Difference between revisions of "Aufgaben:Exercise 1.1: Music Signals"

Revision as of 09:21, 8 April 2021

Music signals, original,
noisy and/or distorted?

On the right you see a $\text{30 ms}$ long section of a music signal $q(t)$. It is the piece "For Elise" by Ludwig van Beethoven.

Underneath are drawn two sink signals $v_1(t)$ and $v_2(t)$, which were recorded after the transmission of the music signal $q(t)$ over two different channels.

The following operating elements allow you to listen to the first fourteen seconds of each of the three audio signals $q(t)$, $v_1(t)$ and $v_2(t)$.

Original signal $q(t)$:

Sink signal $v_1(t)$:

Sink signal $v_2(t)$:

Notes:

The task belongs to the chapter Principles of Communication.

Questions

	The signal frequency is approximately $f = 250\,\text{Hz}$.
	The signal frequency is approximately $f = 500\,\text{Hz}$.
	The signal frequency is about $f = 1\,\text{kHz}$.

	The signal $v_1(t)$ is undistorted compared to $q(t)$.
	The signal $v_1(t)$ shows distortions compared to $q(t)$ .
	The signal $v_1(t)$ is noisy compared to $q(t)$ .

	The signal $v_2(t)$ is undistorted compared to $q(t)$ .
	The signal $v_2(t)$ shows distortions compared to $q(t)$ .
	The signal $v_2(t)$ is noisy compared to $q(t)$ .

$ \alpha \ = \ $

$ \tau \ = \ $

$\ \text{ms}$

Solution

(1) Correct is the solution 2:

In the marked range of $20$ milliseconds approx. $10$ oscillations can be detected.
From this the result follows approximately for the signal frequency; $f = {10}/(20 \,\text{ms}) = 500 \,\text{Hz}$.

(2) Correct is the solution 1:

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

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

(3) Correct are the solutions 1 and 3:

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

(4) The signal $v_1(t)$ is identical in form to the original signal $q(t)$ and differs from it only

by the attenuation factor $\alpha = \underline{\text{0.3}}$ (dies entspricht etwa $\text{–10 dB)}$
and the delay $\tau = \underline{10\,\text{ms}}$.

@@ 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 ca.&nbsp; $\text{30 ms}$&nbsp; long section of a music signal&nbsp; <math>q(t)</math>. It is the piece &bdquo;For Elise&rdquo; 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; "For Elise"&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.
-*The following controls allow you to listen to the first fourteen seconds of each of the three audio signals&nbsp; <math>q(t)</math>,&nbsp; <math>v_1(t)</math>&nbsp; and&nbsp; <math>v_2(t)</math>.
+*The following operating elements allow you to listen to the first fourteen seconds of each of the three audio signals&nbsp; <math>q(t)</math>,&nbsp; <math>v_1(t)</math>&nbsp; and&nbsp; <math>v_2(t)</math>.
-Original signal&nbsp; <math>q(t)</math>
+Original signal&nbsp; <math>q(t)</math>:
 <lntmedia>file:A_ID9__Sig_A1_1Elise10sek22kb.mp3</lntmedia>
-Sink signal&nbsp; <math>v_1(t)</math>
+Sink signal&nbsp; <math>v_1(t)</math>:
 <lntmedia>file:A_ID10__Sig_A1_1Elise10sek30Prozent22kb.mp3</lntmedia>
-Sink signal&nbsp; <math>v_2(t)</math>
+Sink signal&nbsp; <math>v_2(t)</math>:
 <lntmedia>file:A_ID12__Sig_A1_1elise10sek30dB22kb.mp3</lntmedia>

	The signal frequency is approximately \(f = 250\,\text{Hz}\).
	The signal frequency is approximately \(f = 500\,\text{Hz}\).
	The signal frequency is about \(f = 1\,\text{kHz}\).

	The signal \(v_1(t)\) is undistorted compared to \(q(t)\).
	The signal \(v_1(t)\) shows distortions compared to \(q(t)\) .
	The signal \(v_1(t)\) is noisy compared to \(q(t)\) .

	The signal \(v_2(t)\) is undistorted compared to \(q(t)\) .
	The signal \(v_2(t)\) shows distortions compared to \(q(t)\) .
	The signal \(v_2(t)\) is noisy compared to \(q(t)\) .