Aufgaben:Exercise 4.5Z: Simple Phase Modulator - Revision history

Guenter at 14:16, 24 May 2021

2021-05-24T14:16:26Z

Guenter at 13:01, 24 May 2021

2021-05-24T13:01:14Z

Guenter at 16:08, 11 May 2021

2021-05-11T16:08:42Z

Guenter at 16:00, 11 May 2021

2021-05-11T16:00:35Z

Javier: Text replacement - "Low Pass" to "Low-Pass"

2021-05-04T07:33:28Z

Text replacement - "Low Pass" to "Low-Pass"

Javier: Text replacement - "low pass" to "low-pass"

2021-05-03T15:10:39Z

Text replacement - "low pass" to "low-pass"

Guenter at 08:53, 23 April 2021

2021-04-23T08:53:43Z

Javier: Text replacement - "Category:Exercises for Signal Representation" to "Category:Signal Representation: Exercises"

2021-03-23T12:38:57Z

Text replacement - "Category:Exercises for Signal Representation" to "Category:Signal Representation: Exercises"

Noah at 20:45, 15 February 2021

2021-02-15T20:45:07Z

Noah at 14:59, 10 February 2021

2021-02-10T14:59:08Z

Show changes

@@ Line 3: / Line 3: @@
 }}
-[[File:P_ID757__Sig_Z_4_5.png|right|frame|Model of the phase modulator under consideration]]
+[[File:P_ID757__Sig_Z_4_5.png|right|frame|Model of the considered phase modulator]]
 The diagram shows a quite simple arrangement for approximating a phase modulator.&nbsp; All signals are dimensionless.
@@ Line 100: / Line 100: @@
-[[File:P_ID762__Sig_Z_4_5_a.png|right|frame|Locus curve of a simple phase modulator]]
+[[File:P_ID762__Sig_Z_4_5_a.png|right|frame|Locality curve of a simple phase modulator]]
 '''(3)'''&nbsp;  The locality curve is a vertical straight line &nbsp; &rArr; &nbsp;  <u>Proposition 3</u> with the following values:
 :$$s_{\rm TP}(t = 0) = s_{\rm TP}(t = {\rm 50 \hspace{0.05cm} &micro; s})

← Older revision		Revision as of 13:01, 24 May 2021
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−	{{quiz-Header\|Buchseite=Signal_Representation/~~Equivalent_Low_Pass_Signal_and_Its_Spectral_Function~~	+	{{quiz-Header\|Buchseite=Signal_Representation/Equivalent Low-Pass Signal and its Spectral Function
	}}		}}

@@ Line 47: / Line 47: @@
 {Which of the following statements are true for the "Locality Curve"&nbsp; $s_{\rm TP}(t)$ zu?
-|type="[]"}
+|type="()"}
 - The locality curve is a circular arc.
 - The locality curve is a horizontal straight line.
@@ Line 61: / Line 61: @@
 {What is the phase function&nbsp; $\phi(t)$.&nbsp;  What is its maximum value?
+|type="{}"}
 $\phi_{\rm max}\ = \ $ { 45 3% } &nbsp;$\text{deg}$
@@ Line 92: / Line 92: @@
 {\rm e}^{{\rm j}\hspace{0.05cm} \omega_{\rm N} \hspace{0.05cm} t }
 = 1 + {\rm j} \cdot \sin(\omega_{\rm N} \hspace{0.05cm} t ).$$
-*At time&nbsp; $t = 0$ ist $s_{\rm TP}(t) = 1$, is real. Thus:
+*At time&nbsp; $t = 0$ &nbsp; &rArr; &nbsp;  $s_{\rm TP}(t) = 1$, is real. Thus:
 :* $s_{\rm I}(t = 0) = \text{Re}[s_{\rm TP}(t = 0)]\; \underline{= 1}$,
@@ Line 101: / Line 101: @@
 [[File:P_ID762__Sig_Z_4_5_a.png|right|frame|Locus curve of a simple phase modulator]]
-'''(3)'''&nbsp;  The locus curve is a vertical straight line &nbsp; &rArr; &nbsp;  <u>Proposition 3</u> with the following values:
+'''(3)'''&nbsp;  The locality curve is a vertical straight line &nbsp; &rArr; &nbsp;  <u>Proposition 3</u> with the following values:
 :$$s_{\rm TP}(t = 0) = s_{\rm TP}(t = {\rm 50 \hspace{0.05cm} &micro; s})
 = \text{ ...} = 1,$$
@@ Line 115: / Line 115: @@
-'''(5)'''&nbsp;  The real part is always&nbsp; $1$, the imaginary part equal to&nbsp; $\sin(\omega_{\rm N} \cdot t) $. From this follows the phase function:
+'''(5)'''&nbsp;  The real part is always&nbsp; $1$, the imaginary part equal to&nbsp; $\sin(\omega_{\rm N} \cdot t) $.
 :$$\phi(t)= {\rm arctan} \hspace{0.1cm}{\left(\sin(\omega_{\rm N}
 \hspace{0.05cm} t )\right)}.$$

