Aufgaben:Exercise 3.11: Viterbi Receiver and Trellis Diagram - Revision history

Guenter at 13:00, 5 July 2022

2022-07-05T13:00:44Z

Guenter at 12:37, 4 July 2022

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Guenter at 12:16, 4 July 2022

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Guenter at 12:13, 4 July 2022

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Guenter at 11:53, 8 June 2022

2022-06-08T11:53:49Z

Guenter at 11:52, 8 June 2022

2022-06-08T11:52:51Z

Hwang at 08:47, 8 June 2022

2022-06-08T08:47:01Z

Hwang at 14:00, 6 June 2022

2022-06-06T14:00:16Z

Guenter at 07:04, 1 June 2022

2022-06-01T07:04:19Z

Guenter: Guenter moved page Aufgaben:Aufgabe 3.11: Viterbi-Empfänger und Trellisdiagramm to Aufgaben:Exercise 3.11: Viterbi Receiver and Trellis Diagram

2022-06-01T06:57:23Z

Guenter moved page Aufgabe 3.11: Viterbi-Empfänger und Trellisdiagramm to Exercise 3.11: Viterbi Receiver and Trellis Diagram

← Older revision		Revision as of 13:00, 5 July 2022
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	* All quantities here are to be understood normalized. Also assume unipolar and equal probability amplitude coefficients:		* All quantities here are to be understood normalized. Also assume unipolar and equal probability amplitude coefficients:
	:$${\rm Pr} (a_\nu = 0) = {\rm Pr} (a_\nu = 1)= 0.5.$$		:$${\rm Pr} (a_\nu = 0) = {\rm Pr} (a_\nu = 1)= 0.5.$$
−	* The topic is also covered with the interactive SWF applet  [[Applets:Viterbi\|"Properties of the Viterbi Receiver"]].

