Aufgaben:Exercise 1.2: Signal Classification - Revision history

Javier at 08:59, 11 October 2021

2021-10-11T08:59:42Z

Javier at 08:43, 11 October 2021

2021-10-11T08:43:35Z

Javier: Text replacement - "discrete-valued" to "discrete"

2021-10-11T08:27:44Z

Text replacement - "discrete-valued" to "discrete"

Javier: Text replacement - "value-discrete" to "discrete"

2021-10-11T08:27:22Z

Text replacement - "value-discrete" to "discrete"

Javier: Text replacement - "value-continuous" to "continuous"

2021-10-11T08:27:12Z

Text replacement - "value-continuous" to "continuous"

Guenter at 12:01, 9 April 2021

2021-04-09T12:01:23Z

Guenter at 11:54, 9 April 2021

2021-04-09T11:54:13Z

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

2021-03-23T12:39:40Z

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

Noah at 12:55, 25 December 2020

2020-12-25T12:55:13Z

Noah at 11:24, 22 December 2020

2020-12-22T11:24:43Z

@@ Line 63: / Line 63: @@
 *All signals can be described completely in analytical form;&nbsp; therefore they are deterministic.
 *All signals are also clearly defined for all times&nbsp; $t$&nbsp; not only at certain times.&nbsp; Therefore, they are always continuous-time signals.
-*The signal amplitudes of&nbsp; <math>x_2(t)</math>&nbsp; and&nbsp; <math>x_3(t)</math>&nbsp; can take any values between&nbsp; $0$&nbsp; and&nbsp; $1\,\text{V}$&nbsp; they are continuous in value.
+*The signal amplitudes of&nbsp; <math>x_2(t)</math>&nbsp; and&nbsp; <math>x_3(t)</math>&nbsp; can take any values between&nbsp; $0$&nbsp; and&nbsp; $1\,\text{V}$&nbsp: they are <b>continuous in value</b>.
-*On the other hand, with the signal&nbsp; <math>x_1(t)</math>&nbsp; only the two signal values&nbsp; $0$&nbsp; and&nbsp; $1\,\text{V}$&nbsp; are possible; a discrete signal is present.
+*On the other hand, with the signal&nbsp; <math>x_1(t)</math>&nbsp; only the two signal values&nbsp; $0$&nbsp; and&nbsp; $1\,\text{V}$&nbsp; are possible; this signal is <b>discrete in value</b>.

@@ Line 16: / Line 16: @@
 *causal or non&ndash;causal,
 *energy-limited or power-limited,
-*continuous or discrete,
+*continuous-valued or discrete-valued,
-*time-continuous or time-discrete.
+*continuous in time or discrete in time.
@@ Line 62: / Line 62: @@
 '''(1)'''&nbsp;  The <u>solutions 1 and 3</u> are applicable:
 *All signals can be described completely in analytical form;&nbsp; therefore they are deterministic.
-*All signals are also clearly defined for all times&nbsp; $t$&nbsp; not only at certain times.&nbsp; Therefore, they are always time-continuous signals.
+*All signals are also clearly defined for all times&nbsp; $t$&nbsp; not only at certain times.&nbsp; Therefore, they are always continuous-time signals.
 *The signal amplitudes of&nbsp; <math>x_2(t)</math>&nbsp; and&nbsp; <math>x_3(t)</math>&nbsp; can take any values between&nbsp; $0$&nbsp; and&nbsp; $1\,\text{V}$&nbsp; they are continuous in value.
 *On the other hand, with the signal&nbsp; <math>x_1(t)</math>&nbsp; only the two signal values&nbsp; $0$&nbsp; and&nbsp; $1\,\text{V}$&nbsp; are possible; a discrete signal is present.

@@ Line 64: / Line 64: @@
 *All signals are also clearly defined for all times&nbsp; $t$&nbsp; not only at certain times.&nbsp; Therefore, they are always time-continuous signals.
 *The signal amplitudes of&nbsp; <math>x_2(t)</math>&nbsp; and&nbsp; <math>x_3(t)</math>&nbsp; can take any values between&nbsp; $0$&nbsp; and&nbsp; $1\,\text{V}$&nbsp; they are continuous in value.
-*On the other hand, with the signal&nbsp; <math>x_1(t)</math>&nbsp; only the two signal values&nbsp; $0$&nbsp; and&nbsp; $1\,\text{V}$&nbsp; are possible; a discrete-valued signal is present.
+*On the other hand, with the signal&nbsp; <math>x_1(t)</math>&nbsp; only the two signal values&nbsp; $0$&nbsp; and&nbsp; $1\,\text{V}$&nbsp; are possible; a discrete signal is present.

@@ Line 16: / Line 16: @@
 *causal or non&ndash;causal,
 *energy-limited or power-limited,
-*continuous or value-discrete,
+*continuous or discrete,
 *time-continuous or time-discrete.

@@ Line 16: / Line 16: @@
 *causal or non&ndash;causal,
 *energy-limited or power-limited,
-*value-continuous or value-discrete,
+*continuous or value-discrete,
 *time-continuous or time-discrete.

@@ Line 61: / Line 61: @@
 {{ML-Kopf}}
 '''(1)'''&nbsp;  The <u>solutions 1 and 3</u> are applicable:
-*All signals can be described completely in analytical form; therefore they are also deterministic.
+*All signals can be described completely in analytical form;&nbsp; therefore they are deterministic.
-*All signals are also clearly defined for all times&nbsp; $t$&nbsp; not only at certain times. Therefore, they are always time-continuous signals.
+*All signals are also clearly defined for all times&nbsp; $t$&nbsp; not only at certain times.&nbsp; Therefore, they are always time-continuous signals.
-*The signal amplitudes of&nbsp; <math>x_2(t)</math>&nbsp; and&nbsp; <math>x_3(t)</math>&nbsp; can take any values between&nbsp; $0$&nbsp; and&nbsp; $1\,\text{V}$&nbsp; they are therefore continuous in value.
+*The signal amplitudes of&nbsp; <math>x_2(t)</math>&nbsp; and&nbsp; <math>x_3(t)</math>&nbsp; can take any values between&nbsp; $0$&nbsp; and&nbsp; $1\,\text{V}$&nbsp; they are continuous in value.
 *On the other hand, with the signal&nbsp; <math>x_1(t)</math>&nbsp; only the two signal values&nbsp; $0$&nbsp; and&nbsp; $1\,\text{V}$&nbsp; are possible; a discrete-valued signal is present.
@@ Line 69: / Line 69: @@
 '''(2)'''&nbsp;  Correct are the <u>solutions 1 and 2</u>:
-*A signal is called causal if for times&nbsp; $t < 0$&nbsp; it does not exist or is identically zero. This applies to the signals&nbsp; <math>x_1(t)</math>&nbsp; and&nbsp; <math>x_2(t)</math>.
+*A signal is called causal if for times&nbsp; $t < 0$&nbsp; it does not exist or it is identically zero.&nbsp; This applies to the signals&nbsp; <math>x_1(t)</math>&nbsp; and&nbsp; <math>x_2(t)</math>.
 *In contrast,&nbsp; <math>x_3(t)</math>&nbsp; belongs to the class of non-causal signals.
@@ Line 78: / Line 78: @@
 ::<math>E_2=\lim_{T_{\rm M}\to\infty}\int^{T_{\rm M}/2}_{-T_{\rm M}/2}x^2_2(t)\,\hspace{0.1cm}{\rm d}t.</math>
-In this case, the lower integration limit is zero and the upper integration limit&nbsp; $+\infty$. You get:
+In this case, the lower integration limit is zero and the upper integration limit&nbsp; $+\infty$.&nbsp; You get:
 ::<math>E_2=\int^\infty_0 (1{\rm V})^2\cdot{\rm e}^{-2t/(1\rm ms)}\,\hspace{0.1cm}{\rm d}t = 5 \cdot 10^{-4}\hspace{0.1cm} \rm V^2s  \hspace{0.15cm}\underline{= 0.5 \cdot 10^{-3}\hspace{0.1cm} \rm V^2s}.  </math>
-With finite energy, the associated power is always negligible. From this follows&nbsp; $P_2\hspace{0.15cm}\underline{ = 0}$.
+With finite energy, the associated power is always negligible.&nbsp; From this follows&nbsp; $P_2\hspace{0.15cm}\underline{ = 0}$.
@@ Line 93: / Line 93: @@
 :$$E_3= 10^{-3}\hspace{0.1cm} {\rm V^2s}.$$
-*At signal&nbsp; <math>x_1(t)</math>&nbsp; the energy integral diverges:&nbsp; $E_1 \rightarrow \infty$. This signal has a finite power &nbsp; &rArr; &nbsp; $P_1= 0.5 \hspace{0.1cm} {\rm V}^2$.
+*At signal&nbsp; <math>x_1(t)</math>&nbsp; the energy integral diverges:&nbsp; $E_1 \rightarrow \infty$.&nbsp; This signal has a finite power &nbsp; &rArr; &nbsp; $P_1= 0.5 \hspace{0.1cm} {\rm V}^2$.
 *The result also takes into account that the signal&nbsp; <math>x_1(t)</math>&nbsp; in half the time&nbsp; $(t < 0)$&nbsp; is identical to zero.
-* The signal&nbsp; <math>x_1(t)</math>&nbsp; therefore is&nbsp; <u>power limited</u>.
+* The signal&nbsp; <math>x_1(t)</math>&nbsp; therefore is&nbsp; <u>power&ndash;limited</u>.
 {{ML-Fuß}}

