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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