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Prüfung: &=
nbsp; &nbs=
p; Informationstechnik
MT 7D51
Termin:  =
; &n=
bsp; Mon=
tag,
13. Februar 2006
11:00 – 13:00
Prüfer: &=
nbsp; &nbs=
p; Prof.
J. Walter
Hilfsmittel: &=
nbsp; &nbs=
p; beliebig
/ kein Internet / kein WLAN
=
Name: &=
nbsp; &nbs=
p; _________________________
Vorname: &=
nbsp; ______________=
___________
Projekt: &=
nbsp; _________________________
<=
span
style=3D'mso-bidi-font-family:Arial'>bitte keine rote Farbe verwenden<=
/o:p>
<=
span
style=3D'mso-bidi-font-family:Arial'>
<=
span
style=3D'mso-bidi-font-family:Arial'>(nicht ausfüllen) !
Aufgabe
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mögl.
Punkte
|
erreichte
Punkte
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1
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12
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2
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12
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3
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15
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4
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11
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Gesamt
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50
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Note
|
|
Bearbeiten
Sie die Aufgaben nur, falls Sie keine gesundheitlichen Beschwerden haben. <=
o:p>
Viel
Erfolg
Bemerkung:
Sie können die Vorder- und Rückseite benutzten. Es werden =
nur
die auf den Prüfungsblättern vorhandenen oder fest mit den
Prüfungsblättern verbundenen Ergebnisse gewertet.
1. Gauß'sches Prinzip der kleinsten
Fehlerquadrate (12 Punkte)
Die Funktion: =
soll =
im
Bereich =
optimal dur=
ch ein
Polynom =
angenä=
hert
werden.
a) 8P Bestimmen
Sie die Gleichung des Polynoms.
b) 2P Skizzieren
Sie das Ergebnis.
c) 2P An=
welche-r/n
Stelle/n tritt die größte Abweichung auf? =
<=
/span>
<=
/span>
Lösung:
2. DFT&nbs=
p;
(12 Punkte)
=
Eine =
Cosinusfunktion
(Amplitudenwerte +1, -1) mit der Frequenz 100 Hz und dem Offset 0,5 wird mit
der Blockgröße N=3D14 abgetastet. Die Messzeit ist 20ms. =
o:p>
=
a)
1P Trage=
n Sie
die Zeitwerte für die Abtastpunkte in die nachfolgende Tabelle ein.
b)
1P Skizz=
ieren
Sie die Funktion und die Abtastwerte in Bild 1.
c)
8P Berec=
hnen
Sie aus den Abtastwerten die skalierte DFT für m=3D0, m=3D1, m=3D2, m=
=3D3, m=3D4,
d)
1P Zeich=
nen
Sie das Amplitudenspektrum
e)
1P Erkl&=
auml;ren
Sie das Ergebnis für m=3D0
<=
o:p>
<=
span
style=3D'mso-spacerun:yes'> =
Bild 1: Cosinus mit den Abtastpunkten inkl. =
Offset
n=3D=
|
t/ms
|
cos(x)
|
0=
|
=
span>
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span>
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1=
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span>
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span>
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2=
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span>
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span>
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3=
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span>
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span>
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4=
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span>
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span>
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5=
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span>
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span>
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6=
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=
span>
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span>
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7=
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span>
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=
span>
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8
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=
span>
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=
span>
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9
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=
span>
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span>
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10
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span>
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span>
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11
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span>
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span>
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12
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span>
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span>
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13
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span>
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span>
|
&=
nbsp;
&n=
bsp;
&n=
bsp;
&n=
bsp;
3. DGL - Übertragungsfunktion - Systemantw=
ort
(15 Punkte)
Gegeben
ist das R,L,C-Glied:
Schaltung mit R, L und C
a) (3P)
Erstellen Sie die Übertragungsfunktion G1(s)
– Darstellung: Die höchste Potenz im Nenner hat den Faktor 1.
b) (1P)
Erstellen Sie die Übertragungsfunktion G2 (s) für die
Werte =
c)&n=
bsp;
(10P) Bestimmen Sie die Antwort y=
(t)
des Systems G2 (s) <=
/span>auf: =
Hinweis: Schreiben Sie den Ansatz für Maple auf. Als Ergebnis genü=
;gt
die Skizze. Das Ergebnis ist etwas umfangreicher.
d) (2P)
Skizzieren Sie Antwort für t=3D0 bis t=3D2. =
L&o=
uml;sung
Aufgabe 3a
<=
/span>
4 FIR-Filter (11 Punkte)
E=
in Tiefpass
mit der Grenzfrequenz fgunten=3D100Hz ist als FIR-Filter für N=3D8 zu
entwerfen. Die Abtastfrequenz beträgt fa=3D5 kHz.
<=
o:p>
a) Berechnen
Sie die Filtergleichung für das FIR-Filter
=
b) Berechnen
und skizzieren Sie die Antwort y1[n] auf einen Impuls x[n] der Breite 11 des
FIR-Filters.
c) Ein zweiter TP mit den gleichen Daten =
folgt
dem ersten TP. Berechnen und skizzieren Sie die Antwort y2[n], wenn der Aus=
gang
von TP1 wird auf den Eingang von TP2 geschaltet ist.
Lösung:<=
/b>
<=
o:p>
<=
o:p>
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