@@ Line 61: / Line 61: @@
 ===Solution===
 {{ML-Kopf}}
-'''(1)'''&nbsp; The <u>first two solutions</u> are correct:
+'''(1)'''&nbsp; The&nbsp; <u>first two solutions</u>&nbsp; are correct:
-*The signal $m(t)$ after the matched filter $H_{\rm MF}(f)$ has the largest possible signal-to-interference power ratio.
+*The signal&nbsp; $m(t)$&nbsp; after the matched filter&nbsp; $H_{\rm MF}(f)$&nbsp; has the largest possible signal-to-interference power ratio&nbsp; $\rm (SNR)$.
-* However, the noise components of the sequence $&#9001;m_{\rm \nu}&#9002;$ are (strongly) correlated due to the spectral shaping.
+* However,&nbsp; the noise components of the sequence&nbsp; $&#9001;m_{\rm \nu}&#9002;$&nbsp; are (strongly) correlated due to the spectral shaping.
-*The task of the discrete-time decorrelation filter with the frequency response $H_{\rm DF}(f)$ is to dissolve these bonds, which is why the name "whitening filter" is also used for $H_{\rm DF}(f)$.
+*The task of the discrete-time decorrelation filter with the frequency response&nbsp; $H_{\rm DF}(f)$&nbsp; is to dissolve these bindings,&nbsp; which is why the name&nbsp; "whitening filter"&nbsp; is also used for&nbsp; $H_{\rm DF}(f)$.
-*However, this is possible only at the cost of increased noise power &nbsp; &#8658; &nbsp; consequently, the last proposed solution does not apply.
+*However,&nbsp; this is possible only at the cost of increased noise power &nbsp; &#8658; &nbsp; consequently,&nbsp; the last proposed solution does not apply.
-'''(2)'''&nbsp; The two arrows arriving at $\underline {\nu = 1}$ are each drawn in blue and indicate the symbol $a_1 = 0$. Thus, the initial symbol $a_1$ is already fixed at this point. Similarly, the symbols $a_3 = 1$ and $a_5 = 0$ are already fixed at the timesn $\underline {\nu = 3}$ and $\underline {\nu = 5}$, respectively.
+'''(2)'''&nbsp; The two arrows arriving at &nbsp; $\underline {\nu = 1}$&nbsp; are each drawn in blue and indicate the symbol&nbsp; $a_1 = 0$.&nbsp; Thus,&nbsp; the initial symbol&nbsp; $a_1$&nbsp; is already fixed at this point.&nbsp; Similarly,&nbsp; the symbols&nbsp; $a_3 = 1$&nbsp; and&nbsp; $a_5 = 0$&nbsp; are already fixed at times&nbsp; $\underline {\nu = 3}$&nbsp; and&nbsp; $\underline {\nu = 5}$,&nbsp; respectively.
-In contrast, at time $\nu = 2$, a decision regarding symbol $a_2$ is not possible.
+In contrast,&nbsp; at time $\nu = 2$,&nbsp; a decision regarding symbol&nbsp; $a_2$&nbsp; is not possible.
-*Under the hypothesis that the following symbol $a_3 = 0$ would result in symbol $a_2 = 1$ (at "$0$" a red path arrives, thus coming from "$1$").
+*Under the hypothesis that the following symbol&nbsp; $a_3 = 0$&nbsp; would result in symbol&nbsp; $a_2 = 1$&nbsp; $($at&nbsp; "$0$"&nbsp; a red path arrives,&nbsp; thus coming from&nbsp; "$1$"$)$.
-* In contrast, the hypothesis $a_3 = 1$ leads to the result $a_2 = 0$ (the path arriving at "$1$" is blue).
+* In contrast,&nbsp; the hypothesis&nbsp; $a_3 = 1$&nbsp; leads to the result&nbsp; $a_2 = 0$&nbsp; $($the path arriving at&nbsp; "$1$"&nbsp; is blue$)$.
+'''(3)'''&nbsp; From the continuous paths at&nbsp; $\nu = 5$&nbsp; it can be seen:
 :$$a_{1}\hspace{0.15cm}\underline {=0} \hspace{0.05cm},\hspace{0.2cm}
 a_{2}\hspace{0.15cm}\underline { =0} \hspace{0.05cm},\hspace{0.2cm}a_{3}\hspace{0.15cm}\underline {=1}
@@ Line 86: / Line 85: @@
-'''(4)'''&nbsp; Only the <u>second statement</u> is correct:
+'''(4)'''&nbsp; Only the&nbsp; <u>second statement</u>&nbsp; is correct:
-*Since the source symbols "$0$" and "$1$" were assumed to be equally probable, the ML receiver (Viterbi) is identical to the MAP receiver.
+*Since the source symbols&nbsp; "$0$"&nbsp; and&nbsp; "$1$"&nbsp; were assumed to be equally probable,&nbsp; the ML receiver&nbsp; (Viterbi)&nbsp; is identical to the MAP receiver.
-*A threshold decision (which makes a symbol-by-symbol decision at each clock) has the same error probability as the Viterbi receiver only if there is no intersymbol interference.
+*A threshold decision&nbsp; $($which makes a symbol-by-symbol decision at each clock$)$&nbsp; has the same BER as the Viterbi receiver only if there is no intersymbol interference.
-*This is obviously not the case here, otherwise it should be possible to make a final decision at every time $\nu$.
+*This is obviously not the case here,&nbsp; otherwise it should be possible to make a final decision at every time&nbsp; $\nu$.
-*The first statement is also not true. Indeed, this would mean that the Viterbi receiver can have error probability $0$ in the presence of statistical noise. This is not possible for information-theoretic reasons.
+*The first statement is also false.&nbsp; Indeed,&nbsp; this would mean that the Viterbi receiver can have error probability&nbsp; $0$&nbsp; in the presence of AWGN noise.&nbsp; <br>This is not possible for information-theoretic reasons.
 {{ML-Fuß}}

@@ Line 21: / Line 21: @@
 *The exercise belongs to the chapter&nbsp;  [[Digital_Signal_Transmission/Viterbi_Receiver|"Viterbi Receiver"]].
-*Reference is also made to the section&nbsp; [[Digital_Signal_Transmission/Optimal_Receiver_Strategies#MAP_and_Maximum.E2.80.93Likelihood_decision_rule|"MAP and Maximum–Likelihood decision rule"]].
+*Reference is also made to the section&nbsp; [[Digital_Signal_Transmission/Optimal_Receiver_Strategies#Maximum-a-posteriori_and_maximum.E2.80.93likelihood_decision_rule|"Maximum-a-posteriori and Maximum–Likelihood decision rule"]].
 * All quantities here are to be understood normalized. Also assume unipolar and equal probability amplitude coefficients: &nbsp;

