Aufgaben:Exercise 4.5: Locality Curve for DSB-AM - Revision history

Hwang at 13:22, 18 January 2023

2023-01-18T13:22:34Z

Guenter at 14:44, 11 May 2021

2021-05-11T14:44:09Z

Guenter at 14:36, 11 May 2021

2021-05-11T14:36:53Z

Guenter at 14:35, 11 May 2021

2021-05-11T14:35:25Z

Guenter at 14:34, 11 May 2021

2021-05-11T14:34:46Z

Guenter at 14:17, 11 May 2021

2021-05-11T14:17:47Z

Guenter at 14:16, 11 May 2021

2021-05-11T14:16:46Z

Guenter: Guenter moved page Aufgaben:Exercise 4.5: Locus Curve for DSB-AM to Aufgaben:Exercise 4.5: Locality Curve for DSB-AM

2021-05-10T12:10:02Z

Guenter moved page Exercise 4.5: Locus Curve for DSB-AM to Exercise 4.5: Locality Curve for DSB-AM

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"

2021-05-03T15:10:48Z

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

@@ Line 64: / Line 64: @@
 [[File:EN_Sig_A_4_5_a.png|250px|right|frame|Locality curve at time&nbsp; $t = 0$]]
-'''(1)'''&nbsp; If all Dirac lines are shifted to the left by&nbsp; $f_{\rm T} = 50 \ \text{kHz}$&nbsp;, they are located at&nbsp; $-\hspace{-0.08cm}10 \ \text{kHz}$,&nbsp; $0$&nbsp; and&nbsp; $+10 \ \text{kHz}$.
+'''(1)'''&nbsp; If all Dirac delta lines are shifted to the left by&nbsp; $f_{\rm T} = 50 \ \text{kHz}$&nbsp;, they are located at&nbsp; $-\hspace{-0.08cm}10 \ \text{kHz}$,&nbsp; $0$&nbsp; and&nbsp; $+10 \ \text{kHz}$.
 *The equation for&nbsp; $s_{\rm TP}(t)$&nbsp; is with&nbsp; $\omega_{10} = 2 \pi \cdot 10  \ \text{kHz}$:

@@ Line 63: / Line 63: @@
 {{ML-Kopf}}
-[[File:EN_Sig_A_4_5_a.png|250px|right|frame|Locus curve at time&nbsp; $t = 0$]]
+[[File:EN_Sig_A_4_5_a.png|250px|right|frame|Locality curve at time&nbsp; $t = 0$]]
-'''(1)'''&nbsp; If all diraclines are shifted to the left by&nbsp; $f_{\rm C} = 50 \ \text{kHz}$&nbsp;, they are located at&nbsp; $-\hspace{-0.08cm}10 \ \text{kHz}$,&nbsp; $0$&nbsp; and&nbsp; $+10 \ \text{kHz}$.
+'''(1)'''&nbsp; If all Dirac lines are shifted to the left by&nbsp; $f_{\rm T} = 50 \ \text{kHz}$&nbsp;, they are located at&nbsp; $-\hspace{-0.08cm}10 \ \text{kHz}$,&nbsp; $0$&nbsp; and&nbsp; $+10 \ \text{kHz}$.
 *The equation for&nbsp; $s_{\rm TP}(t)$&nbsp; is with&nbsp; $\omega_{10} = 2 \pi \cdot 10  \ \text{kHz}$:
@@ Line 91: / Line 91: @@
 {t}/{T_0}) .$$
-*This shows that&nbsp; $s_{\rm TP}(t)$&nbsp; is real for all times&nbsp; $t$&nbsp .
+*This shows that&nbsp; $s_{\rm TP}(t)$&nbsp; is real for all times&nbsp; $t$.
-*For the numerical values we are looking for, we obtain:
+*We obtain for the numerical values we are looking for:
 :$$s_{\rm TP}(t = {\rm 10 \hspace{0.1cm} {\rm &micro;} s}) = {\rm 1
@@ Line 127: / Line 127: @@
 Re}\left[s_{\rm TP}(t)\right]}$$
-Due to the fact that here&nbsp; ${\rm Im}[s_{\rm TP}(t)] = 0$&nbsp; for all times, one obtains the result from this:
+Due to the fact that here&nbsp; ${\rm Im}[s_{\rm TP}(t)] = 0$&nbsp; for all times, one obtains:
 * If&nbsp; ${\rm Re}[s_{\rm TP}(t)] > 0$&nbsp; holds, the phase&nbsp; $\phi(t) = 0$.
 * On the other hand, if the real part is negative: &nbsp; &nbsp; $\phi(t) = \pi$.
@@ Line 139: / Line 139: @@
 :$$\sin(2 \pi \cdot  {t_1}/{T_0}) = -0.5 \hspace{0.3cm} \Rightarrow
 \hspace{0.3cm} 2 \pi \cdot {t_1}/{T_0} = 2 \pi \cdot
-{7}/{12}\hspace{0.3cm}{\rm (corresponds to}\hspace{0.2cm}210^\circ
+{7}/{12}\hspace{0.3cm}{\text{(corresponds to}}\hspace{0.2cm}210^\circ
 )$$

