Aufgaben:Exercise 4.3: Pointer Diagram Representation - Revision history

Guenter at 14:02, 6 May 2021

2021-05-06T14:02:41Z

Guenter at 13:36, 6 May 2021

2021-05-06T13:36:24Z

Guenter at 13:31, 6 May 2021

2021-05-06T13:31:20Z

Guenter at 13:30, 6 May 2021

2021-05-06T13:30:25Z

Guenter at 13:29, 6 May 2021

2021-05-06T13:29:16Z

Guenter: Guenter moved page Aufgaben:Exercise 4.3: Vector Diagram Representation to Aufgaben:Exercise 4.3: Pointer Diagram Representation

2021-05-06T13:22:21Z

Guenter moved page Exercise 4.3: Vector Diagram Representation to Exercise 4.3: Pointer Diagram Representation

Javier: Text replacement - "bandpass" to "band-pass"

2021-05-03T15:12:59Z

Text replacement - "bandpass" to "band-pass"

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

2021-03-23T12:38:46Z

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

Noah at 21:44, 15 February 2021

2021-02-15T21:44:15Z

Noah at 20:14, 4 February 2021

2021-02-04T20:14:15Z

@@ Line 61: / Line 61: @@
 ===Solution===
 {{ML-Kopf}}
-'''(1)'''&nbsp;  The amplitude of the harmonic oscillation is equal to the pointer length. For all signals&nbsp; $A \; \underline{= 3 \ \text{V}}$.
+'''(1)'''&nbsp;  The amplitude of the harmonic oscillation is equal to the pointer length.&nbsp; For all signals&nbsp; $A \; \underline{= 3 \ \text{V}}$.
@@ Line 81: / Line 81: @@
 This signal is "minus-sine", which can also be read directly from the pointer diagram:
-*The real part of&nbsp; $x_{2+}(t)$&nbsp; at time&nbsp; $t = 0$&nbsp; is zero. Since the pointer turns counterclockwise, the real part is negative at first.
+*The real part of&nbsp; $x_{2+}(t)$&nbsp; at time&nbsp; $t = 0$&nbsp; is zero.&nbsp; Since the pointer turns counterclockwise, the real part is negative at first.
 *After a quarter turn,&nbsp; $x_2(T/4) = - 3 \ \text{V}$.
-*If one continues to turn counterclockwise in steps of&nbsp; $90^\circ$&nbsp; , the signal values&nbsp; $0 \ \text{V}$,&nbsp; $3 \ \text{V}$&nbsp; and&nbsp; $0 \ \text{V}$ result.
+*If one continues to turn counterclockwise in steps of&nbsp; $90^\circ$, the signal values&nbsp; $0 \ \text{V}$,&nbsp; $3 \ \text{V}$&nbsp; and&nbsp; $0 \ \text{V}$ result.
-'''(4)'''&nbsp; This sub-task can be solved analogously to questions&nbsp; '''(2)'''&nbsp; and '''(3)''' : &nbsp;
+'''(4)'''&nbsp; This sub-task can be solved analogously to sub-tasks&nbsp; '''(2)'''&nbsp; and '''(3)''' : &nbsp;
 :$$f_3  \; \underline{= 10 \ \text{kHz}}, \ \varphi_3 \; \underline{= 60^\circ}.$$
-'''(5)'''&nbsp;  The pointer requires exactly the period&nbsp; $T_3 = 1/f_3  \; \underline{= 0.1 \ \text{ms}} \;(= t_1)$ for one revolution..
+'''(5)'''&nbsp;  The pointer requires exactly the period&nbsp; $T_3 = 1/f_3  \; \underline{= 0.1 \ \text{ms}} \;(= t_1)$ for one rotation.
 '''(6)'''&nbsp;  The analytical signal starts at&nbsp; $S_3 = 3 \ \text{V} \cdot \text{e}^{–\text{j}\hspace{0.05cm} \cdot \hspace{0.05cm}60^{\circ}}$.
-*If the signal rotates further by&nbsp; $120^\circ$&nbsp;, exactly the same real part results.
+*If the signal rotates further by&nbsp; $120^\circ$,&nbsp; exactly the same real part results.
 *The following relationship then applies with&nbsp; $t_2 = t_1/3 \; \underline{= 0.033 \ \text{ms}} $&nbsp;:
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 __NOEDITSECTION__
-[[Category:Signal Representation: Exercises|^4.2 Analytical Signal and Its Spectral Function^]]
+[[Category:Signal Representation: Exercises|^4.2 Analytical Signal and its Spectral Function^]]

@@ Line 29: / Line 29: @@
 <quiz display=simple>
-{What are the amplitudes of all signals considered??
+{What are the amplitudes of all signals considered?
 |type="{}"}
 $A\ = \ $  { 3 3% } &nbsp;$\text{V}$
@@ Line 43: / Line 43: @@
 $\varphi_2\ = \ $  { -91--89 } &nbsp;$\text{deg}$
-{What are the values of the frequency and phase of the signal &nbsp; $x_3(t)$?
+{What are the frequency and phase values of the signal &nbsp; $x_3(t)$?
 |type="{}"}
 $f_3\ = \ $  { 10 3% } &nbsp;$\text{kHz}$
 $\varphi_3\ = \ $  { 60 3% } &nbsp;$\text{deg}$
-{After what time&nbsp; $t_1$&nbsp; is the analytical signal&nbsp; $x_{3+}(t)$&nbsp; equal to the initial value&nbsp; $x_{3+}(t = 0)$for the first time again?
+{After what time&nbsp; $t_1$&nbsp; is the analytical signal&nbsp; $x_{3+}(t)$&nbsp; for the first time again equal to the initial value&nbsp; $x_{3+}(t = 0)$?
 |type="{}"}
 $t_1\ = \ $  { 0.1 3% } &nbsp;$\text{ms}$

