söder, G.:  Optimization of Digital Transmission Systems.  Boston – London: Artech House, 1987,  ISBN:  0-89006-225-0.</ref>.<br><br>
	# The AMI code is free of DC signals and can thus also be transmitted over a telephone channel   ⇒   $H_{\rm K}(f=0) = 0$.  This is the decisive reason why the AMI code is used in  [[Examples_of_Communication_Systems/Allgemeine_Beschreibung_von_ISDN\| ISDN]]  ("Integrated Services Digital Network"),  for example,  despite otherwise poor properties.}}<br>		# The AMI code is free of DC signals and can thus also be transmitted over a telephone channel   ⇒   $H_{\rm K}(f=0) = 0$.  This is the decisive reason why the AMI code is used in  [[Examples_of_Communication_Systems/Allgemeine_Beschreibung_von_ISDN\| ISDN]]  ("Integrated Services Digital Network"),  for example,  despite otherwise poor properties.}}<br>

Hwang at 07:13, 11 July 2022

2022-07-11T07:13:27Z

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	The graph shows the half eye opening  $($normalized to  $s_0)$  as a function of the quotient  $f_{\rm G}/R_{\rm B}$  of the Gaussian receiver filter.  In  [[Aufgaben:~~Aufgabe_3~~.4Z:~~_Augenöffnung_und_Stufenzahl~~\|Exercise 3.4Z]],  this is calculated in analytical form as follows:		The graph shows the half eye opening  $($normalized to  $s_0)$  as a function of the quotient  $f_{\rm G}/R_{\rm B}$  of the Gaussian receiver filter.  In  [[Aufgaben:Exercise_3.4Z:_Eye_Opening_and_Level_Number\|Exercise 3.4Z]],  this is calculated in analytical form as follows:
	:$$\ddot{o}_{\rm norm} = \frac{\ddot{o}(T_{\rm D})}{ 2 \cdot s_0} = \frac{M}{ M-1}\cdot \frac{g_0}{		:$$\ddot{o}_{\rm norm} = \frac{\ddot{o}(T_{\rm D})}{ 2 \cdot s_0} = \frac{M}{ M-1}\cdot \frac{g_0}{
	s_0} -1 = \frac{1}{ M-1}\cdot \big [1- 2 \cdot M \cdot {\rm Q} \left(		s_0} -1 = \frac{1}{ M-1}\cdot \big [1- 2 \cdot M \cdot {\rm Q} \left(

Guenter at 14:44, 28 June 2022

2022-06-28T14:44:05Z

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	{{GraueBox\|TEXT=		{{GraueBox\|TEXT=
	$\text{Example 1:}$  Below you can see three eye diagrams  (without noise)  for the level numbers  $M = 2$,  $M = 3$  and  $M = 4$.		$\text{Example 1:}$  Below you can see three eye diagrams  (without noise)  for the level numbers  $M = 2$,  $M = 3$  and  $M = 4$.
	[[File:~~EN_Dig_T_3_4_S1b~~.png\|right\|frame\|Noiseless eye diagrams of a binary,  ternary and quaternary system.   Note:  the normalized cutoff frequency  $f_{\rm G} \cdot T = 0.6$  holds for all three diagrams~~<br><br> '''Korrektur''': Strich~~\|class=fit]]		[[File:EN_Dig_T_3_4_S1b_neu.png\|right\|frame\|Noiseless eye diagrams of a binary,  ternary and quaternary system.   Note:  the normalized cutoff frequency  $f_{\rm G} \cdot T = 0.6$  holds for all three diagrams\|class=fit]]

	*The binary eye diagram is valid for a Gaussian low-pass with the cutoff frequency  $f_{\rm G} \cdot T = 0.6$. With the  "main value"  $g_0 = 0.867 \cdot s_0$,  the  "postcursor"   $g_{1} = 0.067 \cdot s_0$  and  the  "precursor"  $g_{-1} = g_{1}$, the result in this case for the vertical eye opening  (rounding to one decimal place)  is:		*The binary eye diagram is valid for a Gaussian low-pass with the cutoff frequency  $f_{\rm G} \cdot T = 0.6$. With the  "main value"  $g_0 = 0.867 \cdot s_0$,  the  "postcursor"   $g_{1} = 0.067 \cdot s_0$  and  the  "precursor"  $g_{-1} = g_{1}$, the result in this case for the vertical eye opening  (rounding to one decimal place)  is:

Guenter at 14:41, 21 June 2022

2022-06-21T14:41:27Z

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	[[Aufgaben:Exercise_3.4:_Optimization_of_the_Cutoff_Frequency\|Exercise 3.4: Optimization of the Cutoff Frequency]]		[[Aufgaben:Exercise_3.4:_Optimization_of_the_Cutoff_Frequency\|Exercise 3.4: Optimization of the Cutoff Frequency]]

	[[Aufgaben:Exercise_3.4Z:~~_Eye_Opening_and_Number_of_Steps~~\|Exercise 3.4Z: Eye Opening and Number ~~of Steps~~]]		[[Aufgaben:Exercise_3.4Z:_Eye_Opening_and_Level_Number\|Exercise 3.4Z: Eye Opening and Level Number]]

	[[Aufgaben:Exercise_3.5:_Eye_Opening_with_Pseudoternary_Coding\|Exercise 3.5: Eye Opening with Pseudoternary Coding]]		[[Aufgaben:Exercise_3.5:_Eye_Opening_with_Pseudoternary_Coding\|Exercise 3.5: Eye Opening with Pseudoternary Coding]]

Guenter at 12:26, 20 June 2022

2022-06-20T12:26:43Z

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	⇒   Note:  The degradations due to intersymbol interference in AMI and duobinary coding can also be displayed using the HTML5/JavaScript applet  [[Applets:~~Augendiagramm~~\|"Eye Diagram and Eye Opening"]].  However,  the error probabilities apply only to the distortion-free channel  $(a_\star = 0 \ \rm dB)$.<br>		⇒   Note:  The degradations due to intersymbol interference in AMI and duobinary coding can also be displayed using the HTML5/JavaScript applet  [[Applets:Eye_Pattern_and_Worst-Case_Error_Probability\|"Eye Diagram and Eye Opening"]].  However,  the error probabilities apply only to the distortion-free channel  $(a_\star = 0 \ \rm dB)$.<br>

	== Cutoff frequency optimization with pseudo-ternary coding ==		== Cutoff frequency optimization with pseudo-ternary coding ==

Guenter at 12:24, 20 June 2022

2022-06-20T12:24:40Z

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	[[File:EN_Dig_T_3_4_S4.png\|right\|frame\|Eye diagrams for the pseudo-ternary codes  (AMI code,  duobinary code)\|class=fit]]		[[File:EN_Dig_T_3_4_S4.png\|right\|frame\|Eye diagrams for the pseudo-ternary codes  (AMI code,  duobinary code)\|class=fit]]

	*the  [[Digital_Signal_Transmission/~~Symbol~~-~~Wise_Coding_with_Pseudo_Ternary_Codes~~#Properties_of_the_AMI_code\|AMI code]]   (on the left),		*the  [[Digital_Signal_Transmission/Symbolwise_Coding_with_Pseudo-Ternary_Codes#Properties_of_the_AMI_code\|AMI code]]   (on the left),
	*the  [[Digital_Signal_Transmission/~~Symbol~~-~~Wise_Coding_with_Pseudo_Ternary_Codes~~#Properties_of_the_duobinary_code\|duobinary code]]   (on the right).		*the  [[Digital_Signal_Transmission/Symbolwise_Coding_with_Pseudo-Ternary_Codes#Properties_of_the_duobinary_code\|duobinary code]]   (on the right).

Guenter at 12:22, 20 June 2022

2022-06-20T12:22:13Z

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	== Cutoff frequency optimization with pseudo-ternary coding ==		== Cutoff frequency optimization with pseudo-ternary coding ==
	<br>		<br>
	Considering a coaxial transmission channel and the thus necessary channel equalization, the following statements are possible:		Considering a coaxial transmission channel and the thus necessary channel equalization,  the following statements are possible:
	*The AMI code always leads to a worse signal-to-noise ratio than the redundancy-free binary code if the overall frequency response is Gaussian. With the characteristic cable attenuation  $a_\star = 80 \ \rm dB$,  the signal-to-noise ratio loss is about  $11 \ \rm dB$.<br>		*The AMI code always leads to a worse signal-to-noise ratio than the redundancy-free binary code if the overall frequency response is Gaussian.  With the characteristic cable attenuation  $a_\star = 80 \ \rm dB$,  the signal-to-noise ratio loss is about  $11 \ \rm dB$.<br>

			*This loss is due to the fact that,  despite ternary coding,  the symbol rate is not reduced compared to the binary reference system.  This has the consequence that with the AMI code already a cutoff frequency  $f_\text{G} \cdot T < 0.36$  leads to a closed eye.<br>

	*~~This loss is due to the fact that~~, despite ternary coding, the symbol rate is not reduced compared to the binary reference system. This has the consequence that with the AMI code already a cutoff frequency  $f_\text{G} \cdot T < 0.36$  ~~leads to a closed eye.<br>~~		*In contrast,  with the duobinary code a closed eye results only from  $f_\text{G} \cdot T < 0.22$.  As a result,  the optimal cutoff frequency is also smaller than with the binary system.  At 80 dB cable attenuation,  the duobinary code in combination with  $f_\text{G} \cdot T =0.28$  is  $3.3 \ \rm dB$  better than the best value with redundancy-free binary coding.<br>


