Aufgaben:Exercise 3.4Z: Continuous Phase Frequency Shift Keying - Revision history

Guenter at 14:21, 22 January 2023

2023-01-22T14:21:17Z

Guenter at 14:14, 22 January 2023

2023-01-22T14:14:44Z

Guenter at 12:38, 19 January 2023

2023-01-19T12:38:30Z

Guenter at 12:14, 19 January 2023

2023-01-19T12:14:48Z

Guenter at 08:45, 19 January 2023

2023-01-19T08:45:14Z

Noah at 18:53, 17 January 2023

2023-01-17T18:53:58Z

Guenter at 15:38, 11 January 2023

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Guenter at 15:37, 11 January 2023

2023-01-11T15:37:54Z

Noah at 20:47, 9 January 2023

2023-01-09T20:47:40Z

Noah at 20:30, 9 January 2023

2023-01-09T20:30:53Z

← Older revision		Revision as of 14:21, 22 January 2023
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−	'''(7)'''  Correct is the  <u>last proposed solution</u>,  since for this signal $h = 0.5$.	+	'''(7)'''  Correct is the  <u>last proposed solution</u>,  since for this signal   ⇒   $h = 0.5$.
	*This is the smallest possible modulation index for which there is orthogonality between  $f_{1}$  and  $f_{2}$  within the symbol duration  $T$.		*This is the smallest possible modulation index for which there is orthogonality between  $f_{1}$  and  $f_{2}$  within the symbol duration  $T$.

@@ Line 47: / Line 47: @@
 $f_{2} \cdot T \ = \ $ { 3 3% }
-{What are the carrier frequency&nbsp; $f_{\rm T}$,&nbsp; the frequency deviation&nbsp; $\delta f_{\rm A}$&nbsp; and the modulation index&nbsp; $h$&nbsp; for signal&nbsp; $s_{\rm A}(t)$?
+{What are the carrier frequency&nbsp; $f_{\rm T}$,&nbsp; the frequency deviation&nbsp; $\Delta f_{\rm A}$&nbsp; and the modulation index&nbsp; $h$&nbsp; for signal&nbsp; $s_{\rm A}(t)$?
 |type="{}"}
 $f_{\rm T} \cdot T \ = \ $ { 4 3% }