@@ Line 4: / Line 4: @@
 [[File:P_ID757__Sig_Z_4_5.png|right|frame|Model of the phase modulator under consideration]]
-The diagram shows a quite simple arrangement for approximating a phase modulator. All signals are dimensionless quantities.
+The diagram shows a quite simple arrangement for approximating a phase modulator.&nbsp; All signals are dimensionless.
-The sinusoidal message signal&nbsp; $q(t)$&nbsp; of frequency&nbsp; $f_{\rm N} = 10 \ \text{kHz}$&nbsp;  is multiplied by the signal&nbsp; $m(t)$&nbsp;, which results from the cosinusoidal carrier signal&nbsp; $z(t)$&nbsp; by phase shifting by&nbsp; $\phi = 90^\circ$&nbsp;:
+The sinusoidal source signal&nbsp; $q(t)$&nbsp; of frequency&nbsp; $f_{\rm N} = 10 \ \text{kHz}$&nbsp;  is multiplied by the signal&nbsp; $m(t)$, which results from the cosinusoidal carrier signal&nbsp; $z(t)$&nbsp; by phase shifting by&nbsp; $\phi = 90^\circ$&nbsp;:
 :$$m(t) =   {\cos} (  \omega_{\rm T} \cdot t + 90^\circ).$$
@@ Line 14: / Line 14: @@
 *the difference frequency&nbsp; $f_{\rm \Delta} = f_{\rm T} - f_{\rm N} = 0.99 \ \text{MHz}$,
 *the sum frequency&nbsp; $f_{\rm \Sigma} = f_{\rm T} + f_{\rm N} = 1.01\  \text{MHz}$,
-*the two angular frequencies&nbsp; $\omega_{\rm \Delta} = 2\pi \cdot f_{\rm \Delta}$&nbsp; and&nbsp; $\omega_{\rm \Sigma} = 2\pi \cdot f_{\rm \Sigma}$.
+*the two circular frequencies&nbsp; $\omega_{\rm \Delta} = 2\pi \cdot f_{\rm \Delta}$&nbsp; and&nbsp; $\omega_{\rm \Sigma} = 2\pi \cdot f_{\rm \Sigma}$.
@@ Line 23: / Line 21: @@
 ''Hints:''
-*This exercise belongs to the chapter&nbsp; [[Signal_Representation/Equivalent_Low_Pass_Signal_and_Its_Spectral_Function|Equivalent Low-Pass Signal and Its Spectral Function]].
+*This exercise belongs to the chapter&nbsp; [[Signal_Representation/Equivalent_Low-Pass_Signal_and_its_Spectral_Function|Equivalent Low-Pass Signal and its Spectral Function]].
 *Consider the trigonomic transformations
@@ Line 42: / Line 40: @@
-{Calculate the equivalent low-pass signal&nbsp; $s_{\rm TP}(t)$. What are the inphase and quadrature components at time&nbsp; $t = 0$?
+{Calculate the equivalent low-pass signal&nbsp; $s_{\rm TP}(t)$.&nbsp; What are the inphase and quadrature components at time&nbsp; $t = 0$?
 |type="{}"}
 $s_{\rm I}(t = 0)\ = \ $  { 1 3% }
@@ Line 48: / Line 46: @@
-{Which of the following statements are true for the locus curve&nbsp; $s_{\rm TP}(t)$ zu?
+{Which of the following statements are true for the "Locality Curve"&nbsp; $s_{\rm TP}(t)$ zu?
 |type="[]"}
-- The locus curve is a circular arc.
+- The locality curve is a circular arc.
-- The locus curve is a horizontal straight line.
+- The locality curve is a horizontal straight line.
-+ The locus curve is a vertical straight line.
++ The locality curve is a vertical straight line.
@@ Line 62: / Line 60: @@
-{What is the phase function&nbsp; $\phi(t)$.  What is its maximum value?
+{What is the phase function&nbsp; $\phi(t)$.&nbsp;  What is its maximum value?
 $\phi_{\rm max}\ = \ $ { 45 3% } &nbsp;$\text{deg}$

@@ Line 23: / Line 23: @@
 ''Hints:''
-*This exercise belongs to the chapter&nbsp; [[Signal_Representation/Equivalent_Low_Pass_Signal_and_Its_Spectral_Function|Equivalent Low Pass Signal and Its Spectral Function]].
+*This exercise belongs to the chapter&nbsp; [[Signal_Representation/Equivalent_Low_Pass_Signal_and_Its_Spectral_Function|Equivalent Low-Pass Signal and Its Spectral Function]].
 *Consider the trigonomic transformations

@@ Line 42: / Line 42: @@
-{Calculate the equivalent low pass signal&nbsp; $s_{\rm TP}(t)$. What are the inphase and quadrature components at time&nbsp; $t = 0$?
+{Calculate the equivalent low-pass signal&nbsp; $s_{\rm TP}(t)$. What are the inphase and quadrature components at time&nbsp; $t = 0$?
 |type="{}"}
 $s_{\rm I}(t = 0)\ = \ $  { 1 3% }
@@ Line 86: / Line 86: @@
 :$$S_{\rm +}(f) = \delta (f - f_{\rm T}) - 0.5 \cdot \delta (f -
 f_{\rm \Delta})+ 0.5 \cdot \delta (f - f_{\rm \Sigma}) .$$
-*By shitfing&nbsp; $f_{\rm T}$&nbsp; one arrives at the spectrum of the equivalent low pass signal:
+*By shitfing&nbsp; $f_{\rm T}$&nbsp; one arrives at the spectrum of the equivalent low-pass signal:
 :$$S_{\rm TP}(f) = \delta (f ) - 0.5 \cdot \delta (f + f_{\rm N})+
 .5 \cdot \delta (f - f_{\rm N}) .$$

← Older revision		Revision as of 08:53, 23 April 2021
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−	[[Category:Signal Representation: Exercises\|^4.3 Equivalent ~~Low Pass~~ Signal and ~~Its~~ Spectral Function^]]	+	[[Category:Signal Representation: Exercises\|^4.3 Equivalent LP Signal and its Spectral Function^]]

← Older revision		Revision as of 12:38, 23 March 2021
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	__NOEDITSECTION__		__NOEDITSECTION__
−	[[Category:~~Exercises for~~ Signal Representation\|^4.3 Equivalent Low Pass Signal and Its Spectral Function^]]	+	[[Category:Signal Representation: Exercises\|^4.3 Equivalent Low Pass Signal and Its Spectral Function^]]