Ðàñ÷åò öèôðîâîãî êîððåêòîðà
Ðàñ÷åò öèôðîâîãî êîððåêòîðà
Êîíòðîëüíàÿ ðàáîòà
ñòóäåíòîâ-çàî÷íèêîâ ïî äèñöèïëèíå
«Öèôðîâàÿ îáðàáîòêà ñèãíàëîâ»
Ðàñ÷åò öèôðîâîãî
êîððåêòîðà
Çàäàí êàíàë ïåðåäà÷è äèñêðåòíûõ ñîîáùåíèé. Ìåæñèãíàëüíàÿ
èíòåðôåðåíöèÿ
ñèãíàëîâ â êàíàëå îïðåäåëÿåòñÿ èìïóëüñíîé õàðàêòåðèñòèêîé, îòñ÷åòû êîòîðîé
ðàâíû:
g0g(0)=(-1)*(m+1)/20
g1 g(t)=1
g2g(2T)=(-1)*(n+1)/20
ãäå m-ïðåäïîñëåäíÿÿ
öèôðà ¹ çà÷åòíîé êíèæêè
n-ïîñëåäíÿÿ
öèôðà ¹çà÷åòíîé êíèæêè
1.Èñïîëüçóÿ
âûðàæåíèå äèñêðåòíîé ñâåðòêè, ðàññ÷èòàòü ñèãíàë íà âûõîäå êàíàëà â îòñ÷åòíûå
ìîìåíòû 0,1,2,3 äëÿ ïîñëåäîâàòåëüíîñòè âõîäíûõ ñèãíàëîâ u(0),u(T)
a)
u(0)=U, u(T)=0
Ãäå U=n+1
b)
u(0)=U, u(T)=U
 äðóãèå îòñ÷åòíûå
ìîìåíòû u(2T)=u(3T)=0
2.Ðàññ÷èòàòü
êîýôôèöèåíòû öèôðîâîãî êîððåêòîðà C,C,C,îáåñïå÷èâàþùèå âûõîäíîé ñèãíàë “010” ïðè
ïîäà÷å íà
âõîä êàíàëà ñèãíàëà
“100”.
3.Ðàññ÷èòàòü
ñèãíàëû íà âûõîäå êîððåêòîðà ïðè âõîäíûõ ñèãíàëàõ (a),(b).Ïðîàíàëèçèðîâàòü
ýôôåêòèâíîñòü ðàáîòû êîððåêòîðà.
Ïðèìåð
âûïîëíåíèÿ äëÿ m=3,n=10
Îòñ÷åòû èìïóëüñíîé
õàðàêòåðèñòèêè ðàâíû
g0=0.2; g1=1; g2= -0.5; U=11
Çàäàíèå 1
Ïóñòü u1(kT)-ñèãàë
íà âûõîäå êàíàëà ñâÿçè (âõîäå êîððåêòîðà)
 ñîîòâåòñòâèè ñ
âûðàæåíèåì äèñêðåòíîé ñâåðòêè îí ðàâåí
u1(kT)= k=0,1,2,3
Ó÷èòûâàÿ,÷òî u(jT)=0 äëÿ j1 è g(mT)=0 äëÿ m2, ïîëó÷àåì
k=0 u1(0)=u(0)*g(0)=u(0)*g0
k=1 u1(T)=u(0)*g(T)+u(T)*g(0)=u(0)*g1+u(T)*g0
k=2 u1(2T)=u(0)*g(2T)+u(T)*g(T)=u(0)*g2+u(T)*g1
k=3 u1(3T)=u(T)*g(2T)=u(T)*g2
Äëÿ âàðèàíòà (à) u(0)=11,u(T)=0
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u1(0)=11*0.2=2.2
u1(T)=11*1+0*0.2=11
u1(2T)=11*(-0.55)+0*1=-6.05
u1(3T)0*(-0.55)=0
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U1=
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Äëÿ âàðèàíòà (á) u(0)=11,u(T)=11
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u1(0)=11*0.2=2.2
u1(T)=11*1+11*0.2=13.2
u1(2T)=11*(-0.55)+11*1=4.95
u1(3T)=11*(-0.55)=-6.05
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U1=
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Çàäàíèå
2(ïîÿñíåíèå)
0 T 2T
g g1
2T
0 T
g2
C
Ñ
Ñ
ñèñòåìà èç 3-õ
óðàâíåíèé Ìàòðèöà êîýô- Âåêòîð Âåêòîð
ñ 3-ìÿ íåèçâåñòíûìè ôèöèåíòîâ
íåèçâåñòíîãî ïðàâ.