@@ Line 2: / Line 2: @@
 {{quiz-Header|Buchseite=Digital_Signal_Transmission/Viterbi_Receiver}}
-[[File:P_ID1475__Dig_A_3_11.png|right|frame|Trellis diagram for a precursor]]
+[[File:P_ID1475__Dig_A_3_11.png|right|frame|Trellis diagram <br>for one precursor]]
-The Viterbi receiver allows a low-effort realization of the maximum likelihood decision rule. It contains the system components listed below:
+The Viterbi receiver allows a low-effort realization of the maximum likelihood decision rule.&nbsp; It contains the system components listed below:
-* a matched filter adapted to the basic transmission pulse with frequency response &nbsp;$H_{\rm MF}(f)$&nbsp; and output signal &nbsp; $m(t)$,
+* A matched filter adapted to the basic transmission pulse with frequency response &nbsp;$H_{\rm MF}(f)$&nbsp; and output signal &nbsp; $m(t)$,
 *Reference is also made to the section&nbsp; [[Digital_Signal_Transmission/Optimal_Receiver_Strategies#MAP_and_Maximum.E2.80.93Likelihood_decision_rule|"MAP and Maximum–Likelihood decision rule"]].
-* All quantities here are to be understood normalized. Also assume unipolar and equal probability amplitude coefficients: &nbsp;${\rm Pr} (a_\nu = 0) = {\rm Pr} (a_\nu = 1)= 0.5.$
+* All quantities here are to be understood normalized. Also assume unipolar and equal probability amplitude coefficients: &nbsp;
-* The topic is also covered in the interactive applet&nbsp;  [[Applets:Viterbi|"Properties of the Viterbi Receiver"]].
+:$${\rm Pr} (a_\nu = 0) = {\rm Pr} (a_\nu = 1)= 0.5.$$
@@ Line 31: / Line 34: @@
 + The matched filter &nbsp;$H_{\rm MF}(f)$&nbsp; is mainly used for noise power limitation.
 + The decorrelation filter removes ties between samples.
-- The noise power is only affected by &nbsp;$H_{\rm MF}(f)$, not by &nbsp;$H_{\rm DF}(f)$.&nbsp;
+- The noise power is only affected by &nbsp;$H_{\rm MF}(f)$,&nbsp; not by &nbsp;$H_{\rm DF}(f)$.&nbsp;
 {At what times &nbsp;$\nu$&nbsp; can we finally decide the current symbol &nbsp;$a_{\rm \nu}$?&nbsp;
@@ Line 41: / Line 44: @@
 + $\nu = 5.$
-{What is the sequence decided by the Viterbi receiver?
+{What is the total sequence decided by the Viterbi receiver?
 |type="{}"}
 $a_1 \ = \ $ { 0. }

← Older revision		Revision as of 11:53, 8 June 2022
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−	[[Category:Digital Signal Transmission: Exercises\|^3.8 ~~Basis Functions & Vector Spaces~~^]]	+	[[Category:Digital Signal Transmission: Exercises\|^3.8 Viterbi Receiver^]]

← Older revision		Revision as of 11:52, 8 June 2022
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−	[[Category:Digital Signal Transmission: Exercises\|^3.8 ~~Viterbi Receiver~~^]]	+	[[Category:Digital Signal Transmission: Exercises\|^3.8 Basis Functions & Vector Spaces^]]

@@ Line 33: / Line 33: @@
 - The noise power is only affected by &nbsp;$H_{\rm MF}(f)$, not by &nbsp;$H_{\rm DF}(f)$.&nbsp;
-{Zu welchen Zeiten &nbsp;$\nu$&nbsp; kann man das aktuelle Symbol &nbsp;$a_{\rm \nu}$&nbsp; endgültig entscheiden?
+{At what times &nbsp;$\nu$&nbsp; can we finally decide the current symbol &nbsp;$a_{\rm \nu}$?&nbsp;
 |type="[]"}
 + $\nu = 1,$
@@ Line 41: / Line 41: @@
 + $\nu = 5.$
-{Wie lautet die vom Viterbi&ndash;Empfänger entschiedene Folge?
+{What is the sequence decided by the Viterbi receiver?
 |type="{}"}
 $a_1 \ = \ $ { 0. }
@@ Line 49: / Line 49: @@
 $a_5 \ = \ $ { 0. }
-{Welche der folgenden Aussagen  sind zutreffend?
+{Which of the following statements are true?
 |type="[]"}
-- Es ist sicher, dass die erkannte Folge auch gesendet wurde.
+- It is certain that the detected sequence was also sent.
-+ Ein MAP&ndash;Empfänger hätte die gleiche Fehlerwahrscheinlichkeit.
++ A MAP receiver would have the same error probability.
-- Schwellenwertentscheidung ist gleich gut wie dieser Maximum&ndash;Likelihood&ndash;Empfänger.
+- Threshold decision is the same as this maximum likelihood receiver.
 </quiz>
-===Musterlösung===
+===Solution===
 {{ML-Kopf}}
-'''(1)'''&nbsp; Richtig sind die <u>beiden ersten Lösungsvorschläge</u>:
+'''(1)'''&nbsp; The <u>first two solutions</u> are correct:
-*Das Signal $m(t)$ nach dem Matched&ndash;Filter $H_{\rm MF}(f)$ weist das größtmögliche Signal&ndash;zu&ndash;Störleistungsverhältnis auf.
+*The signal $m(t)$ after the matched filter $H_{\rm MF}(f)$ has the largest possible signal-to-interference power ratio.
-* Die Störanteile der Folge $&#9001;m_{\rm \nu}&#9002;$ sind aber aufgrund der spektralen Formung (stark) korreliert.
+* However, the noise components of the sequence $&#9001;m_{\rm \nu}&#9002;$ are (strongly) correlated due to the spectral shaping.
-*Aufgabe des zeitdiskreten Dekorrelationsfilters mit dem Frequenzgang $H_{\rm DF}(f)$ ist es, diese Bindungen aufzulösen, weshalb für $H_{\rm DF}(f)$ auch der Name "Whitening&ndash;Filter" verwendet wird.
+*The task of the discrete-time decorrelation filter with the frequency response $H_{\rm DF}(f)$ is to dissolve these bonds, which is why the name "whitening filter" is also used for $H_{\rm DF}(f)$.
-*Dies ist allerdings nur auf Kosten einer erhöhten Störleistung möglich &nbsp; &#8658; &nbsp; der letzte Lösungsvorschlag trifft demnach nicht zu.
+*However, this is possible only at the cost of increased noise power &nbsp; &#8658; &nbsp; consequently, the last proposed solution does not apply.
-'''(2)'''&nbsp; Die beiden bei $\underline {\nu = 1}$ ankommenden Pfeile sind jeweils blau gezeichnet und kennzeichnen das Symbol $a_1 = 0$. Somit ist bereits zu diesem Zeitpunkt das Ausgangssymbol $a_1$ festgelegt. Ebenso stehen die Symbole $a_3 = 1$ und $a_5 = 0$ bereits zu den Zeitpunkten $\underline {\nu = 3}$ bzw. $\underline {\nu = 5}$ fest.
