Aufgaben:Exercise 2.1Z: Sum Signal - Revision history

Guenter at 12:33, 12 April 2021

2021-04-12T12:33:12Z

Guenter at 12:17, 12 April 2021

2021-04-12T12:17:19Z

Guenter at 12:11, 12 April 2021

2021-04-12T12:11:00Z

Guenter: Guenter moved page Aufgaben:Exercise 2.1Z: Summing Signal to Aufgaben:Exercise 2.1Z: Sum Signal

2021-04-12T12:00:50Z

Guenter moved page Exercise 2.1Z: Summing Signal to Exercise 2.1Z: Sum Signal

Guenter at 11:35, 12 April 2021

2021-04-12T11:35:12Z

Noah at 09:52, 26 March 2021

2021-03-26T09:52:01Z

Noah at 09:51, 26 March 2021

2021-03-26T09:51:28Z

Noah at 09:16, 26 March 2021

2021-03-26T09:16:05Z

Noah at 09:14, 26 March 2021

2021-03-26T09:14:05Z

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"

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 :$$f_y \hspace{0.15cm}\underline{= 0.4\,  \text{kHz}}.$$
 '''(3)'''&nbsp;  The basic frequency&nbsp; $f_s$&nbsp; of the sum signal&nbsp; $s(t)$&nbsp; is the greatest common divisor&nbsp; $f_x = 1 \,\text{kHz}$&nbsp; and&nbsp; $f_y = 0.4 \,\text{kHz}$.
-*Daraus folgt&nbsp; $f_s = 200 \,\text{Hz}$&nbsp; und die Periodendauer&nbsp; $T_s\hspace{0.15cm}\underline{ = 5 \,\text{ms}}$, wie auch aus der grafischen Darstellung des Signals&nbsp; ${s(t)}$&nbsp; auf der Angabenseite hervorgeht.
+[[File:P_ID320__Sig_Z_2_1_d_neu.png|right|frame|Difference&nbsp; $d(t) = x(t) - y(t)$]]
-[[File:P_ID320__Sig_Z_2_1_d_neu.png|right|frame|Difference $d(t) = x(t) - y(t)$]]
+'''(5)'''&nbsp;  The greatest common divisor of&nbsp; $f_u = 998 \,\text{Hz}$&nbsp; and&nbsp; $f_{v} = 1002 \,\text{Hz}$&nbsp; is&nbsp; $f_w = 2 \,\text{Hz}$.&nbsp; The inverse of this gives the period duration&nbsp;  $T_w \hspace{0.15cm}\underline{= 500 \,\text{ms}}$.
 {{ML-Fuß}}

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 ===Solution===
 {{ML-Kopf}}
-'''(1)'''&nbsp;  The following applies to the square wave signal:&nbsp; $T_x = 1 \,\text{ms}$  &nbsp; &rArr; &nbsp; $f_x \hspace{0.15cm}\underline{= 1 \, \text{kHz}}$.
+'''(1)'''&nbsp;  The following applies to the rectangular signal:&nbsp; $T_x = 1 \,\text{ms}$  &nbsp; &rArr; &nbsp;
+'''(3)'''&nbsp;  The basic frequency&nbsp; $f_s$&nbsp; of the sum signal&nbsp; $s(t)$&nbsp; is the greatest common divisor&nbsp; $f_x = 1 \,\text{kHz}$&nbsp; and&nbsp; $f_y = 0.4 \,\text{kHz}$.
 *Daraus folgt&nbsp; $f_s = 200 \,\text{Hz}$&nbsp; und die Periodendauer&nbsp; $T_s\hspace{0.15cm}\underline{ = 5 \,\text{ms}}$, wie auch aus der grafischen Darstellung des Signals&nbsp; ${s(t)}$&nbsp; auf der Angabenseite hervorgeht.