@@ Line 26: / Line 26: @@
 ''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]].
 *You can check your solution with the interactive applet&nbsp; [[Applets:Physical_Signal_%26_Equivalent_Lowpass_Signal|Physical Signal & Equivalent Low-Pass Signal]]&nbsp; &nbsp; &rArr; &nbsp; "Locality Curve".

@@ Line 5: / Line 5: @@
 [[File:P_ID751__Sig_A_4_5_neu.png|250px|right|frame|Spectrum of the analytical signal]]
-We consider a similar transmission scenario as in&nbsp; [[Aufgaben:Aufgabe_4.4:_Zeigerdiagramm_bei_ZSB-AM|Exrcise 4.4]]&nbsp; (but not the same):
+We consider a similar transmission scenario as in&nbsp; [[Aufgaben:Exercise_4.4:_Pointer_Diagram_for_DSB-AM|Exrcise 4.4]]&nbsp; (but not the same):
 * A sinusoidal source signal with amplitude&nbsp; $A_{\rm N} = 2 \ \text{V}$&nbsp;  and frequency&nbsp; $f_{\rm N} = 10 \ \text{kHz}$,
 *Double-Sideband Amplitude Modulation without carrier suppression with carrier frequency&nbsp; $f_{\rm T} = 50 \ \text{kHz}$.