+'''(2)'''&nbsp; The two arrows arriving at $\underline {\nu = 1}$ are each drawn in blue and indicate the symbol $a_1 = 0$. Thus, the initial symbol $a_1$ is already fixed at this point. Similarly, the symbols $a_3 = 1$ and $a_5 = 0$ are already fixed at the timesn $\underline {\nu = 3}$ and $\underline {\nu = 5}$, respectively.
-Dagegen ist zum Zeitpunkt $\nu = 2$ eine Entscheidung bezüglich des Symbols $a_2$ nicht möglich.
+In contrast, at time $\nu = 2$, a decision regarding symbol $a_2$ is not possible.
-*Unter der Hypothese, dass das nachfolgende Symbol $a_3 = 0$ sein wird, würde sich Symbol $a_2 = 1$ ergeben (bei "$0$" kommt ein roter Pfad an, also von "$1$" kommend).
+*Under the hypothesis that the following symbol $a_3 = 0$ would result in symbol $a_2 = 1$ (at "$0$" a red path arrives, thus coming from "$1$").
-* Dagegen führt die Hypothese $a_3 = 1$ zum Ergebnis $a_2 = 0$ (der bei "$1$" ankommende Pfad ist blau).
+* In contrast, the hypothesis $a_3 = 1$ leads to the result $a_2 = 0$ (the path arriving at "$1$" is blue).
-Ähnlich verhält es sich zum Zeitpunkt $\nu = 4$.
+The situation is similar at time $\nu = 4$.
-'''(3)'''&nbsp; Aus den durchgehenden Pfaden bei $\nu = 5$ ist ersichtlich:
+'''(3)'''&nbsp; From the continuous paths at $\nu = 5$ it can be seen:
 :$$a_{1}\hspace{0.15cm}\underline {=0} \hspace{0.05cm},\hspace{0.2cm}
 a_{2}\hspace{0.15cm}\underline { =0} \hspace{0.05cm},\hspace{0.2cm}a_{3}\hspace{0.15cm}\underline {=1}
@@ Line 83: / Line 83: @@
-'''(4)'''&nbsp; Richtig ist nur die <u>zweite Aussage</u>:
+'''(4)'''&nbsp; Only the <u>second statement</u> is correct:
-*Da die Quellensymbole "$0$" und "$1$" als gleichwahrscheinlich vorausgesetzt wurden, ist der ML&ndash;Empfänger (Viterbi) identisch mit dem MAP&ndash;Empfänger.
+*Since the source symbols "$0$" and "$1$" were assumed to be equally probable, the ML receiver (Viterbi) is identical to the MAP receiver.
-*Ein Schwellenwertentscheider (der zu jedem Takt eine symbolweise Entscheidung trifft) hat nur dann die gleiche Fehlerwahrscheinlichkeit wie der Viterbi&ndash;Empfänger, wenn es keine Impulsinterferenzen gibt.
+*A threshold decision (which makes a symbol-by-symbol decision at each clock) has the same error probability as the Viterbi receiver only if there is no intersymbol interference.
-*Dies ist hier offensichtlich nicht der Fall, sonst müsste zu jedem Zeitpunkt $\nu$ eine endgültige Entscheidung getroffen werden können.
+*This is obviously not the case here, otherwise it should be possible to make a final decision at every time $\nu$.
-*Die erste Aussage trifft ebenfalls nicht zu. Das würde nämlich bedeuten, dass der Viterbi&ndash;Empfänger bei Vorhandensein von statistischem Rauschen die Fehlerwahrscheinlichkeit $0$ haben kann. Dies ist aus informationstheoretischen Gründen nicht möglich.
+*The first statement is also not true. Indeed, this would mean that the Viterbi receiver can have error probability $0$ in the presence of statistical noise. This is not possible for information-theoretic reasons.
 {{ML-Fuß}}