@@ Line 50: / Line 50: @@
 |type="{}"}
 $f_{\rm T} \cdot T \ = \ $ { 4 3% }
-$\delta f_{\rm A} \cdot T \ = \ $ { 1 3% }
+$\Delta f_{\rm A} \cdot T \ = \ $ { 1 3% }
 $h \ = \ $ { 2 3% }
@@ Line 67: / Line 67: @@
 + $s_{\rm C}(t)$.
-{What signals describe&nbsp; ''Minimum Shift Keying''&nbsp; (MSK)?
+{What signals describe&nbsp; "Minimum Shift Keying"&nbsp; $\rm (MSK)$?
 |type="[]"}
 - $s_{\rm A}(t)$,
@@ Line 79: / Line 79: @@
 {{ML-Kopf}}
 '''(1)'''&nbsp; <u>All statements except the third are true</u>:
-*Generally nonlinear FSK can only be demodulated coherently, while MSK can also use a noncoherent demodulation method.
+*Generally nonlinear FSK can only be demodulated coherently,&nbsp; while MSK can also use a noncoherent demodulation method.
-*Compared to QPSK with coherent demodulation, MSK requires $3 \ \rm dB$ more $E_{\rm B}/N_{0}$ (energy per bit related to the noise power density) for the same bit error rate.
-*The first zero in the power density spectrum occurs later in MSK than in QSPK, but it shows a faster asymptotic decay than in QSPK.
+*Compared to QPSK with coherent demodulation,&nbsp; MSK requires&nbsp; $3 \ \rm dB$&nbsp; more&nbsp; $E_{\rm B}/N_{0}$&nbsp; $($energy per bit related to the noise power density$)$&nbsp; for the same bit error rate.
 '''(2)'''&nbsp; One can see from the graph five and three oscillations per symbol duration, respectively:
 :$$f_{\rm 1} \cdot T \hspace{0.15cm} \underline {= 5}\hspace{0.05cm},\hspace{0.2cm}f_{\rm 2} \cdot T \hspace{0.15cm} \underline { = 3}\hspace{0.05cm}.$$
-'''(3)'''&nbsp; For FSK with rectangular pulse shape, only the two instantaneous frequencies $f_{1} = f_{\rm T} + \Delta f_{\rm A}$ and $f_{2} = f_{\rm T} - \Delta f_{\rm A}$ occur.
+'''(3)'''&nbsp; For FSK with rectangular pulse shape,&nbsp; only the two instantaneous frequencies&nbsp; $f_{1} = f_{\rm T} + \Delta f_{\rm A}$&nbsp; and&nbsp; $f_{2} = f_{\rm T} - \Delta f_{\rm A}$&nbsp; occur.
-*With the result from '''(2)''' we thus obtain:
+*With the result from subtask&nbsp; '''(2)'''&nbsp; we thus obtain:
 :$$f_{\rm T} \ = \ \frac{f_{\rm 1}+f_{\rm 2}}{2}\hspace{0.3cm}\Rightarrow \hspace{0.3cm}f_{\rm T} \cdot T \hspace{0.15cm} \underline {= 4}\hspace{0.05cm},$$
 :$$ \Delta f_{\rm A} \ = \ \frac{f_{\rm 1}-f_{\rm 2}}{2}\hspace{0.3cm}\Rightarrow \hspace{0.3cm}\Delta f_{\rm A} \cdot T \hspace{0.15cm} \underline { = 1}\hspace{0.05cm},$$
@@ Line 98: / Line 101: @@
-'''(4)'''&nbsp; From the graph one can see the frequencies $f_{1} \cdot T = 4.5$ and $f_{2} \cdot T = 3.5$.
+'''(4)'''&nbsp; From the graph one can see the frequencies&nbsp; $f_{1} \cdot T = 4.5$&nbsp; and&nbsp; $f_{2} \cdot T = 3.5$.
-*This results in the frequency deviation $\Delta f_{\rm A} \cdot T = 0.5$ and the modulation index $\underline{h = 1}$.
+*This results in the frequency deviation&nbsp; $\Delta f_{\rm A} \cdot T = 0.5$&nbsp; and the modulation index&nbsp; $\underline{h = 1}$.
-'''(5)'''&nbsp; Here the two (normalized) frequencies $f_{1} \cdot T = 4.25$ and $f_{2} \cdot T = 3.75$ occur,
+'''(5)'''&nbsp; Here the two&nbsp; $($normalized$)$&nbsp; frequencies&nbsp; $f_{1} \cdot T = 4.25$&nbsp; and&nbsp; $f_{2} \cdot T = 3.75$&nbsp; occur,
-*which results in the frequency deviation $\Delta f_{\rm A} \cdot T = 0.25$ and the modulation index $\underline{h = 0.5}$ can be calculated.
+*which results in the frequency deviation&nbsp; $\Delta f_{\rm A} \cdot T = 0.25$&nbsp; and the modulation index&nbsp; $\underline{h = 0.5}$.
-'''(6)'''&nbsp; Correct are the <u>solutions 2 and 3</u>:
+'''(6)'''&nbsp; Correct are the&nbsp; <u>solutions 2 and 3</u>:
-*Only at $s_{\rm A}(t)$ was no phase adjustment made.
+*Only at&nbsp; $s_{\rm A}(t)$&nbsp; was no phase adjustment made.&nbsp; Here,&nbsp; the signal waveforms in the region of the first and second bit&nbsp; $(a_{1} = a_{2} = +1)$&nbsp; are each cosinusoidal like the carrier signal&nbsp; $($with respect to the symbol boundary$)$.
-*Here, the signal waveforms in the region of the first and second bit ($a_{1} = a_{2} = +1$) are each cosinusoidal like the carrier signal (with respect to the symbol boundary).
-*In contrast, in the second symbol of $s_{\rm B}(t)$ a minus-cosine-shaped course (initial phase $\phi_{0} = π$ corresponding to $180^\circ$) can be seen and in the second symbol of $s_{\rm C}(t)$ a minus-sine-shaped course ($\phi_{0} = π /2$ or $90^\circ$).
+*In contrast,&nbsp; in the second symbol of&nbsp; $s_{\rm B}(t)$&nbsp; a minus-cosine-shaped course&nbsp; $($initial phase&nbsp; $\phi_{0} = π$,&nbsp; corresponding to&nbsp; $180^\circ)$&nbsp; can be seen and in the second symbol of&nbsp; $s_{\rm C}(t)$&nbsp; a minus-sine-shaped course&nbsp; $(\phi_{0} = π /2$&nbsp; or&nbsp; $90^\circ)$.
-*For $s_{\rm A}(t)$ the initial phase is always $0$, for $s_{\rm B}(t)$ either $0$ or $π$, while for the signal $s_{\rm C}(t)$ with modulation index $h = 0.5$ a total of four initial phases are possible: $0^\circ, \ 90^\circ, \ 180^\circ$ and $270^\circ$.
-'''(7)'''&nbsp; Correct is the <u>last proposed solution</u>, since for this signal $h = 0.5$ holds.
+'''(7)'''&nbsp; Correct is the&nbsp; <u>last proposed solution</u>,&nbsp; since for this signal $h = 0.5$.
-*This is the smallest possible modulation index for which there is orthogonality between $f_{1}$ and $f_{2}$ within the symbol duration $T$.
+*This is the smallest possible modulation index for which there is orthogonality between&nbsp; $f_{1}$&nbsp; and&nbsp; $f_{2}$&nbsp; within the symbol duration&nbsp; $T$.
 {{ML-Fuß}}

@@ Line 3: / Line 3: @@
 }}
-[[File:P_ID1231__Bei_Z_3_4.png|right|frame|Signals for&nbsp; "Continuous Phase FSK"]]
+[[File:P_ID1231__Bei_Z_3_4.png|right|frame|Signals for&nbsp; $\text{CP-FSK}$]]
 The graph shows three frequency shift keying&nbsp; $\rm (FSK)$&nbsp; transmitted signals which differ with respect to the frequency deviation&nbsp; $\Delta f_{\rm A}$&nbsp; distinguish and thus also by their modulation index
 :$$h = 2 \cdot \Delta f_{\rm A} \cdot T.$$
@@ Line 34: / Line 34: @@
 <quiz display=simple>
-{Which statements are true for the FSK and specifically for the MSK?
+{Which statements are true for FSK and specifically for MSK?
 |type="[]"}
 + FSK is generally a nonlinear modulation method.
@@ Line 42: / Line 42: @@
 + The MSK envelope is constant even with spectral shaping.
-{What frequencies&nbsp; $f_{1}$&nbsp; $($for amplitude coefficient&nbsp; $a_{\nu} = +1)$&nbsp; and $f_{2}$&nbsp; $($for&nbsp; $a_{\nu} = -1)$&nbsp; does the signal&nbsp; $s_{\rm A}(t)$ contain?
+{What frequencies&nbsp; $f_{1}$&nbsp; $($for amplitude coefficient&nbsp; $a_{\nu} = +1)$&nbsp; and $f_{2}$&nbsp; $($for&nbsp; $a_{\nu} = -1)$&nbsp; does the signal&nbsp; $s_{\rm A}(t)$&nbsp; contain?
 |type="{}"}
 $f_{1} \cdot T \ = \ $ { 5 3% }
 $f_{2} \cdot T \ = \ $ { 3 3% }
-{For the signal&nbsp; $s_{\rm A}(t)$&nbsp; what are the carrier frequency&nbsp; $f_{\rm T}$, frequency deviation&nbsp; $\delta f_{\rm A}$&nbsp; and modulation index&nbsp; $h$?
+{What are the carrier frequency&nbsp; $f_{\rm T}$,&nbsp; the frequency deviation&nbsp; $\delta f_{\rm A}$&nbsp; and the modulation index&nbsp; $h$&nbsp; for signal&nbsp; $s_{\rm A}(t)$?
 |type="{}"}
 $f_{\rm T} \cdot T \ = \ $ { 4 3% }
@@ Line 53: / Line 53: @@
 $h \ = \ $ { 2 3% }
-{What is the modulation index at signal&nbsp; $s_{\rm B}(t)$?
+{What is the modulation index for signal&nbsp; $s_{\rm B}(t)$?
 |type="{}"}
 $h \ = \ $ { 1 3% }
-{What is the modulation index at signal&nbsp; $s_{\rm C}(t)$?
+{What is the modulation index for signal&nbsp; $s_{\rm C}(t)$?
 |type="{}"}
 $h \ = \ $ { 0.5 3% }

@@ Line 3: / Line 3: @@
 }}
-[[File:P_ID1231__Bei_Z_3_4.png|right|frame|Signals for&nbsp; $\text{CP-FSK}$]]
+[[File:P_ID1231__Bei_Z_3_4.png|right|frame|Signals for&nbsp; "Continuous Phase FSK"]]
 The graph shows three frequency shift keying&nbsp; $\rm (FSK)$&nbsp; transmitted signals which differ with respect to the frequency deviation&nbsp; $\Delta f_{\rm A}$&nbsp; distinguish and thus also by their modulation index
 :$$h = 2 \cdot \Delta f_{\rm A} \cdot T.$$

@@ Line 3: / Line 3: @@
 }}
-[[File:P_ID1231__Bei_Z_3_4.png|right|frame|Signals for&nbsp; $\rm CP FSK$]]
+[[File:P_ID1231__Bei_Z_3_4.png|right|frame|Signals for&nbsp; $\text{CP-FSK$}]]
-The graph shows three FSK transmit signals which differ with respect to the frequency deviation&nbsp; $\Delta f_{\rm A}$&nbsp; and thus also by their modulation index
+The graph shows three frequency shift keying&nbsp; $\rm (FSK)$&nbsp; transmitted signals which differ with respect to the frequency deviation&nbsp; $\Delta f_{\rm A}$&nbsp; distinguish and thus also by their modulation index
-:$$h = 2 \cdot \Delta f_{\rm A} \cdot T$$
+:$$h = 2 \cdot \Delta f_{\rm A} \cdot T.$$
-distinguish.
-The digital source signal&nbsp; $q(t)$ underlying the signals&nbsp; $s_{\rm A}(t),&nbsp; s_{\rm B}(t)$&nbsp; and&nbsp; $s_{\rm C}(t)$&nbsp; is shown above. All considered signals are normalized to amplitude&nbsp; $1$&nbsp; and time duration&nbsp; $T$&nbsp; and are based on a cosine carrier with frequency $f_{\rm T}$.
+The digital source signal&nbsp; $q(t)$ underlying the signals&nbsp; $s_{\rm A}(t),&nbsp; s_{\rm B}(t)$&nbsp; and&nbsp; $s_{\rm C}(t)$&nbsp; is shown above.&nbsp; All considered signals are normalized to amplitude&nbsp; $1$&nbsp; and time duration&nbsp; $T$&nbsp; and based on a cosine carrier with frequency&nbsp; $f_{\rm T}$.
-With binary FSK (''Binary Frequency Shift Keying'') only two different frequencies occur.
+With binary FSK&nbsp; $($"Binary Frequency Shift Keying"$)$&nbsp; only two different frequencies occur,&nbsp; each of which remains constant over a bit duration:
 *$f_{1}$&nbsp; $($if&nbsp; $a_{\nu} = +1)$,
-Hints:
+*Reference is made in particular to the section&nbsp; [[Examples_of_Communication_Systems/Radio_Interface#Continuous_phase_adjustment_with_FSK|"Continuous phase adjustment with FSK]].
 ===Questions===

@@ Line 3: / Line 3: @@
 }}
-[[File:P_ID1231__Bei_Z_3_4.png|right|frame|Signale zu&nbsp; $\rm CP&ndash; FSK$]]
+[[File:P_ID1231__Bei_Z_3_4.png|right|frame|Signals for&nbsp; $\rm CP FSK$]]
-Die Grafik zeigt drei FSK–Sendesignale, die sich hinsichtlich des  Frequenzhubs&nbsp; $\Delta f_{\rm A}$&nbsp; und somit auch durch ihren Modulationsindex
+The graph shows three FSK transmit signals which differ with respect to the frequency deviation&nbsp; $\Delta f_{\rm A}$&nbsp; and thus also by their modulation index
 :$$h = 2 \cdot \Delta f_{\rm A} \cdot T$$
-unterscheiden.
+distinguish.
-Das digitale Quellensignal&nbsp; $q(t)$, das den Signalen&nbsp; $s_{\rm A}(t),&nbsp; s_{\rm B}(t)$&nbsp; und&nbsp; $s_{\rm C}(t)$&nbsp; zugrundeliegt, ist oben dargestellt. Alle betrachteten Signale sind auf die Amplitude&nbsp; $1$&nbsp; und die Zeitdauer&nbsp; $T$&nbsp; normiert und basieren auf einem Cosinusträger mit der Frequenz $f_{\rm T}$.
+The digital source signal&nbsp; $q(t)$ underlying the signals&nbsp; $s_{\rm A}(t),&nbsp; s_{\rm B}(t)$&nbsp; and&nbsp; $s_{\rm C}(t)$&nbsp; is shown above. All considered signals are normalized to amplitude&nbsp; $1$&nbsp; and time duration&nbsp; $T$&nbsp; and are based on a cosine carrier with frequency $f_{\rm T}$.
-Bei binärer FSK (''Binary Frequency Shift Keying'') treten nur zwei verschiedene Frequenzen
+With binary FSK (''Binary Frequency Shift Keying'') only two different frequencies occur.
-*$f_{1}$&nbsp; $($falls&nbsp; $a_{\nu} = +1)$,
+*$f_{1}$&nbsp; $($if&nbsp; $a_{\nu} = +1)$,
-*$f_{2}$&nbsp; $($falls&nbsp; $a_{\nu} = -1)$
+*$f_{2}$&nbsp; $($if&nbsp; $a_{\nu} = -1)$
-auf, die jeweils über eine Bitdauer konstant bleiben.
+each of which remains constant over a bit duration.
-Ist der Modulationsindex kein Vielfaches von&nbsp; $2$, so ist eine kontinuierliche Phasenanpassung erforderlich, um Phasensprünge zu vermeiden. Man spricht dann von&nbsp; ''Continuous Phase Frequency Shift Keying'' &nbsp;$ (\rm CP&ndash; FSK)$.
+If the modulation index is not a multiple of&nbsp; $2$, continuous phase adjustment is required to avoid phase jumps. This is called&nbsp; ''Continuous Phase Frequency Shift Keying'' &nbsp;$ (\rm CP&ndash; FSK)$.
-Ein wichtiger Sonderfall stellt die binäre FSK mit dem Modulationsindex&nbsp; $h = 0.5$&nbsp; dar, die auch als&nbsp; ''Minimum Shift Keying''&nbsp;  $(\rm MSK)$ bezeichnet wird. Diese wird in dieser Aufgabe  behandelt.
+An important special case is represented by binary FSK with modulation index&nbsp; $h = 0.5$&nbsp; which is also called&nbsp; ''Minimum Shift Keying''&nbsp; $(\rm MSK)$. This will be discussed in this exercise.
@@ Line 28: / Line 28: @@
-''Hinweise:''
+Hints:
-*Diese Aufgabe gehört zum Kapitel&nbsp;  [[Examples_of_Communication_Systems/Funkschnittstelle|Funkschnittstelle]].
+*This exercise belongs to the chapter&nbsp; [[Examples_of_Communication_Systems/Radio_Interface|"Radio Interface"]].
-*Bezug genommen wird insbesondere auf die Seite&nbsp; [[Examples_of_Communication_Systems/Funkschnittstelle#Kontinuierliche_Phasenanpassung_bei_FSK|Kontinuierliche Phasenanpassung bei FSK]].
+*Reference is made in particular to the page&nbsp; [[Examples_of_Communication_Systems/Radio_Interface#Continuous_phase_adjustment_with_FSK|"Continuous phase adjustment with FSK]].
-*Das interaktive Applet&nbsp; [[Applets:Frequency_Shift_Keying_%26_Continuous_Phase_Modulation|Frequency Shift Keying und Continuous Phase Modulation]]&nbsp; verdeutlicht die hier behandelte Thematik.
+*The interactive applet&nbsp; [[Applets:Frequency_Shift_Keying_%26_Continuous_Phase_Modulation|"Frequency Shift Keying & Continuous Phase Modulation"]]&nbsp; illustrates the topic covered here.
-===Fragebogen===
+===Questions===
 <quiz display=simple>

← Older revision		Revision as of 20:30, 9 January 2023
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−	{{quiz-Header\|Buchseite=~~Beispiele von Nachrichtensystemen~~/~~Funkschnittstelle~~	+	{{quiz-Header\|Buchseite=Examples_of_Communication_Systems/Radio_Interface
	}}		}}