	*In contrast, with the duobinary code a closed eye results only from  $f_\text{G} \cdot T < 0.22$. As a result, the optimal cutoff frequency is also smaller than with the binary system. At 80 dB cable attenuation, the duobinary code in combination with  $f_\text{G} \cdot T =0.28$  is  $3.3 \ \rm dB$  better than the best value with redundancy-free binary coding.<br>


	{{BlaueBox\|TEXT=		{{BlaueBox\|TEXT=
	$\text{However, it has to be taken into account:}$  All results in this chapter are valid under the condition  $H_{\rm K}(f=0) = 1$.		$\text{However, it has to be taken into account:}$  All results in this chapter are valid under the condition  $H_{\rm K}(f=0) = 1$.
	*If a redundancy-free signal or the duobinary-coded signal is to be transmitted over a DC-impermeable channel, a complex DC recovery is required, which is always associated with a degradation of the S/N ratio as well  [TS87]<ref>Tröndle, K.; Söder, G.:  Optimization of Digital Transmission Systems.  Boston – London: Artech House, 1987,  ISBN:  0-89006-225-0.</ref>.<br><br>		#If a redundancy-free signal or the duobinary-coded signal is to be transmitted over a DC-impermeable channel,  a complex DC recovery is required,  which is always associated with a degradation of the S/N ratio as well  [TS87]<ref>Tröndle, K.; Söder, G.:  Optimization of Digital Transmission Systems.  Boston – London: Artech House, 1987,  ISBN:  0-89006-225-0.</ref>.<br><br>
			# The AMI code is free of DC signals and can thus also be transmitted over a telephone channel   ⇒   $H_{\rm K}(f=0) = 0$.  This is the decisive reason why the AMI code is used in  [[Examples_of_Communication_Systems/Allgemeine_Beschreibung_von_ISDN\| ISDN]]  ("Integrated Services Digital Network"),  for example,  despite otherwise poor properties.}}<br>
	* The AMI code is free of DC signals and can thus also be transmitted over a telephone channel   ⇒   $H_{\rm K}(f=0) = 0$.  This is the decisive reason why the AMI code is used in  [[Examples_of_Communication_Systems/Allgemeine_Beschreibung_von_ISDN\| "ISDN"]]  (~~<i>~~Integrated Services Digital Network~~</i>~~), for example, despite otherwise poor properties.}}<br>

	==Exercises for the chapter==		==Exercises for the chapter==

Guenter at 16:44, 19 June 2022

2022-06-19T16:44:30Z

Show changes

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	[[Aufgaben:Exercise_3.4:_Optimization_of_the_Cutoff_Frequency\|Exercise 3.4: Optimization of the Cutoff Frequency]]		[[Aufgaben:Exercise_3.4:_Optimization_of_the_Cutoff_Frequency\|Exercise 3.4: Optimization of the Cutoff Frequency]]

	[[Aufgaben:Exercise_3.4Z:~~_Eye_Opening_and_Number_of_Steps~~\|Exercise 3.4Z: Eye Opening and Number ~~of Steps~~]]		[[Aufgaben:Exercise_3.4Z:_Eye_Opening_and_Level_Number\|Exercise 3.4Z: Eye Opening and Level Number]]

	[[Aufgaben:Exercise_3.5:_Eye_Opening_with_Pseudoternary_Coding\|Exercise 3.5: Eye Opening with Pseudoternary Coding]]		[[Aufgaben:Exercise_3.5:_Eye_Opening_with_Pseudoternary_Coding\|Exercise 3.5: Eye Opening with Pseudoternary Coding]]

← Older revision		Revision as of 14:24, 20 June 2022
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	[[File:EN_Dig_T_3_4_S4.png\|right\|frame\|Eye diagrams for the pseudo-ternary codes  (AMI code,  duobinary code)\|class=fit]]		[[File:EN_Dig_T_3_4_S4.png\|right\|frame\|Eye diagrams for the pseudo-ternary codes  (AMI code,  duobinary code)\|class=fit]]

	*the  [[Digital_Signal_Transmission/~~Symbol~~-~~Wise_Coding_with_Pseudo_Ternary_Codes~~#Properties_of_the_AMI_code\|AMI code]]   (on the left),		*the  [[Digital_Signal_Transmission/Symbolwise_Coding_with_Pseudo-Ternary_Codes#Properties_of_the_AMI_code\|AMI code]]   (on the left),
	*the  [[Digital_Signal_Transmission/~~Symbol~~-~~Wise_Coding_with_Pseudo_Ternary_Codes~~#Properties_of_the_duobinary_code\|duobinary code]]   (on the right).		*the  [[Digital_Signal_Transmission/Symbolwise_Coding_with_Pseudo-Ternary_Codes#Properties_of_the_duobinary_code\|duobinary code]]   (on the right).