@@ Line 1: / Line 1: @@
-{{quiz-Header|Buchseite=Digitalsignalübertragung/Viterbi–Empfänger}}
+{{quiz-Header|Buchseite=Digital_Signal_Transmission/Viterbi_Receiver}}
-[[File:P_ID1475__Dig_A_3_11.png|right|frame|Trellisdiagramm für einen Vorläufer]]
+[[File:P_ID1475__Dig_A_3_11.png|right|frame|Trellis diagram for a precursor]]
-Der Viterbi&ndash;Empfänger erlaubt eine aufwandsgünstige Realisierung der Maximum&ndash;Likelihood&ndash;Entscheidungsregel. Er beinhaltet die im Folgenden aufgeführten Systemkomponenten:
+The Viterbi receiver allows a low-effort realization of the maximum likelihood decision rule. It contains the system components listed below:
-* ein an den Sendegrundimpuls angepasstes Matched&ndash;Filter mit Frequenzgang &nbsp;$H_{\rm MF}(f)$&nbsp; und Ausgangssignal&nbsp; $m(t)$,
+* a matched filter adapted to the basic transmission pulse with frequency response &nbsp;$H_{\rm MF}(f)$&nbsp; and output signal &nbsp; $m(t)$,
-* einen Abtaster im Abstand der Symboldauer (Bitdauer)&nbsp; $T$, der das zeitkontinuierliche Signal&nbsp; $m(t)$&nbsp; in die zeitdiskrete Folge&nbsp; $&#9001;m_{\rm \nu}&#9002;$&nbsp; wandelt,
+* a sampler spaced at the symbol duration (bit duration)&nbsp; $T$, which converts the continuous-time signal &nbsp; $m(t)$&nbsp; into the discrete-time sequence &nbsp; $&#9001;m_{\rm \nu}&#9002;$,&nbsp;
-* ein Dekorrelationsfilter mit Frequenzgang&nbsp; $H_{\rm DF}(f)$&nbsp; zur Entfernung statistischer Bindungen zwischen den Störanteilen der Folge&nbsp; $&#9001;d_{\rm \nu}&#9002;$,
+* a decorrelation filter with frequency response &nbsp; $H_{\rm DF}(f)$&nbsp; for removing statistical ties between the noise components of the sequence &nbsp; $&#9001;d_{\rm \nu}&#9002;$,
-* den Viterbi&ndash;Entscheider, der mit einem trellisbasierten Algorithmus die Sinkensymbolfolge&nbsp; $&#9001;v_{\rm \nu}&#9002;$&nbsp; gewinnt.
+* the Viterbi decision, which uses a trellis-based algorithm to obtain the sink symbol sequence&nbsp; $&#9001;v_{\rm \nu}&#9002;$.&nbsp;
-Die Grafik zeigt das vereinfachte Trellisdiagramm der beiden Zustände "$0$" und "$1$" für die Zeitpunkte&nbsp; $\nu &#8804; 5$. Dieses Diagramm erhält man als Ergebnis der Auswertung der beiden minimalen Gesamtfehlergrößen&nbsp; ${\it \Gamma}_{\rm \nu}(0)$&nbsp; und&nbsp; ${\it \Gamma}_{\rm \nu}(1)$&nbsp; entsprechend der&nbsp; [[Aufgaben:3.11Z_Maximum-Likelihood-Fehlergrößen| Aufgabe 3.11Z]].
+The graph shows the simplified trellis diagram of the two states "$0$" and "$1$" for time points &nbsp; $\nu &#8804; 5$. This diagram is obtained as a result of evaluating the two minimum total error quantities &nbsp; ${\it \Gamma}_{\rm \nu}(0)$&nbsp; and&nbsp; ${\it \Gamma}_{\rm \nu}(1)$&nbsp; corresponding to &nbsp; [[Aufgaben:Exercise_3.11Z:_Maximum_Likelihood_Error_Variables|"Exercise 3.11Z"]].
@@ Line 17: / Line 17: @@
-''Hinweise:''
+''Notes:''
-*Die Aufgabe gehört zum  Kapitel&nbsp;  [[Digitalsignal%C3%BCbertragung/Viterbi%E2%80%93Empf%C3%A4nger|Viterbi&ndash;Empfänger]].
+*The exercise belongs to the chapter &nbsp;  [[Digital_Signal_Transmission/Viterbi_Receiver|"Viterbi Receiver"]].
-*Bezug genommen wird auch auf den Abschnitt&nbsp; [[Digital_Signal_Transmission/Optimale_Empfängerstrategien#MAP.E2.80.93_und_Maximum.E2.80.93Likelihood.E2.80.93Entscheidungsregel|MAP&ndash; und Maximum&ndash;Likelihood&ndash;Entscheidungsregel]].
+*Reference is also made to the section&nbsp; [[Digital_Signal_Transmission/Optimal_Receiver_Strategies#MAP_and_Maximum.E2.80.93Likelihood_decision_rule|"MAP and Maximum–Likelihood decision rule"]].
-* Alle Größen sind hier normiert zu verstehen. Gehen Sie zudem von unipolaren und gleichwahrscheinlichen Amplitudenkoeffizienten aus: &nbsp;${\rm Pr} (a_\nu = 0) = {\rm Pr} (a_\nu = 1)= 0.5.$
+* All quantities here are to be understood normalized. Also assume unipolar and equal probability amplitude coefficients: &nbsp;${\rm Pr} (a_\nu = 0) = {\rm Pr} (a_\nu = 1)= 0.5.$
-* Die Thematik wird auch im interaktiven Applet&nbsp;  [[Applets:Viterbi|Eigenschaften des Viterbi&ndash;Empfängers]] behandelt.
+* The topic is also covered in the interactive applet&nbsp;  [[Applets:Viterbi|"Properties of the Viterbi Receiver"]].
-===Fragebogen===
+===Questions===
 <quiz display=simple>
-{Welche der folgenden Aussagen sind zutreffend?
+{Which of the following statements are true?
 |type="[]"}
-+ Das Matched&ndash;Filter &nbsp;$H_{\rm MF}(f)$&nbsp; dient vorwiegend der Störleistungsbegrenzung.
++ The matched filter &nbsp;$H_{\rm MF}(f)$&nbsp; is mainly used for noise power limitation.
-+ Das Dekorrelationsfilter entfernt Bindungen zwischen den Abtastwerten.
++ The decorrelation filter removes ties between samples.
-- Die Störleistung wird nur von &nbsp;$H_{\rm MF}(f)$, nicht von &nbsp;$H_{\rm DF}(f)$&nbsp; beeinflusst.
+- The noise power is only affected by &nbsp;$H_{\rm MF}(f)$, not by &nbsp;$H_{\rm DF}(f)$.&nbsp;
 {Zu welchen Zeiten &nbsp;$\nu$&nbsp; kann man das aktuelle Symbol &nbsp;$a_{\rm \nu}$&nbsp; endgültig entscheiden?

← Older revision		Revision as of 07:04, 1 June 2022
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−	[[Category:Digital Signal Transmission: Exercises\|^3.8 Viterbi~~-Empfänger~~^]]	+	[[Category:Digital Signal Transmission: Exercises\|^3.8 Viterbi Receiver^]]