Aufgaben:Exercise 1.2: ISDN and PCM - Revision history

Hwang at 15:36, 23 January 2023

2023-01-23T15:36:14Z

Hwang at 14:35, 9 November 2022

2022-11-09T14:35:35Z

Guenter at 11:23, 18 October 2022

2022-10-18T11:23:22Z

Guenter at 16:17, 17 October 2022

2022-10-17T16:17:53Z

Guenter at 13:38, 15 October 2022

2022-10-15T13:38:00Z

Guenter at 13:22, 15 October 2022

2022-10-15T13:22:30Z

Guenter at 16:32, 14 October 2022

2022-10-14T16:32:44Z

Hwang at 08:36, 2 October 2022

2022-10-02T08:36:51Z

Guenter at 15:20, 9 September 2022

2022-09-09T15:20:03Z

Guenter: Guenter moved page Aufgaben:Aufgabe 1.2: ISDN und PCM to Aufgaben:Exercise 1.2: ISDN and PCM

2022-09-09T15:17:49Z

Guenter moved page Aufgabe 1.2: ISDN und PCM to Exercise 1.2: ISDN and PCM

@@ Line 4: / Line 4: @@
 [[File:EN_Bei_A_1_2.png|right|frame|Components of PCM transmitter]]
-The conversion of the analog voice signal&nbsp; $q(t)$&nbsp; into the binary signal&nbsp; $q_{\rm C}(t)$&nbsp; is done at&nbsp;  $\rm ISDN$&nbsp; ("Integrated Services Digital Network")&nbsp; according to the guidelines of&nbsp; "pulse code modulation"&nbsp; $\rm (PCM)$&nbsp; by
+The conversion of the analog speech signal&nbsp; $q(t)$&nbsp; into the binary signal&nbsp; $q_{\rm C}(t)$&nbsp; is done at&nbsp;  $\rm ISDN$&nbsp; ("Integrated Services Digital Network")&nbsp; according to the guidelines of&nbsp; "pulse code modulation"&nbsp; $\rm (PCM)$&nbsp; by
 *sampling in the interval&nbsp; $T_{\rm A} = 1/f_{\rm A}$,

@@ Line 86: / Line 86: @@
 :$$\rho_{v} \approx \rho_{\rm Q} = 2^{2M} = 2^{16} \hspace{0.3cm}\Rightarrow \hspace{0.3cm} \rho_{v} \approx 48\, {\rm dB}\hspace{0.05cm}.$$
-*With larger noise interference,&nbsp; $\rho_{v}$&nbsp; can further&nbsp; (significantly)&nbsp; reduced by the transmission errors.
+*With larger noise interference,&nbsp; $\rho_{v}$&nbsp; can further&nbsp; (significantly)&nbsp; be reduced by the transmission errors.
 *In contrast,&nbsp; sampling results in no loss of quality if the sampling theorem is obeyed.

@@ Line 3: / Line 3: @@
 }}
-[[File:EN_Bei_A_1_2.png|right|frame|Components of PCM transmitter '''Korrektur''']]
+[[File:EN_Bei_A_1_2.png|right|frame|Components of PCM transmitter]]
 The conversion of the analog voice signal&nbsp; $q(t)$&nbsp; into the binary signal&nbsp; $q_{\rm C}(t)$&nbsp; is done at&nbsp;  $\rm ISDN$&nbsp; ("Integrated Services Digital Network")&nbsp; according to the guidelines of&nbsp; "pulse code modulation"&nbsp; $\rm (PCM)$&nbsp; by
 *sampling in the interval&nbsp; $T_{\rm A} = 1/f_{\rm A}$,

@@ Line 3: / Line 3: @@
 }}
-[[File:P_ID1578__Bei_A_1_2.png|right|frame|Components of PCM transmitter '''Korrektur''']]
+[[File:EN_Bei_A_1_2.png|right|frame|Components of PCM transmitter '''Korrektur''']]
 The conversion of the analog voice signal&nbsp; $q(t)$&nbsp; into the binary signal&nbsp; $q_{\rm C}(t)$&nbsp; is done at&nbsp;  $\rm ISDN$&nbsp; ("Integrated Services Digital Network")&nbsp; according to the guidelines of&nbsp; "pulse code modulation"&nbsp; $\rm (PCM)$&nbsp; by
 *sampling in the interval&nbsp; $T_{\rm A} = 1/f_{\rm A}$,