@@ Line 22: / Line 22: @@
 ''Hints:''
 *This exercise belongs to the chapter&nbsp; [[Signal_Representation/Analytical_Signal_and_Its_Spectral_Function|Analytical Signal and its Spectral Function]].
-*The interactive applet&nbsp; [[Physical_Signal_%26_Analytic_Signal|Physical and Analytical Signal]]&nbsp; illustrates the topic covered here.
+*The interactive applet&nbsp; [[Applets:Physical_Signal_%26_Analytic_Signal|Physical and Analytical Signal]]&nbsp; illustrates the topic covered here.

@@ Line 22: / Line 22: @@
 ''Hints:''
 *This exercise belongs to the chapter&nbsp; [[Signal_Representation/Analytical_Signal_and_Its_Spectral_Function|Analytical Signal and its Spectral Function]].
-*The interactive applet&nbsp; [[Applets:Physikalisches_Signal_%26_Analytisches_Signal|Physical signal & Analytical Signal]]&nbsp; illustrates the topic covered here.
+*The interactive applet&nbsp; [[Physical_Signal_%26_Analytic_Signal|Physical and Analytical Signal]]&nbsp; illustrates the topic covered here.

@@ Line 5: / Line 5: @@
 [[File:P_ID716__Sig_A_4_3.png|250px|right|frame|Pointer diagram of a harmonic]]
-We consider an analytical signal&nbsp; $x_+(t)$, which is defined by the drawn diagram in the complex plane. Depending on the choice of signal parameters, this results in three physical band-pass signals&nbsp; $x_1(t)$,&nbsp; $x_2(t)$&nbsp; and&nbsp; $x_3(t)$, which differ by different starting points&nbsp; $S_i = x_i(t = 0)$&nbsp; unterscheiden (blue, green and red point). In addition, the angular velocities of the three constellations are also different:
+We consider an analytical signal&nbsp; $x_+(t)$, which is defined by the drawn diagram in the complex plane.&nbsp; Depending on the choice of signal parameters, this results in three physical band-pass signals&nbsp; $x_1(t)$,&nbsp; $x_2(t)$&nbsp; and&nbsp; $x_3(t)$, which differ by different starting points&nbsp; $S_i = x_i(t = 0)$.
 *The analytical signal&nbsp; $x_{1+}(t)$&nbsp; starts at&nbsp; $S_1 = 3 \ \rm V$. The angular velocity is&nbsp; $\omega_1 = \pi \cdot 10^{4} \ 1/\text{s}$.
 *The signal&nbsp; $x_{2+}(t)$&nbsp; starts at the green starting point&nbsp; $S_2 = {\rm j} \cdot 3 \ \text{V}$&nbsp; and, compared to&nbsp; $x_{1+}(t)$&nbsp;, rotates with twice the angular velocity&nbsp; &rArr; &nbsp; $\omega_2 = 2 \cdot \omega_1$.
-*The signal $x_{3+}(t)$ starts at the red marked starting point&nbsp; $S_3 = 3 \ \text{V} \cdot \text{e}^{–\text{j}\hspace{0.05cm}\cdot\hspace{0.05cm}\pi /3}$&nbsp; and rotates with the same speed as the signal&nbsp; $x_{2+}(t)$.
+*The signal $x_{3+}(t)$ starts at the red starting point&nbsp; $S_3 = 3 \ \text{V} \cdot \text{e}^{–\text{j}\hspace{0.05cm}\cdot\hspace{0.05cm}\pi /3}$&nbsp; and rotates with same speed as the signal&nbsp; $x_{2+}(t)$.
@@ Line 19: / Line 21: @@
 ''Hints:''
-*This exercise belongs to the chapter&nbsp; [[Signal_Representation/Analytical_Signal_and_Its_Spectral_Function|Analytical Signal and Its Spectral Function]].
+*This exercise belongs to the chapter&nbsp; [[Signal_Representation/Analytical_Signal_and_Its_Spectral_Function|Analytical Signal and its Spectral Function]].
 *The interactive applet&nbsp; [[Applets:Physikalisches_Signal_%26_Analytisches_Signal|Physical signal & Analytical Signal]]&nbsp; illustrates the topic covered here.

← Older revision	Revision as of 13:22, 6 May 2021
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← Older revision		Revision as of 12:38, 23 March 2021
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	__NOEDITSECTION__		__NOEDITSECTION__
−	[[Category:~~Exercises for~~ Signal Representation\|^4.2 Analytical Signal and Its Spectral Function^]]	+	[[Category:Signal Representation: Exercises\|^4.2 Analytical Signal and Its Spectral Function^]]

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 }}
-[[File:P_ID716__Sig_A_4_3.png|250px|right|frame|Zeigerdiagramm einer Harmonischen]]
+[[File:P_ID716__Sig_A_4_3.png|250px|right|frame|Pointer diagram of a harmonic]]
 We consider an analytical signal&nbsp; $x_+(t)$, which is defined by the drawn diagram in the complex plane. Depending on the choice of signal parameters, this results in three physical bandpass signals&nbsp; $x_1(t)$,&nbsp; $x_2(t)$&nbsp; and&nbsp; $x_3(t)$, which differ by different starting points&nbsp; $S_i = x_i(t = 0)$&nbsp; unterscheiden (blue, green and red point). In addition, the angular velocities of the three constellations are also different: