Aufgaben:Exercise 1.1: Music Signals - Revision history

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	[[Category:Signal Representation: Exercises\|^1.1 Principles of Communication^]]		[[Category:Signal Representation: Exercises\|^1.1 Principles of Communication^]]
	[[de:Aufgaben:1.~~1_Musiksignale~~]]		[[de:Aufgaben:Aufgabe 1.1: Musiksignale]]

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	[[Category:Signal Representation: Exercises\|^1.1 Principles of Communication^]]		[[Category:Signal Representation: Exercises\|^1.1 Principles of Communication^]]
			[[de:Aufgaben:1.1_Musiksignale]]

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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  $\text{–10 dB)}$,

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	'''(1)'''  Correct is <u>solution 2</u>:		'''(1)'''  Correct is <u>solution 2</u>:
	*In the marked range of  $20$  milliseconds approx.  $10$  oscillations can be detected.		*In the marked range of  $20$  milliseconds   ⇒   approx.  $10$  oscillations can be detected.

	*From this the result  follows approximately for the signal frequency:  $f = {10}/(20 \,\text{ms}) = 500 \,\text{Hz}$.		*From this the result  follows approximately for the signal frequency:  $f = {10}/(20 \,\text{ms}) = 500 \,\text{Hz}$.

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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«]].

Guenter at 14:21, 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 form 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  $\text{–10 dB)}$,

	*and the delay time  $\tau = \underline{10\,\text{ms}}$.		*and the delay time  $\tau = \underline{10\,\text{ms}}$.
	{{ML-Fuß}}		{{ML-Fuß}}

Guenter at 14:20, 12 January 2024

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	===Solution===		===Solution===
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	'''(1)'''  Correct is ~~the~~ <u>solution 2</u>:		'''(1)'''  Correct is <u>solution 2</u>:
	*In the marked range of  $20$  milliseconds approx.  $10$  oscillations can be detected.		*In the marked range of  $20$  milliseconds approx.  $10$  oscillations can be detected.
	*From this the result  follows approximately for the signal frequency:  $f = {10}/(20 \,\text{ms}) = 500 \,\text{Hz}$.		*From this the result  follows approximately for the signal frequency:  $f = {10}/(20 \,\text{ms}) = 500 \,\text{Hz}$.
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	'''(2)'''  Correct is ~~the~~ <u>solution 1</u>:		'''(2)'''  Correct is <u>solution 1</u>:
	*The signal  <math>v_1(t)</math>  is undistorted compared to the original signal <math>q(t)</math>.  The following applies:   $v_1(t)=\alpha \cdot q(t-\tau)$.		*The signal  <math>v_1(t)</math>  is undistorted compared to the original signal <math>q(t)</math>.  The following applies:   $v_1(t)=\alpha \cdot q(t-\tau)$.

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	'''(3)'''  Correct are the <u>solutions 1 and 3</u>:		'''(3)'''  Correct are the <u>solutions 1 and 3</u>:
	*One can recognize additive noise both in the displayed signal  <math>v_2(t)</math>  and in the audio signal    ⇒   <u>solution 3</u>.		*One can recognize additive noise both in the displayed signal  <math>v_2(t)</math>  and in the audio signal    ⇒   <u>solution 3</u>.
	*The signal-to-noise ratio is approx.  $\text{30 dB}$  $($but this cannot be seen from ~~this representation~~$)$.
			*The signal-to-noise ratio is approx.  $\text{30 dB}$  $($but this cannot be seen from the mentioned data$)$.

	*Correct is also <u>solution 1</u>:   Without this noise component  <math>v_2(t)</math>  would be identical with  <math>q(t)</math>.		*Correct is also <u>solution 1</u>:   Without this noise component  <math>v_2(t)</math>  would be identical with  <math>q(t)</math>.

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	{{quiz-Header\|Buchseite=Signal_Representation/Principles_of_communication}}		{{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  $\text{30 ms}$  long section of a music signal  <math>q(t)</math>.  It is the piece  »For Elise«  by Ludwig van Beethoven.		On the right you see a  $\text{30 ms}$  long section of a music signal  <math>q(t)</math>.  It is the piece  »For Elise«  by Ludwig van Beethoven.

Guenter at 15:42, 9 January 2024

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Guenter at 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?]]

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	[[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?]]
	On the right you see a  $\text{30 ms}$  long section of a music signal  <math>q(t)</math>.  It is the piece  "For Elise"  by Ludwig van Beethoven.		On the right you see a  $\text{30 ms}$  long section of a music signal  <math>q(t)</math>.  It is the piece  »For Elise«  by Ludwig van Beethoven.

	*Underneath are drawn two sink signals  <math>v_1(t)</math>  and  <math>v_2(t)</math>, which were recorded after the transmission of the music signal  <math>q(t)</math>  over two different channels.		*Underneath are drawn two sink signals  <math>v_1(t)</math>  and  <math>v_2(t)</math>, which were recorded after the transmission of the music signal  <math>q(t)</math>  over two different channels.
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	''Notes:''		''Notes:''
	*The ~~task~~ 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«]].


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	- The signal frequency is approximately  <math>f = 250\,\text{Hz}</math>.		- The signal frequency is approximately  <math>f = 250\,\text{Hz}</math>.
	+ The signal frequency is approximately  <math>f = 500\,\text{Hz}</math>.		+ The signal frequency is approximately  <math>f = 500\,\text{Hz}</math>.
	- The signal frequency is ~~about~~  <math>f = 1\,\text{kHz}</math>.		- The signal frequency is approximately  <math>f = 1\,\text{kHz}</math>.

	{Which statements are true for the signal  <math>v_1(t)</math> ?		{Which statements are true for the signal  <math>v_1(t)</math> ?
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	'''(1)'''  Correct is the <u>solution 2</u>:		'''(1)'''  Correct is the <u>solution 2</u>:
	*In the marked range of  $20$  milliseconds approx.  $10$  oscillations can be detected.		*In the marked range of  $20$  milliseconds approx.  $10$  oscillations can be detected.
	*From this the result  follows approximately for the signal frequency  $f = {10}/(20 \,\text{ms}) = 500 \,\text{Hz}$.		*From this the result  follows approximately for the signal frequency:  $f = {10}/(20 \,\text{ms}) = 500 \,\text{Hz}$.


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	*The signal  <math>v_1(t)</math>  is undistorted compared to the original signal <math>q(t)</math>.  The following applies:   $v_1(t)=\alpha \cdot q(t-\tau)$.		*The signal  <math>v_1(t)</math>  is undistorted compared to the original signal <math>q(t)</math>.  The following applies:   $v_1(t)=\alpha \cdot q(t-\tau)$.

	*An attenuation  <math>\alpha</math>  and a delay  <math>\tau</math>  do not cause distortion, but the signal is then only quieter and delayed in time, compared to the original.		*An attenuation  <math>\alpha</math>  and a delay time  <math>\tau</math>  do not cause distortion, but the signal is then only quieter and delayed in time, compared to the original.


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	'''(3)'''  Correct are the <u>solutions 1 and 3</u>:		'''(3)'''  Correct are the <u>solutions 1 and 3</u>:
	*One can recognize additive noise both in the displayed signal  <math>v_2(t)</math>  and in the audio signal    ⇒   <u>solution 3</u>.		*One can recognize additive noise both in the displayed signal  <math>v_2(t)</math>  and in the audio signal    ⇒   <u>solution 3</u>.
	*The signal-to-noise ratio is approx.  $\text{30 dB}$;  but this cannot be seen from this representation.		*The signal-to-noise ratio is approx.  $\text{30 dB}$  $($but this cannot be seen from this representation$)$.
	*Correct is also ~~the~~ <u>solution 1</u>:   Without this noise component  <math>v_2(t)</math>  would be identical with  <math>q(t)</math>.		*Correct is also <u>solution 1</u>:   Without this noise component  <math>v_2(t)</math>  would be identical with  <math>q(t)</math>.


	'''(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 form 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  $\text{–10 dB)}$
	*and the delay  $\tau = \underline{10\,\text{ms}}$.		*and the delay time  $\tau = \underline{10\,\text{ms}}$.
	{{ML-Fuß}}		{{ML-Fuß}}

	__NOEDITSECTION__		__NOEDITSECTION__
	[[Category:Signal Representation: Exercises\|^1.1 Principles of Communication^]]		[[Category:Signal Representation: Exercises\|^1.1 Principles of Communication^]]