@@ Line 5: / Line 5: @@
 [[File:P_ID751__Sig_A_4_5_neu.png|250px|right|frame|Spectrum of the analytical signal]]
-We consider a similar transmission scenario as in&nbsp; [[Aufgaben:Aufgabe_4.4:_Zeigerdiagramm_bei_ZSB-AM|task 4.4]]&nbsp; (but not the same):
+We consider a similar transmission scenario as in&nbsp; [[Aufgaben:Aufgabe_4.4:_Zeigerdiagramm_bei_ZSB-AM|Exrcise 4.4]]&nbsp; (but not the same):
-* a sinusoidal message signal with amplitude&nbsp; $A_{\rm N} = 2 \ \text{V}$&nbsp;  and the frequency&nbsp; $f_{\rm N} = 10 \ \text{kHz}$,
+* A sinusoidal source signal with amplitude&nbsp; $A_{\rm N} = 2 \ \text{V}$&nbsp;  and frequency&nbsp; $f_{\rm N} = 10 \ \text{kHz}$,
-*DSB-Amplitude Modulation without carrier suppression with carrier frequency&nbsp; $f_{\rm T} = 50 \ \text{kHz}$.
+*Double-Sideband Amplitude Modulation without carrier suppression with carrier frequency&nbsp; $f_{\rm T} = 50 \ \text{kHz}$.
 Opposite you see the spectral function&nbsp; $S_+(f)$&nbsp; of the analytical signal&nbsp; $s_+(t)$.
-When solving, take into account that the equivalent low-pass signal is also in the form
+When solving, take into account that the equivalent low-pass signal is in the form
-:$$s_{\rm TP}(t) = a(t) \cdot {\rm e}^{{\rm j}\hspace{0.05cm}\cdot \hspace{0.05cm} \phi(t)} $$
+:$$s_{\rm TP}(t) = a(t) \cdot {\rm e}^{{\rm j}\hspace{0.05cm}\cdot \hspace{0.05cm} \phi(t)},\hspace{0.5cm}  a(t) ≥ 0.$$
-where&nbsp; $a(t) ≥ 0$&nbsp; shall hold. For&nbsp; $\phi(t)$&nbsp;, the range of values&nbsp; $–\pi < \phi(t) \leq +\pi$&nbsp; is permissible and the generally valid equation applies:
+For&nbsp; $\phi(t)$,&nbsp; the range&nbsp; $–\pi < \phi(t) \leq +\pi$&nbsp; is permissible and the generally valid equation applies:
 :$$\phi(t)= {\rm arctan} \hspace{0.1cm}\frac{{\rm Im}\big[s_{\rm
 TP}(t)\big]}{{\rm Re}\big[s_{\rm TP}(t)\big]}.$$
@@ Line 29: / Line 26: @@
 ''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]].
-*You can check your solution with the interactive applet&nbsp; [[Applets:Physikalisches_Signal_%26_Äquivalentes_TP-Signal|Physical signal & equivalent LP signal]]&nbsp; &nbsp; &rArr; &nbsp; &bdquo;locus curve&rdquo;.
+*You can check your solution with the interactive applet&nbsp; [[Applets:Physical_Signal_%26_Equivalent_Lowpass_Signal|Physical Signal & Equivalent Low-Pass Signal]]&nbsp; &nbsp; &rArr; &nbsp; "Locality Curve".
@@ Line 37: / Line 34: @@
 <quiz display=simple>
-{Calculate the equivalent low-pass signal&nbsp; $s_{\rm TP}(t)$&nbsp; in the frequency and time domain. What is the value of&nbsp; $s_{\rm TP}(t)$&nbsp; at the start time&nbsp; $t = 0$?
+{Calculate the equivalent low-pass signal&nbsp; $s_{\rm TP}(t)$&nbsp; in the frequency and time domain.&nbsp; What is the value of&nbsp; $s_{\rm TP}(t)$&nbsp; at the start time&nbsp; $t = 0$?
 |type="{}"}
 $\text{Re}[s_{\text{TP}}(t=0)]\ = \ $  { 1 3% }  &nbsp;$\text{V}$
 $\text{Im}[s_{\text{TP}}(t=0 )]\ = \ $ { 0. } &nbsp;$\text{V}$
-{What are the values of&nbsp; $s_{\rm TP}(t)$&nbsp; at&nbsp; $t = 10 \ {\rm &micro;} \text{s}= T_0/10$, &nbsp; &nbsp; $t = 25 \ {\rm &micro;} \text{s}= T_0/4$, &nbsp; &nbsp; $t = 75 \ {\rm &micro;} \text{s}= 3T_0/4$&nbsp; and&nbsp; $T_0 = 100 \ {\rm &micro;}s$? <br>Show that all values are purely real.
+{What are the values of&nbsp; $s_{\rm TP}(t)$&nbsp; at&nbsp; $t = 10 \ {\rm &micro;} \text{s}= T_0/10$, &nbsp; &nbsp; $t = 25 \ {\rm &micro;} \text{s}= T_0/4$, &nbsp; &nbsp; $t = 75 \ {\rm &micro;} \text{s}= 3T_0/4$&nbsp; and&nbsp; $T_0 = 100 \ {\rm &micro;s}$? <br>Show that all values are purely real.
 |type="{}"}
 $\text{Re}[s_{\text{TP}}(t=10 \ {\rm &micro;} \text{s})]\ = \ $ { 2.176 3% } &nbsp;$\text{V}$
@@ Line 49: / Line 46: @@
 $\text{Re}[s_{\text{TP}}(t=100 \ {\rm &micro;} \text{s})]\ = \ $ { 1 3% } &nbsp;$\text{V}$
-{What is the magnitude function&nbsp; $a(t)$&nbsp; im Zeitbereich? in the time domain? What are the values at times&nbsp; $t = 25 \ {\rm &micro;} \text{s}$&nbsp; and&nbsp; $t = 75 \ {\rm &micro;} \text{s}$?
+{What is the magnitude function&nbsp; $a(t)$&nbsp;  in the time domain?&nbsp; What are the values at times&nbsp; $t = 25 \ {\rm &micro;} \text{s}$&nbsp; and&nbsp; $t = 75 \ {\rm &micro;} \text{s}$?
 |type="{}"}
 $a(t=25 \ {\rm &micro;} \text{s})\ = \ $ { 3 3% } &nbsp;$\text{V}$
 $a(t=75 \ {\rm &micro;} \text{s})\ = \ $ { 1 3% } &nbsp;$\text{V}$
-{Give the phase function&nbsp; $\phi(t)$&nbsp;  in the time domain in general. What values result at the times&nbsp; $t = 25 \ {\rm &micro;} \text{s}$&nbsp; and&nbsp; $t = 75 \ {\rm &micro;} \text{s}$?
+{Give the phase function&nbsp; $\phi(t)$&nbsp;  in the time domain.&nbsp; What values result at the times&nbsp; $t = 25 \ {\rm &micro;} \text{s}$&nbsp; and&nbsp; $t = 75 \ {\rm &micro;} \text{s}$?
 |type="{}"}
 $\phi(t=25 \ {\rm &micro;} \text{s}) \ = \ $ { 0. } &nbsp;$\text{Grad}$

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← Older revision		Revision as of 14:16, 11 May 2021
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← Older revision	Revision as of 12:10, 10 May 2021
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