Applets:Eye Pattern and Worst-Case Error Probability - Revision history

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Guenter at 15:22, 10 April 2023

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 This interactive calculation tool was designed and implemented at the&nbsp; [https://www.ei.tum.de/en/lnt/home/ Institute for Communications Engineering]&nbsp; at the&nbsp; [https://www.tum.de/en Technical University of Munich].
-*The first version was created in 2008 by [[Biographies_and_Bibliographies/Students_involved_in_LNTwww#Thomas_Gro.C3.9Fer_.28Diplomarbeit_LB_2006.2C_danach_freie_Mitarbeit_bis_2010.29|Thomas Großer]]&nbsp; as part of his diploma thesis with “FlashMX – Actionscript” (Supervisor: [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.28am_LNT_seit_1974.29|Günter Söder]]).
+*The first version was created in 2008 by [[Biographies_and_Bibliographies/Students_involved_in_LNTwww#Thomas_Gro.C3.9Fer_.28Diplomarbeit_LB_2006.2C_danach_freie_Mitarbeit_bis_2010.29|Thomas Großer]]&nbsp; as part of his diploma thesis with “FlashMX – Actionscript” (Supervisor: [[Biographies_and_Bibliographies/LNTwww_members_from_LNT#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.28am_LNT_seit_1974.29|Günter Söder]]).
 *Last revision and English version 2020/2021 by&nbsp; [[Biographies_and_Bibliographies/Students_involved_in_LNTwww#Carolin_Mirschina_.28Ingenieurspraxis_Math_2019.2C_danach_Werkstudentin.29|Carolin Mirschina]]&nbsp; in the context of a working student activity.&nbsp;

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 This interactive calculation tool was designed and implemented at the&nbsp; [https://www.ei.tum.de/en/lnt/home/ Institute for Communications Engineering]&nbsp; at the&nbsp; [https://www.tum.de/en Technical University of Munich].
-*The first version was created in 2008 by [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#Thomas_Gro.C3.9Fer_.28Diplomarbeit_LB_2006.2C_danach_freie_Mitarbeit_bis_2010.29|Thomas Großer]]&nbsp; as part of his diploma thesis with “FlashMX – Actionscript” (Supervisor: [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.28am_LNT_seit_1974.29|Günter Söder]]).
+*The first version was created in 2008 by [[Biographies_and_Bibliographies/Students_involved_in_LNTwww#Thomas_Gro.C3.9Fer_.28Diplomarbeit_LB_2006.2C_danach_freie_Mitarbeit_bis_2010.29|Thomas Großer]]&nbsp; as part of his diploma thesis with “FlashMX – Actionscript” (Supervisor: [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.28am_LNT_seit_1974.29|Günter Söder]]).
-*Last revision and English version 2020/2021 by&nbsp; [[Biografien_und_Bibliografien/An_LNTwww_beteiligte_Studierende#Carolin_Mirschina_.28Ingenieurspraxis_Math_2019.2C_danach_Werkstudentin.29|Carolin Mirschina]]&nbsp; in the context of a working student activity.&nbsp;
+*Last revision and English version 2020/2021 by&nbsp; [[Biographies_and_Bibliographies/Students_involved_in_LNTwww#Carolin_Mirschina_.28Ingenieurspraxis_Math_2019.2C_danach_Werkstudentin.29|Carolin Mirschina]]&nbsp; in the context of a working student activity.&nbsp;

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 <br>
 [[File:Anleitung_Auge.png|right|600px|frame|Screenshot of the German version]]
-&nbsp; &nbsp; '''(A)''' &nbsp; &nbsp; Selection: &nbsp; Coding <br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;(binary,&nbsp; quaternary,&nbsp; AMI code,&nbsp; duobinary code)
+&nbsp; &nbsp; '''(A)''' &nbsp; &nbsp; Selection: &nbsp; Encoding <br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;(binary,&nbsp; quaternary,&nbsp; AMI code,&nbsp; duobinary code)
 &nbsp; &nbsp; '''(B)''' &nbsp; &nbsp; Selection: &nbsp; Basic detection pulse<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (according to Gauss&ndash;TP,&nbsp; CRO&ndash;Nyquist,&nbsp; according to gap&ndash;TP}

@@ Line 112: / Line 112: @@
 ===Intersymbol interference system with Gaussian receiver filter===
-[[File:EN_Auge_4.png|right|frame|System with Gaussian receiver filter]]
+[[File:EN_Auge_4_neu.png|right|frame|System with Gaussian receiver filter]]
 We start from the block diagram sketched on the right. Further it shall be valid:

@@ Line 112: / Line 112: @@
 ===Intersymbol interference system with Gaussian receiver filter===
-[[File:EN_Auge_4.png|right|frame|System with Gaussian receiver filter '''Korrektur''']]
+[[File:EN_Auge_4.png|right|frame|System with Gaussian receiver filter]]
 We start from the block diagram sketched on the right. Further it shall be valid:

@@ Line 200: / Line 200: @@
 This ensures that there are no long&nbsp; "+1"&ndash;&nbsp; or&nbsp; "&ndash;1" sequences in the AMI-encoded signal, which would be problematic for an DC signal-free channel.&nbsp;
 <br>
-[[File:Auge_16a.png|left|frame| '''Korrektur'''|class=fit]]
+[[File:EN_Auge_16a.png|left|frame| |class=fit]]
@@ Line 219: / Line 219: @@
 *&nbsp;Also the duobinary encoded sequence consists to 50% of zeros. The enhancement factor due to the smaller &nbsp;$E_{\rm B}/ N_0$&nbsp; is equal to&nbsp; $\sqrt{1/2} \approx 0.707$, as in the AMI code.
-[[File:Auge_17a.png|left|frame| '''Korrektur'''|class=fit]]
+[[File:EN_Auge_17a.png|left|frame| |class=fit]]
 <br>
 The eye diagram is shown on the left.

@@ Line 75: / Line 75: @@
 ===Nyquist system with raised cosine overall frequency response===
-[[File:Auge_2_neu.png|right|frame|Raised cosine overall frequency response '''Korrektur''']]
+[[File:EN_Auge_2.png|right|frame|Raised cosine overall frequency response]]
 We assume that the overall frequency response between the Dirac-shaped source to the decision has the shape of a&nbsp; [[Linear_and_Time_Invariant_Systems/Some_Low-Pass_Functions_in_Systems_Theory#Raised-cosine_low-pass_filter|"raised cosine low-pass"]]&nbsp; &nbsp; &rArr; &nbsp; $H_{\rm S}(f)\cdot H_{\rm E}(f) = H_{\rm CRO}(f)$&nbsp;.
@@ Line 112: / Line 112: @@
 ===Intersymbol interference system with Gaussian receiver filter===
-[[File:Auge_4.png|right|frame|System with Gaussian receiver filter '''Korrektur''']]
+[[File:EN_Auge_4.png|right|frame|System with Gaussian receiver filter '''Korrektur''']]
 We start from the block diagram sketched on the right. Further it shall be valid:
@@ Line 169: / Line 169: @@
 In symbolwise coding, each incoming source symbol &nbsp;$q_\nu$&nbsp; generates an encoder symbol &nbsp;$c_\nu$&nbsp; that depends not only on the current input symbol &nbsp;$q_\nu$&nbsp; but also on the &nbsp;$N_{\rm C}$&nbsp; preceding symbols &nbsp;$q_{\nu-1}$, ... , $q_{\nu-N_{\rm C}} $.&nbsp; &nbsp;$N_{\rm C}$&nbsp; is referred to as the ''order''&nbsp; of the code.&nbsp; It is typical for a symbolwise coding that
-[[File:Dig_T_2_4_S1_v1_neu.png|right|frame|Block diagram and equivalent circuit of a pseudo-ternary encoder '''Korrektur'''|class=fit]]
+[[File:EN_Dig_T_2_4_S1_v26.png|right|frame|Block diagram and equivalent circuit of a pseudo-ternary encoder|class=fit]]
 *the symbol duration &nbsp;$T$&nbsp; of the encoded signal (and of the transmitted signal) coincides with the bit duration &nbsp;$T_{\rm B}$&nbsp; of the binary source signal, and

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 The minimum error probability results for the case considered here &nbsp;$H_{\rm K}(f) =1$&nbsp; with the matched filter receiver, i.e. when&nbsp; $h_{\rm E}(t)$&nbsp; is equal in shape to the NRZ basic transmission pulse&nbsp; $g_s(t)$.&nbsp; The rectangular impulse response &nbsp;$h_{\rm E}(t)$&nbsp; then has duration&nbsp; $T_{\rm E} = T$&nbsp; and height&nbsp; $1/T$.
-[[File:Auge_1neu.png|center|frame|Binary baseband transmission system;&nbsp; the sketch for &nbsp;$h_{\rm E}(t)$&nbsp; applies only to the matched filter receiver ]]
+[[File:EN_Dig_T_1_4_S1_v2.png|right|frame|Binary baseband transmission system <br> &nbsp; <u>Note:</u>&nbsp; The sketch for &nbsp;$h_{\rm E}(t)$&nbsp; applies only to the matched filter receiver ]]
 *The basic detection pulse &nbsp;$g_d(t)$&nbsp; is triangular with maximum&nbsp; $s_0$&nbsp; at&nbsp; $t=0$&nbsp;; &nbsp;$g_d(t)=0$&nbsp; for&nbsp; $|t| \ge T$. Due to this tight temporal constraint, there is no intersymbol interference &nbsp; &rArr; &nbsp; $d_{\rm S}(t = \nu \cdot T) = \pm s_0$ &nbsp; &rArr; &nbsp; the distance of all useful samples from the threshold &nbsp;$E = 0$&nbsp; is always&nbsp; $|d_{\rm S}(t = \nu \cdot T)| = s_0$.
@@ Line 76: / Line 75: @@
 ===Nyquist system with raised cosine overall frequency response===
-[[File:Auge_2_neu.png|right|frame|Raised cosine overall frequency response ]]
+[[File:Auge_2_neu.png|right|frame|Raised cosine overall frequency response '''Korrektur''']]
 We assume that the overall frequency response between the Dirac-shaped source to the decision has the shape of a&nbsp; [[Linear_and_Time_Invariant_Systems/Some_Low-Pass_Functions_in_Systems_Theory#Raised-cosine_low-pass_filter|"raised cosine low-pass"]]&nbsp; &nbsp; &rArr; &nbsp; $H_{\rm S}(f)\cdot H_{\rm E}(f) = H_{\rm CRO}(f)$&nbsp;.
@@ Line 113: / Line 112: @@
 ===Intersymbol interference system with Gaussian receiver filter===
-[[File:Auge_4.png|right|frame|System with Gaussian receiver filter]]
+[[File:Auge_4.png|right|frame|System with Gaussian receiver filter '''Korrektur''']]
 We start from the block diagram sketched on the right. Further it shall be valid:
@@ Line 170: / Line 169: @@
 In symbolwise coding, each incoming source symbol &nbsp;$q_\nu$&nbsp; generates an encoder symbol &nbsp;$c_\nu$&nbsp; that depends not only on the current input symbol &nbsp;$q_\nu$&nbsp; but also on the &nbsp;$N_{\rm C}$&nbsp; preceding symbols &nbsp;$q_{\nu-1}$, ... , $q_{\nu-N_{\rm C}} $.&nbsp; &nbsp;$N_{\rm C}$&nbsp; is referred to as the ''order''&nbsp; of the code.&nbsp; It is typical for a symbolwise coding that
-[[File:Dig_T_2_4_S1_v1_neu.png|right|frame|Block diagram and equivalent circuit of a pseudo-ternary encoder|class=fit]]
+[[File:Dig_T_2_4_S1_v1_neu.png|right|frame|Block diagram and equivalent circuit of a pseudo-ternary encoder '''Korrektur'''|class=fit]]
 *the symbol duration &nbsp;$T$&nbsp; of the encoded signal (and of the transmitted signal) coincides with the bit duration &nbsp;$T_{\rm B}$&nbsp; of the binary source signal, and
@@ Line 201: / Line 200: @@
 This ensures that there are no long&nbsp; "+1"&ndash;&nbsp; or&nbsp; "&ndash;1" sequences in the AMI-encoded signal, which would be problematic for an DC signal-free channel.&nbsp;
 <br>
-[[File:Auge_16a.png|left|frame|class=fit]]
+[[File:Auge_16a.png|left|frame| '''Korrektur'''|class=fit]]
@@ Line 220: / Line 219: @@
 *&nbsp;Also the duobinary encoded sequence consists to 50% of zeros. The enhancement factor due to the smaller &nbsp;$E_{\rm B}/ N_0$&nbsp; is equal to&nbsp; $\sqrt{1/2} \approx 0.707$, as in the AMI code.
-[[File:Auge_17a.png|left|frame|class=fit]]
+[[File:Auge_17a.png|left|frame| '''Korrektur'''|class=fit]]
 <br>
 The eye diagram is shown on the left.