êîýôôèöèåíòà ÷àñòåé
êîððåêòîðà
G= C= H=
Â
âåêòîðíî-ìàòðè÷íîé ôîðìå G*C=H
*=
Óìíîæàåì
ñëåâà íà îáðàòíóþ ìàòðèöó G
G*G*C= G*H,îòêóäà Ñ= G*H,ãäå
Óìíîæàåì ñëåâà íà
îáðàòíóþ ìàòðèöó G
G*G*C= G*H, îòêóäà Ñ= G*H,ãäå
(G*G)-åäèíè÷íàÿ ìàòðèöà
Ðåøåíèå ñ ïîìîùüþ ñèñòåìû Mathcad
Ââåäèòå
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Çàäàéòå ìàòðèöó G:=
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Âåêòîð H:=
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Âû÷èñëèòå C:=G*H
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Ðàññ÷èòàéòå
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Ðåøåíèå
ñèñòåìû óðàâíåíèé ïî ôîðìóëå Êðàìåðà
Ñ=D/D C=D/D C=D/D
ãäå D-
îïðåäåëèòåëü ìàòðèöû G
D== =g1-g2*g0*g1-g1*g2*g0=
=1-2*g0*g2=1-2*0.2*(-0.55)=1.22
D=1.22
D-îïðåäåëèòåëü ìàòðèöû G,ãäå
1-é ñòîëáåö çàìåíåí íà âåêòîð H
D==0-g1*1*g0=-g0=-0.2
D-îïðåäåëüòåëü ìàòðèöû G ,ãäå
2-é ñòîëáåö çàìåíåí íà H
D==g1-0=1
D-îïðåäåëèòåëü ìàòðèöû G,ãäå
3-é ñòîëáåö çàìåíåí íà H
D==0-g2*1*g1=0.55
Òàêèì îáðàçîì,
êîýôôèöèåíòû Âåêòîð êîýôôèöèåíòîâ
êîððåêòîðà
ðàâíû
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Ñ= D/D=
-0.2/1.22= -0.164
C= D/D=1/1.22=0.82
C= D/D=0.55/1.22=0.451
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Ñ=
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Çàäàíèå 3
Ïðîõîæäåíèå ñèãíàëà
U1(kT) ÷åðåç êîððåêòîð èëëþñòðèðóåòñÿ
ñõåìîé:
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U1(kT
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V(0)=U1(0)*C
V(T)=U1(T)*C+U1(0)*C
V(2T)=U1(2T)*C+U1(T)*C+U1(0)*C
V(2T)=U1(3T)*C+U1(2T)*C+U1(T)*C
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C
Ñ
Ñ
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V(kT)
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V(0)=2.2*(-0.164)=-0.361
V(T)=11*(-0.164)+2.2*0.82=0
V(2T)=(-0.6.05)*
(-0.164)=11*0.82+2.2*0.451=11.004
V(3T)=0*(-0.164)+
(-6.05)*0.82+11*0.451
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Âåêòîð âûõîäíîãî
ñèãíàëà
(à) Îæèäàåìûé
(á) Îæèäàåìûé
ñèãíàë
ñèãíàë
V= V=
Ìàêñèìàëüíûé
ìîäóëü ðàçíîñòè ìåæäó îæèäàåìûì è ïîëó÷åííûì âûõîäíûì ñèãíàëîì
(à)
(á)
V=0,361
V=0.361
V0 V0
Íà âûõîäå
êîððåêòîðà:
(à) îæèäàåìûé
(á) îæèäàåìûé
ñèãíàë ñèãíàë
U1= U1=
U1=6.05 U1=6.05
U1=0 U1=6.05
Ñîïîñòàâëåíèå
ìàêñèìàëüíûõ ïîãðåøíîñòåé äî êîððåêöèè è ïîñëå êîððåêöèè:
(à)
(á)
U1 V1 U1 V1
U1= V1 U1 V1
ñâèäåòåëüñòâóåò îá
ýôôåêòèâíîé ðàáîòå êîððåêòîðà.
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