@@ Line 71: / Line 71: @@
 '''(2)'''&nbsp;  For the bit rate,&nbsp; $R_{\rm B} = N \cdot f_{\rm A}$.
-*Thus, from&nbsp; $R_{\rm B} = 64 \ \rm  kbit/s$&nbsp; and&nbsp; $N = 8$,&nbsp; we get&nbsp; $f_{\rm A} \hspace{0.15cm}\underline{= 8 \ \rm kHz}$.
+*Thus,&nbsp; from&nbsp; $R_{\rm B} = 64 \ \rm  kbit/s$&nbsp; and&nbsp; $N = 8$,&nbsp; we get&nbsp; $f_{\rm A} \hspace{0.15cm}\underline{= 8 \ \rm kHz}$.
-'''(3)'''&nbsp;  Due to the bandwidth limitation, the highest frequency contained in the signal&nbsp; $q(t)$&nbsp; is equal to&nbsp; $3.4 \ \rm kHz$.
+'''(3)'''&nbsp;  Due to the bandwidth limitation,&nbsp; the highest frequency contained in the signal&nbsp; $q(t)$&nbsp; is equal to&nbsp; $3.4 \ \rm kHz$.
 *Therefore, according to the sampling theorem,&nbsp; $f_{\rm A} ≥ 6.8 \ \rm kHz$&nbsp; should hold.
 *With&nbsp;  $f_{\rm A} = 8 \ \rm kHz$&nbsp; the condition is fulfilled &nbsp; &rArr; &nbsp; $\underline {\rm YES}$.
-'''(4)'''&nbsp;  The <u>last statement</u> is correct:
+'''(4)'''&nbsp;  The&nbsp; <u>last statement</u>&nbsp; is correct:
-*Even if the influence of the AWGN noise is small $($small noise power density&nbsp; $N_{0})$, the sink SNR&nbsp; $\rho_{v}$&nbsp; cannot fall below a limit given by the quantization noise:
+*Even if the influence of the AWGN noise is small&nbsp; $($small noise power density&nbsp; $N_{0})$,&nbsp; the sink SNR&nbsp; $\rho_{v}$&nbsp; cannot fall below a limit given by the quantization noise:
 :$$\rho_{v} \approx \rho_{\rm Q} = 2^{2M} = 2^{16} \hspace{0.3cm}\Rightarrow \hspace{0.3cm} \rho_{v} \approx 48\, {\rm dB}\hspace{0.05cm}.$$
-*With larger noise interference,&nbsp; $\rho_{v}$&nbsp; is further (significantly) reduced by the transmission errors then present.
+*With larger noise interference,&nbsp; $\rho_{v}$&nbsp; can further&nbsp; (significantly)&nbsp; reduced by the transmission errors.
 *In contrast, sampling results in no loss of quality if the sampling theorem is obeyed.
-*Sampling can then be completely undone if the source signal&nbsp; $q(t)$&nbsp; is bandlimited and the signal reconstruction is correctly dimensioned:&nbsp;   ideal low-pass.
+*In contrast,&nbsp; sampling results in no loss of quality if the sampling theorem is obeyed.
 {{ML-Fuß}}

@@ Line 4: / Line 4: @@
 [[File:P_ID1578__Bei_A_1_2.png|right|frame|Components of PCM transmitter '''Korrektur''']]
-The conversion of the analog voice signal&nbsp; $q(t)$&nbsp; into the binary signal&nbsp; $q_{\rm C}(t)$&nbsp; is done at ISDN&nbsp; ("Integrated Services Digital Network")&nbsp; according to the guidelines of pulse code modulation&nbsp; $\rm (PCM)$&nbsp; by
+The conversion of the analog voice signal&nbsp; $q(t)$&nbsp; into the binary signal&nbsp; $q_{\rm C}(t)$&nbsp; is done at&nbsp;  $\rm ISDN$&nbsp; ("Integrated Services Digital Network")&nbsp; according to the guidelines of&nbsp; "pulse code modulation"&nbsp; $\rm (PCM)$&nbsp; by
 *sampling in the interval&nbsp; $T_{\rm A} = 1/f_{\rm A}$,
@@ Line 12: / Line 12: @@
-The net data rate of a so-called&nbsp; $\rm B$ channel&nbsp; ("Bearer Channel") is&nbsp; $64 \ \rm kbit/s$&nbsp; and corresponds to the bit rate of the redundancy-free binary signal&nbsp; $q_{\rm C}(t)$.&nbsp; However,&nbsp; because of the subsequent redundant channel coding and the inserted signaling bits,&nbsp; the gross data rate – i.e., the transmission rate of the transmitted signal&nbsp; $s(t)$&nbsp; – is greater.
+The net data rate of a&nbsp; $\rm B$ channel&nbsp; ("Bearer Channel") is&nbsp; $64 \ \rm kbit/s$&nbsp; and corresponds to the bit rate of the redundancy-free binary signal&nbsp; $q_{\rm C}(t)$.&nbsp;
 A measure for the quality of the entire ISDN transmission system is the sink SNR
 :$$\rho_{v} = \frac{P_q}{P_{\varepsilon}} = \frac{\overline{q(t)^2}}{\overline{[\upsilon(t) - q(t)]^2}}$$
-as the ratio of the powers of the analog signal&nbsp; $q(t)$&nbsp; bandlimited to the range&nbsp; $300 \ {\rm Hz}\  \text{...}\  3400 \ {\rm Hz}$&nbsp; and the error signal&nbsp; $\varepsilon (t) = v (t) - q(t)$.
+as the ratio of the powers
-An ideal signal reconstruction with an ideal rectangular low-pass filter is assumed here for the sink signal&nbsp; $v (t)$.&nbsp;
+*and the error signal&nbsp; $\varepsilon (t) = v (t) - q(t)$.
-''Notes:''
+*Reference is also made to the chapter&nbsp; [[Modulation_Methods/Pulse_Code_Modulation|"Pulse Code Modulation"]]&nbsp; of the book&nbsp; "Modulation Methods".
@@ Line 38: / Line 41: @@
 <quiz display=simple>
-{With how many bits&nbsp; $(N)$&nbsp; is each (quantized) sample represented?
+{With how many bits&nbsp; $(N)$&nbsp; is each quantized sample represented?
 |type="{}"}
 $N \ = \ $ { 8 3% }
@@ Line 53: / Line 56: @@
 {Is the sink SNR&nbsp; $\rho_{v}$&nbsp; at ISDN limited by the following effects?
 |type="[]"}
-- Sampling (if sampling theorem is satisfied),
+- Sampling&nbsp; (if sampling theorem is satisfied),
-+ AWGN noise (transmission error).
++ AWGN noise&nbsp; (transmission error).

@@ Line 1: / Line 1: @@
-{{quiz-Header|Buchseite=Beispiele von Nachrichtensystemen/Allgemeine Beschreibung von ISDN
+{{quiz-Header|Buchseite=Examples_of_Communication_Systems/General_Description_of_ISDN
 }}
-[[File:P_ID1578__Bei_A_1_2.png|right|frame|Komponenten des PCM-Senders]]
+[[File:P_ID1578__Bei_A_1_2.png|right|frame|Components of the PCM transmitter]]
-Die Umwandlung des analogen Sprachsignals&nbsp; $q(t)$&nbsp; in das Binärsignal&nbsp; $q_{\rm C}(t)$&nbsp; geschieht bei ISDN&nbsp; (''Integrated Services Digital Network'')&nbsp; entsprechend den Richtlinien der Pulscodemodulation (PCM) durch
+The conversion of the analog voice signal&nbsp; $q(t)$&nbsp; into the binary signal&nbsp; $q_{\rm C}(t)$&nbsp; is done at ISDN&nbsp; (''Integrated Services Digital Network'')&nbsp; according to the guidelines of pulse code modulation (PCM) by
-*Abtastung im Abstand&nbsp; $T_{\rm A} = 1/f_{\rm A}$,
+*sampling in the interval&nbsp; $T_{\rm A} = 1/f_{\rm A}$,
-*Quantisierung auf&nbsp; $M = 256$&nbsp; diskrete Werte,
+*quantization to&nbsp; $M = 256$&nbsp; discrete values,
-*binäre PCM–Codierung mit&nbsp; $N$&nbsp; Bit pro Quantisierungswert.
+*binary PCM coding with&nbsp; $N$&nbsp; bits per quantization value.
-Die Netto–Datenrate eines so genannten&nbsp; $\rm B$–Kanals&nbsp; (''Bearer Channel'') ist&nbsp; $64 \ \rm kbit/s$&nbsp; und entspricht der Bitrate des redundanzfreien Binärsignals&nbsp; $q_{\rm C}(t)$. Wegen der anschließenden redundanten Kanalcodierung und der eingefügten Signalisierungsbits ist allerdings die Brutto–Datenrate – also die Übertragungsrate des Sendesignals&nbsp; $s(t)$&nbsp; – größer.
+The net data rate of a so-called&nbsp; $\rm B$ channel&nbsp; (''Bearer Channel'') is&nbsp; $64 \ \rm kbit/s$&nbsp; and corresponds to the bit rate of the redundancy-free binary signal&nbsp; $q_{\rm C}(t)$. However, because of the subsequent redundant channel coding and the inserted signaling bits, the gross data rate – i.e., the transmission rate of the transmitted signal&nbsp; $s(t)$&nbsp; – is greater.
-Ein Maß für die Qualität des gesamten (ISDN–)Übertragungssystems ist das Sinken–SNR
+A measure for the quality of the entire (ISDN) transmission system is the sink SNR
 :$$\rho_{v} = \frac{P_q}{P_{\varepsilon}} = \frac{\overline{q(t)^2}}{\overline{[\upsilon(t) - q(t)]^2}}$$
-als das Verhältnis der Leistungen des auf den Bereich&nbsp; $300 \ {\rm Hz}\  \text{...}\  3400 \ {\rm Hz}$&nbsp; bandbegrenzten Analogsignals&nbsp; $q(t)$&nbsp; und des Fehlersignals&nbsp; $\varepsilon (t) = v (t) - q(t)$.
+as the ratio of the powers of the analog signal&nbsp; $q(t)$&nbsp; bandlimited to the range&nbsp; $300 \ {\rm Hz}\  \text{...}\  3400 \ {\rm Hz}$&nbsp; and the error signal&nbsp; $\varepsilon (t) = v (t) - q(t)$.
-Für das Sinkensignal&nbsp; $v (t)$&nbsp; wird hierbei eine ideale Signalrekonstruktion mit einem idealen rechteckförmigen Tiefpass vorausgesetzt.
+An ideal signal reconstruction with an ideal rectangular low-pass filter is assumed here for the sink signal&nbsp; $v (t)$.&nbsp;
@@ Line 26: / Line 26: @@
-''Hinweis:''
+''Notes:''
-*Die Aufgabe bezieht sich auf das Kapitel&nbsp; [[Examples_of_Communication_Systems/Allgemeine_Beschreibung_von_ISDN|Allgemeine Beschreibung von ISDN]] dieses Buches.
+*The exercise refers to the chapter&nbsp; [[Examples_of_Communication_Systems/General_Description_of_ISDN|"General Description of ISDN"]] of this book.
-*Bezug genommen wird auch auf das Kapitel&nbsp; [[Modulation_Methods/Pulscodemodulation|Pulscodemodulation]]&nbsp; des Buches „Modulationsverfahren”.
+*Reference is also made to the chapter&nbsp; [[Modulation_Methods/Pulse_Code_Modulation|"Pulse Code Modulation"]]&nbsp; of the book "Modulation Methods".
-===Fragebogen===
+===Questions===
 <quiz display=simple>
-{Mit wievielen Bit&nbsp; $(N)$&nbsp; wird jeder (quantisierte) Abtastwert repräsentiert?
+{With how many bits&nbsp; $(N)$&nbsp; is each (quantized) sample represented?
 |type="{}"}
 $N \ = \ $ { 8 3% }
-{Wie groß ist die Abtastrate&nbsp; $f_{\rm A} $?