@@ Line 3: / Line 3: @@
 }}
-[[File:P_ID319__Sig_Z_2_1.png|right|frame|Square wave signal, triangular signal and sum signal]]
+[[File:P_ID319__Sig_Z_2_1.png|right|frame|Rectangular signal, triangular signal, sum signal]]
-The adjacent diagram shows the two periodic signals&nbsp; ${x(t)}$&nbsp; and&nbsp; ${y(t)}$&nbsp;, from which the sum &nbsp; ${s(t)}$&nbsp; – sketched in the lower picture – and the difference&nbsp; ${d(t)}$&nbsp; are formed.
+The adjacent diagram shows the periodic signals&nbsp; ${x(t)}$&nbsp; and&nbsp; ${y(t)}$,&nbsp; from which the sum &nbsp; ${s(t)}$&nbsp; – sketched in the lower diagram – and the difference&nbsp; ${d(t)}$&nbsp; are formed.
-Furthermore, in this task we consider the signa&nbsp; ${w(t)}$, which results from the sum of the two periodic signals&nbsp; ${u(t)}$&nbsp; und&nbsp; $v(t)$&nbsp;. The base frequencies of the signals are
+Furthermore, in this task we consider the signal&nbsp; ${w(t)}$, which results from the sum of two periodic signals&nbsp; ${u(t)}$&nbsp; and&nbsp; $v(t)$&nbsp;.&nbsp; The base frequencies of these signals are
 :* $f_u = 998 \,\text{Hz},$
@@ Line 12: / Line 12: @@
 :* $f_v = 1002 \,\text{Hz}.$
-That is all we know about the signals&nbsp; ${u(t)}$&nbsp; and&nbsp; $v(t)$&nbsp;.
+That is all we know about the signals&nbsp; ${u(t)}$&nbsp; and&nbsp; $v(t)$.
@@ Line 22: / Line 22: @@
 ''Hints:''
 *The exercise belongs to the chapter&nbsp; [[Signal_Representation/General_Description|General description of periodic signals]].
-*With the interactive applet&nbsp; [[Applets:Periodendauer_periodischer_Signale|Periodendauer periodischer Signale]]&nbsp; the resulting period duration of two harmonic oscillations can be determined.
+*With the interactive applet&nbsp; [[Applets:Period_Duration_of_Periodic_Signals|Period Duration of Periodic Signals]]&nbsp; the resulting period duration of two harmonic oscillations can be determined.
@@ Line 29: / Line 29: @@
 <quiz display=simple>
-{What is the period duration&nbsp; $T_x$&nbsp; and the base frequency&nbsp; $f_x$&nbsp; of the signal&nbsp; ${x(t)}$?
+{What is the period duration&nbsp; $T_x$&nbsp; and the basic frequency&nbsp; $f_x$&nbsp; of the signal&nbsp; ${x(t)}$?
 |type="{}"}
 $f_x\ = \ $  { 1 3% } &nbsp; $\text{kHz}$
-{What is the period duration&nbsp; $T_y$&nbsp; and the base frequency&nbsp; $f_y$&nbsp; of the signal&nbsp; ${y(t)}$?
+{What is the period duration&nbsp; $T_y$&nbsp; and the basic frequency&nbsp; $f_y$&nbsp; of the signal&nbsp; ${y(t)}$?
 |type="{}"}
 $f_y\ = \ $ { 0.4 3% } &nbsp; $\text{kHz}$
-{Determine the base frequency&nbsp; $f_s$&nbsp; as well as the period duration&nbsp; $T_s$&nbsp; of the sum signal&nbsp; ${s(t)}$&nbsp; and verify your results with the help of the sketched signal.
+{Determine the basic frequency&nbsp; $f_s$&nbsp; and the period duration&nbsp; $T_s$&nbsp; of the sum signal&nbsp; ${s(t)}$.&nbsp; <br>Verify your results with the help of the sketched signal.
 |type="{}"}
 $T_s\ = \ $ { 5 3% } &nbsp; $\text{ms}$

← Older revision		Revision as of 11:35, 12 April 2021
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−	[[Category:Signal Representation: Exercises\|^2.1 ~~General~~ Description ~~about~~ Periodic Signals^]]	+	[[Category:Signal Representation: Exercises\|^2.1 Description of Periodic Signals^]]

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 [[File:P_ID319__Sig_Z_2_1.png|right|frame|Square wave signal, triangular signal and sum signal]]
-The adjacent diagram shows the two periodic signals&nbsp; ${x(t)}$&nbsp; and&nbsp; ${y(t)}$&nbsp;, from which the sum &nbsp; ${s(t)}$&nbsp; – sketched in the lower picture – and the difference &nbsp; ${d(t)}$&nbsp; are formed.
+The adjacent diagram shows the two periodic signals&nbsp; ${x(t)}$&nbsp; and&nbsp; ${y(t)}$&nbsp;, from which the sum &nbsp; ${s(t)}$&nbsp; – sketched in the lower picture – and the difference&nbsp; ${d(t)}$&nbsp; are formed.
 Furthermore, in this task we consider the signa&nbsp; ${w(t)}$, which results from the sum of the two periodic signals&nbsp; ${u(t)}$&nbsp; und&nbsp; $v(t)$&nbsp;. The base frequencies of the signals are

← Older revision	Revision as of 12:00, 12 April 2021
(No difference)

← Older revision		Revision as of 12:38, 23 March 2021
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−	[[Category:~~Exercises for~~ Signal Representation\|^2.1 General Description about Periodic Signals^]]	+	[[Category:Signal Representation: Exercises\|^2.1 General Description about Periodic Signals^]]