@@ Line 1: / Line 1: @@
 {{quiz-Header|Buchseite=Signal_Representation/Signal_classification}}
-[[File:P_ID341_Sig_A_1_2.png|right|frame|predetermined characteristics]]
+[[File:P_ID341_Sig_A_1_2.png|right|frame|Preset signal waveforms]]
 Three signal curves are shown on the right:
 *The blue signal&nbsp; <math>x_1(t)</math>&nbsp; is switched on at time&nbsp; $t = 0$&nbsp; and has the value&nbsp; $1\,\text{V}\,$ for&nbsp; $t > 0$&nbsp;.
-*The blue signal&nbsp; <math>x_2(t)</math>&nbsp; equals zero for&nbsp; $t < 0$&nbsp; and jumps to&nbsp; $1\,\text{V}$&nbsp; at&nbsp; $t = 0$&nbsp;. It then decreases with the time constant&nbsp; $1\,\text{ms}$&nbsp;. For&nbsp; $t > 0$&nbsp; the following applies:
+*The red signal&nbsp; <math>x_2(t)\equiv 0</math>&nbsp;  for&nbsp; $t < 0$&nbsp; and jumps to&nbsp; $1\,\text{V}$&nbsp; at&nbsp; $t = 0$&nbsp;.&nbsp; It then decreases with the time constant&nbsp; $1\,\text{ms}$&nbsp;.&nbsp; <br>For&nbsp; $t > 0$&nbsp; the following applies:
 ::<math>x_2(t) = 1\,\text{V} \cdot {\rm e}^{- {t}/(1\,\text{ms})}.</math>
@@ Line 14: / Line 14: @@
 You should now classify these three signals according to the following criteria:
 *deterministic or stochastic,
-*causal or acausal,
+*causal or non&ndash;causal,
-*energy limited or power limited,
+*energy-limited or power-limited,
 *value-continuous or value-discrete,
 *time-continuous or time-discrete.
@@ Line 23: / Line 23: @@
-''Notes:''
+''Note:''
 * This exercise belongs to the chapter&nbsp;[[Signal_Representation/Signal_classification|Signal Classification]].
@@ Line 44: / Line 44: @@
 - <math>x_3(t)</math>.
-{Calculate the energy&nbsp; $R = 1\ Ω$&nbsp; related to the unit resistance&nbsp; <math>E_2</math>&nbsp; of the signal&nbsp; <math>x_2(t)</math>. <br>What is the power&nbsp; <math>P_2</math>&nbsp; of this signal?
+{Calculate the energy&nbsp; $E_2$&nbsp; of the signal&nbsp; <math>x_2(t)</math> related to the unit resistance&nbsp; $R = 1\ Ω$. <br>What is the power&nbsp; <math>P_2</math>&nbsp; of this signal?
 |type="{}"}
 <math>E_2 \ = \ </math>{ 0.5 5% }  $\ \cdot 10^{-3}\,\text{V}^2\text{s}$

← Older revision		Revision as of 12:39, 23 March 2021
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−	[[Category:~~Exercises for~~ Signal Representation\|^1.2 Signal Classification^]]	+	[[Category:Signal Representation: Exercises\|^1.2 Signal Classification^]]

← Older revision		Revision as of 11:24, 22 December 2020
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	''Notes:''		''Notes:''
−	* This exercise belongs to the chapter  [[Signal_Representation/Signal_classification\|Signal Classification]].	+	* This exercise belongs to the chapter [[Signal_Representation/Signal_classification\|Signal Classification]].