Aufgaben:Exercise 1.1: Music Signals - Revision history

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← Older revision		Revision as of 14:29, 12 January 2024
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−	'''(4)'''  The signal  <math>v_1(t)</math>  is identical in ~~form~~ to the original signal  <math>q(t)</math>  and differs from it only	+	'''(4)'''  The signal  <math>v_1(t)</math>  is identical in shape to the original signal  <math>q(t)</math>  and differs from it only
	*by the attenuation factor  $\alpha = \underline{\text{0.3}}$   $($this corresponds to about  $\text{–10 dB)}$,		*by the attenuation factor  $\alpha = \underline{\text{0.3}}$   $($this corresponds to about  $\text{–10 dB)}$,

@@ Line 61: / Line 61: @@
 {{ML-Kopf}}
 '''(1)'''&nbsp;  Correct is <u>solution 2</u>:
-*In the marked range of&nbsp; $20$&nbsp; milliseconds approx.&nbsp; $10$&nbsp; oscillations can be detected.
+*In the marked range of&nbsp; $20$&nbsp; milliseconds &nbsp; &rArr; &nbsp; approx.&nbsp; $10$&nbsp; oscillations can be detected.
 *From this the result&nbsp; follows approximately for the signal frequency:&nbsp; $f = {10}/(20 \,\text{ms}) =  500 \,\text{Hz}$.

← Older revision		Revision as of 14:22, 12 January 2024
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−	''Notes:''	+	<u>Notes:</u>  The exercise belongs to the chapter [[Signal_Representation/Principles_of_Communication\|»Principles of Communication«]].
−	*The exercise belongs to the chapter [[Signal_Representation/Principles_of_Communication\|»Principles of Communication«]].

@@ Line 83: / Line 83: @@
 '''(4)'''&nbsp;  The signal&nbsp; <math>v_1(t)</math>&nbsp; is identical in form to the original signal&nbsp; <math>q(t)</math>&nbsp; and differs from it only
-*by the attenuation factor&nbsp; $\alpha = \underline{\text{0.3}}$ &nbsp;   $($this corresponds to about&nbsp; $\text{–10 dB)}$
+*by the attenuation factor&nbsp; $\alpha = \underline{\text{0.3}}$ &nbsp;   $($this corresponds to about&nbsp; $\text{–10 dB)}$,
 *and the delay time&nbsp;  $\tau = \underline{10\,\text{ms}}$.
 {{ML-Fuß}}

@@ Line 61: / Line 61: @@
 ===Solution===
 {{ML-Kopf}}
-'''(1)'''&nbsp;  Correct is the <u>solution 2</u>:
+'''(1)'''&nbsp;  Correct is <u>solution 2</u>:
 *In the marked range of&nbsp; $20$&nbsp; milliseconds approx.&nbsp; $10$&nbsp; oscillations can be detected.
 *From this the result&nbsp; follows approximately for the signal frequency:&nbsp; $f = {10}/(20 \,\text{ms}) =  500 \,\text{Hz}$.
@@ Line 67: / Line 67: @@
-'''(2)'''&nbsp; Correct is the <u>solution 1</u>:
+'''(2)'''&nbsp; Correct is <u>solution 1</u>:
 *The signal&nbsp; <math>v_1(t)</math>&nbsp; is undistorted compared to the original signal <math>q(t)</math>.&nbsp; The following applies: &nbsp; $v_1(t)=\alpha \cdot q(t-\tau)$.
@@ Line 75: / Line 75: @@
 '''(3)'''&nbsp; Correct are the <u>solutions 1 and 3</u>:
 *One can recognize additive noise both in the displayed signal&nbsp; <math>v_2(t)</math>&nbsp; and in the audio signal&nbsp; &nbsp; ⇒ &nbsp; <u>solution 3</u>.
-*The signal-to-noise ratio is approx.&nbsp; $\text{30 dB}$&nbsp; $($but this cannot be seen from this representation$)$.
 *Correct is also <u>solution 1</u>: &nbsp; Without this noise component&nbsp; <math>v_2(t)</math>&nbsp; would be identical with&nbsp; <math>q(t)</math>.

@@ Line 1: / Line 1: @@
 {{quiz-Header|Buchseite=Signal_Representation/Principles_of_communication}}
-[[File:P_ID339__Sig_A_1_1.png|right|frame|Music signals, original, <br> noisy and/or distorted?]]
+[[File:P_ID339__Sig_A_1_1.png|right|frame|Music signals, <br>original, noisy and/or distorted?]]
 On the right you see a&nbsp; $\text{30 ms}$&nbsp; long section of a music signal&nbsp; <math>q(t)</math>.&nbsp; It is the piece&nbsp; &raquo;For Elise&laquo;&nbsp; by Ludwig van Beethoven.

@@ Line 2: / Line 2: @@
 [[File:P_ID339__Sig_A_1_1.png|right|frame|Music signals, original, <br> noisy and/or distorted?]]
-On the right you see a&nbsp; $\text{30 ms}$&nbsp; long section of a music signal&nbsp; <math>q(t)</math>.&nbsp; It is the piece&nbsp; "For Elise"&nbsp; by Ludwig van Beethoven.
+On the right you see a&nbsp; $\text{30 ms}$&nbsp; long section of a music signal&nbsp; <math>q(t)</math>.&nbsp; It is the piece&nbsp; &raquo;For Elise&laquo;&nbsp; by Ludwig van Beethoven.
 *Underneath are drawn two sink signals&nbsp; <math>v_1(t)</math>&nbsp; and&nbsp; <math>v_2(t)</math>, which were recorded after the transmission of the music signal&nbsp; <math>q(t)</math>&nbsp; over two different channels.
@@ Line 25: / Line 25: @@
 ''Notes:''
-*The task belongs to the chapter&nbsp;[[Signal_Representation/Principles_of_Communication|Principles of Communication]].
+*The exercise belongs to the chapter&nbsp;[[Signal_Representation/Principles_of_Communication|&raquo;Principles of Communication&laquo;]].
@@ Line 37: / Line 37: @@
 - The signal frequency is approximately&nbsp; <math>f = 250\,\text{Hz}</math>.
 + The signal frequency is approximately&nbsp; <math>f = 500\,\text{Hz}</math>.
-- The signal frequency is about&nbsp; <math>f = 1\,\text{kHz}</math>.
+- The signal frequency is approximately&nbsp; <math>f = 1\,\text{kHz}</math>.
 {Which statements are true for the signal&nbsp; <math>v_1(t)</math>&nbsp;?
@@ Line 63: / Line 63: @@
 '''(1)'''&nbsp;  Correct is the <u>solution 2</u>:
 *In the marked range of&nbsp; $20$&nbsp; milliseconds approx.&nbsp; $10$&nbsp; oscillations can be detected.
-*From this the result&nbsp; follows approximately for the signal frequency&nbsp; $f = {10}/(20 \,\text{ms}) =  500 \,\text{Hz}$.
+*From this the result&nbsp; follows approximately for the signal frequency:&nbsp; $f = {10}/(20 \,\text{ms}) =  500 \,\text{Hz}$.
@@ Line 70: / Line 70: @@
 *The signal&nbsp; <math>v_1(t)</math>&nbsp; is undistorted compared to the original signal <math>q(t)</math>.&nbsp; The following applies: &nbsp; $v_1(t)=\alpha \cdot q(t-\tau)$.
-*An attenuation&nbsp; <math>\alpha</math>&nbsp; and a delay&nbsp; <math>\tau</math>&nbsp; do not cause distortion, but the signal is then only quieter and delayed in time, compared to the original.
+*An attenuation&nbsp; <math>\alpha</math>&nbsp; and a delay time&nbsp; <math>\tau</math>&nbsp; do not cause distortion, but the signal is then only quieter and delayed in time, compared to the original.
@@ Line 76: / Line 76: @@
 '''(3)'''&nbsp; Correct are the <u>solutions 1 and 3</u>:
 *One can recognize additive noise both in the displayed signal&nbsp; <math>v_2(t)</math>&nbsp; and in the audio signal&nbsp; &nbsp; ⇒ &nbsp; <u>solution 3</u>.
-*The signal-to-noise ratio is approx.&nbsp; $\text{30 dB}$;&nbsp; but this cannot be seen from this representation.
+*The signal-to-noise ratio is approx.&nbsp; $\text{30 dB}$&nbsp; $($but this cannot be seen from this representation$)$.
-*Correct is also the <u>solution 1</u>: &nbsp; Without this noise component&nbsp; <math>v_2(t)</math>&nbsp; would be identical with&nbsp; <math>q(t)</math>.
+*Correct is also <u>solution 1</u>: &nbsp; Without this noise component&nbsp; <math>v_2(t)</math>&nbsp; would be identical with&nbsp; <math>q(t)</math>.
 '''(4)'''&nbsp;  The signal&nbsp; <math>v_1(t)</math>&nbsp; is identical in form to the original signal&nbsp; <math>q(t)</math>&nbsp; and differs from it only
 *by the attenuation factor&nbsp; $\alpha = \underline{\text{0.3}}$ &nbsp;   $($this corresponds to about&nbsp; $\text{–10 dB)}$
-*and the delay&nbsp;  $\tau = \underline{10\,\text{ms}}$.
+*and the delay time&nbsp;  $\tau = \underline{10\,\text{ms}}$.
 {{ML-Fuß}}
 __NOEDITSECTION__
 [[Category:Signal Representation: Exercises|^1.1 Principles of Communication^]]

← Older revision		Revision as of 09:47, 22 May 2021
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−	{{quiz-Header\|Buchseite=~~Signaldarstellung~~/~~Prinzip der Nachrichtenübertragung~~}}	+	{{quiz-Header\|Buchseite=Signal_Representation/Principles_of_communication}}

	[[File:P_ID339__Sig_A_1_1.png\|right\|frame\|Music signals, original, <br> noisy and/or distorted?]]		[[File:P_ID339__Sig_A_1_1.png\|right\|frame\|Music signals, original, <br> noisy and/or distorted?]]

@@ Line 41: / Line 41: @@
 {Which statements are true for the signal&nbsp; <math>v_1(t)</math>&nbsp;?
 |type="[]"}
-+  The signal&nbsp; <math>v_1(t)</math>&nbsp; is undistorted compared to <math>q(t)</math>.
++  The signal&nbsp; <math>v_1(t)</math>&nbsp; is undistorted compared to&nbsp; <math>q(t)</math>.
 -  The signal&nbsp; <math>v_1(t)</math>&nbsp; shows distortions compared to&nbsp; <math>q(t)</math>&nbsp;.
 -  The signal&nbsp; <math>v_1(t)</math>&nbsp; is noisy compared to&nbsp; <math>q(t)</math>&nbsp;.