soal pengolahan sinyal


SOAL

Dua buah sinyal x(n) = 0 0 2 4 1 3 0 0 dan y(n) = 0 1 2 2 3 1 2 5

Tentukanlah deret relaksasi silang rxy (l).

Penyelesaian:

Untuk harga l yang positif

rxy (o) =  maka rxy(0) =

n
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x(n)

0
0
0
0
2
4
1
3
0
0
0



y(n)

0
0
0
1
2
2
3
1
2
5
0
0


x(n).y(n)
0
0
0
0
0
4
8
3
3
0
0





rxy(0) = 0+4+8+3+3+0 = 18



rxy (1) =  

n
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x(n)



0
0
2
4
1
3
0
0
0



x(n-1)

0
0
0
0
0
2
4
1
3
0
0
0


y(n)

0
0
0
1
2
2
3
1
2
5
0
0


x(n-1).y(n)




0
0
4
12
1
6
0





rxy(1) = 0+0+4+12+1+6+0 = 23



rxy (1) =

n
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x(n)



0
0
2
4
1
3
0
0
0



x(n-1)

0
0
0
0
0
0
2
4
1
3
0
0


y(n)

0
0
0
1
2
2
3
1
2
5
0
0


x(n-1).y(n)




0
0
0
6
4
2
15
0
0



rxy(2) = 0+6+4+2+15+0 = 27

rxy (1) =  

n
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x(n)



0
0
2
4
1
3
0
0
0



x(n-1)

0
0
0
0
0
0
0
2
4
1
3
0
0

Y(n)

0
0
0
1
2
2
3
1
2
5
0
0


x(n-1).y(n)




0
0
0
0
2
8
5
0
0



rxy(3) = 0+2+8+5+0 = 15



rxy (1) =  

n
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x(n)



0
0
2
4
1
3
0
0
0



x(n-1)

0
0
0
0
0
0
0
0
2
4
1
3
0
0
y(n)

0
0
0
1
2
2
3
1
2
5
0
0


x(n-1).y(n)




0
0
0
0
0
4
20
0
0



rxy(4) = 0+4+20+0 = 24



rxy (l) =

n
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
x(n)



0
0
2
4
1
3
0
0
0




x(n-1)

0
0
0
0
0
0
0
0
0
2
4
1
3
0
0
y(n)

0
0
0
1
2
2
3
1
2
5
0
0
0


x(n-1).y(n)




0
0
0
0
0
0
10
0
0
0



rxy(5) = 0+10+0 = 10



rxy (l) =

n
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
x(n)



0
0
2
4
1
3
0
0
0




x(n-1)

0
0
0
0
0
0
0
0
0
0
2
4
1
3
0
y(n)

0
0
0
1
2
2
3
1
2
5
0
0
0


x(n-1).y(n)




0
0
0
0
0
0
0
0
0
0



rxy(6) = 0+0+0 = 0







Untuk harga l yang negatif

rxy (l) =

n
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
x(n)



0
0
2
4
1
3
0
0
0




x(n-1)

0
0
0
2
4
1
3
0
0






y(n)

0
0
0
1
2
2
3
1
2
5
0
0



x(n-1).y(n)



0
2
8
2
9
0








rxy(-1) = 0+2+8+2+9+0 = 21





rxy (l) =

n
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
x(n)



0
0
2
4
1
3
0
0
0




x(n-1)

0
0
2
4
1
3
0
0
0






y(n)

0
0
0
1
2
2
3
1
2
5
0
0



x(n-1).y(n)



0
4
2
6
0
0








rxy(-2) = 0+4+2+6+0 = 12



rxy (l) =

n
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
x(n)



0
0
2
4
1
3
0
0
0




x(n-1)
0
0
2
4
1
3
0
0
0
0






y(n)

0
0
0
1
2
2
3
1
2
5
0
0



x(n-1).y(n)



0
1
6
0
0
0








rxy(-3) = 0+1+6+0 = 7



rxy (l) =

n
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
x(n)



0
0
2
4
1
3
0
0
0




x(n-1)
0
2
4
1
3
0
0
0
0
0






Y(n)

0
0
0
1
2
2
3
1
2
5
0
0



x(n-1).y(n)



0
3
0
0
0
0








rxy(-4) = 0+3+0 = 3



rxy (l) =

N
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
x(n)



0
0
2
4
1
3
0
0
0




x(n-1)
2
4
1
3
0
0
0
0
0
0






Y(n)

0
0
0
1
2
2
3
1
2
5
0
0



x(n-1).y(n)



0
0
0
0
0
0








rxy(-5) = 0+0+0 = 0



rxy (l) = 0 0 3 7 12 21 18 23 27 15 24 10 0




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