+{What is the sampling rate&nbsp; $f_{\rm A} $?
 |type="{}"}
 $f_{\rm A} \ = \ $ { 8 3% } $ \ \rm kHz $
-{Ist damit das Abtasttheorem erfüllt?
+{Does this satisfy the sampling theorem?
 |type="()"}
-+ Ja,
++ Yes,
-- nein.
+- no.
-{Ist das Sinken–SNR&nbsp; $\rho_{v}$&nbsp; bei ISDN durch folgende Effekte begrenzt?
+{Is the sink SNR&nbsp; $\rho_{v}$&nbsp; at ISDN limited by the following effects?
 |type="[]"}
-- Abtastung (falls Abtasttheorem erfüllt),
+- Sampling (if sampling theorem is satisfied),
-+ AWGN–Rauschen (Übertragungsfehler).
++ AWGN noise (transmission error).
 </quiz>
-===Musterlösung===
+===Solution===
 {{ML-Kopf}}
-'''(1)'''&nbsp; Die Quantisierungsstufenzahl&nbsp; $M$&nbsp; wird meist als Zweierpotenz gewählt und für die Bitanzahl&nbsp; $N = {\log_2}\hspace{0.05cm}(M)$.
+'''(1)'''&nbsp; The quantization level number&nbsp; $M$&nbsp; is usually chosen as a power of two and for the number of bits&nbsp; $N = {\log_2}\hspace{0.05cm}(M)$.
-*Aus&nbsp; $M = 2^{8} = 256$&nbsp; folgt&nbsp; $\underline{N = 8}$.
+*From&nbsp; $M = 2^{8} = 256$&nbsp; follows&nbsp; $\underline{N = 8}$.
-'''(2)'''&nbsp;  Für die Bitrate gilt&nbsp; $R_{\rm B} = N \cdot f_{\rm A}$.
+'''(2)'''&nbsp;  For the bit rate,&nbsp; $R_{\rm B} = N \cdot f_{\rm A}$.
-*Aus&nbsp; $R_{\rm B} = 64 \ \rm  kbit/s$&nbsp; und&nbsp; $N = 8$&nbsp; erhält man somit&nbsp; $f_{\rm A} \hspace{0.15cm}\underline{= 8 \ \rm kHz}$.
+*Thus, from&nbsp; $R_{\rm B} = 64 \ \rm  kbit/s$&nbsp; and&nbsp; $N = 8$,&nbsp; we get&nbsp; $f_{\rm A} \hspace{0.15cm}\underline{= 8 \ \rm kHz}$.
-'''(3)'''&nbsp;  Durch die Bandbegrenzung ist die höchste im Signal&nbsp; $q(t)$&nbsp; enthaltene Frequenz gleich&nbsp; $3.4 \ \rm kHz$.
+'''(3)'''&nbsp;  Due to the bandwidth limitation, the highest frequency contained in the signal&nbsp; $q(t)$&nbsp; is equal to&nbsp; $3.4 \ \rm kHz$.
-*Nach dem Abtasttheorem müsste deshalb&nbsp; $f_{\rm A} ≥ 6.8 \ \rm kHz$&nbsp; gelten.
+*Therefore, according to the sampling theorem,&nbsp; $f_{\rm A} ≥ 6.8 \ \rm kHz$&nbsp; should hold.
-*Mit&nbsp;  $f_{\rm A} = 8 \ \rm kHz$&nbsp; ist die Bedingung erfüllt &nbsp; &rArr; &nbsp; $\underline {\rm JA}$.
+*With&nbsp;  $f_{\rm A} = 8 \ \rm kHz$&nbsp; the condition is fulfilled &nbsp; &rArr; &nbsp; $\underline {\rm YES}$.
-'''(4)'''&nbsp;  Richtig ist die <u>letzte Aussage</u>:
+'''(4)'''&nbsp;  The <u>last statement</u> is correct:
-*Auch wenn der Einfluss des AWGN–Rauschens gering ist $($kleine Rauschleistungsdichte&nbsp; $N_{0})$, kann das Sinken–SNR&nbsp; $\rho_{v}$&nbsp; einen durch das Quantisierungsrauschen gegebenen Grenzwert nicht unterschreiten:
+*Even if the influence of the AWGN noise is small $($small noise power density&nbsp; $N_{0})$, the sink SNR&nbsp; $\rho_{v}$&nbsp; cannot fall below a limit given by the quantization noise:
 :$$\rho_{v} \approx \rho_{\rm Q} = 2^{2M} = 2^{16} \hspace{0.3cm}\Rightarrow \hspace{0.3cm} \rho_{v} \approx 48\, {\rm dB}\hspace{0.05cm}.$$
-*Bei größerer Rauschstörung wird&nbsp; $\rho_{v}$&nbsp; durch die dann vorhandenen Übertragungsfehler weiter (signifikant) verringert.
+*With larger noise interference,&nbsp; $\rho_{v}$&nbsp; is further (significantly) reduced by the transmission errors then present.
-*Dagegen führt die Abtastung zu keinem Qualitätsverlust, wenn das Abtasttheorem eingehalten wird.
+*In contrast, sampling results in no loss of quality if the sampling theorem is obeyed.
-*Die Abtastung kann dann vollständig rückgängig gemacht werden, wenn das Quellensignal&nbsp; $q(t)$&nbsp; bandbegrenzt ist und die Signalrekonstruktion richtig dimensioniert ist:&nbsp;   idealer Tiefpass.
+*Sampling can then be completely undone if the source signal&nbsp; $q(t)$&nbsp; is bandlimited and the signal reconstruction is correctly dimensioned:&nbsp;   ideal low-pass.
 {{ML-Fuß}}

← Older revision		Revision as of 15:20, 9 September 2022
Line 87:		Line 87:


−	[[Category:Examples of Communication Systems: Exercises\|^1.1 ~~Allgemeine Beschreibung von~~ ISDN^]]	+	[[Category:Examples of Communication Systems: Exercises\|^1.1 General Description of ISDN^]]