Contoh Soal decimation –in- frequency FFT
description
Transcript of Contoh Soal decimation –in- frequency FFT
)245(245)3(
2)2(
245245)1(
36)0(
jY
jY
jY
Y
Contoh Soal decimation –in- frequency FFTBila diketahui 8-point DFT dari output suatu sistem adalah :
245245)7(
2)6(
245245)5(
0)4(
jY
jY
jY
Y
Tentukan output y(n) dari sistem tersebut menggunakan decimation-in-frequency algoritm
Nj
N eWFFTN
IFFT21
Jawab :
Algoritma dari IFFT hampir sama dengan algoritma dari FFT, hanya definisi WN –nya berbeda
Y(0)
Y(1)
Y(2)
Y(3)
Y(4)
Y(5)
Y(6)
Y(7)
F0
F1
F2
F3
F4
F5
F6
F7
18
08
W)5(Y)1(Y5F
)5(Y)1(Y1F
W)4(Y)0(Y4F
)4(Y)0(Y0F
38
28
W)7(Y)3(Y7F
)7(Y)3(Y3F
W)6(Y)2(Y6F
)6(Y)2(Y2F
j16)88(j)88(22
1j2
2
128j28
22
1j2
2
1245j245245(j245W)7(Y)3(Y7F
j1010245j245)245(j245)7(Y)3(Y3F
4jj2j2W)6(Y)2(Y6F
0j2j2)6(Y)2(Y2F
j16)88(j)88(22
1j2
2
128j28
22
1j2
2
1245j245245j245W)5(Y)1(Y5F
)10(j10245j245245j245)5(Y)1(Y1F
36)1(036W)4(Y)0(Y4F
36036)4(Y)0(Y0F
245j245)7(Yj2)6(Y245j245)5(Y0)4(Y
)245(j245)3(Yj2)2(Y245j245)1(Y36)0(Y
38
28
18
08
F0
F1
F2
F3
F4
F5
F6
F7
G0
G1
G2
G3
G4
G5
G6
G7
2
8
08
W)3(F)1(F3G
)3(F)1(F1G
W)2(F)0(F2G
)2(F)0(F0G
2
8
08
W)7(F)5(F7G
)7(F)5(F5G
W)6(F)4(F6G
)6(F)4(F4G
32)j(j16j16W)7(F)5(F7G
0j16j16)7(F)5(F5G
32)1(436W)6(F)4(F6G
40436)6(F)4(F4G
20jj1010)10(j10W)3(F)1(F3G
20j1010)10(j10)3(F)1(F1G
36)1(036W)2(F)0(F2G
36036)2(F)0(F0G
j167Fj10103F46F02F
j165F)10(j101F364F360F
28
08
28
08
G0
G1
G2
G3
G4
G5
G6
G7
0
8
08
28
08
W)7(G)6(G7H
)7(G)6(G6H
W)5(G)4(G5H
)5(G)4(G4H
W)3(G)2(G3H
)3(G)2(G2H
W)1(G)0(G1H
)1(G)0(G0H
H0
H1
H2
H3
H4
H5
H6
H7
]02578752[)n(y
032328
1W)7(G)6(G
8
1)7(y
832328
1)7(G)6(G
8
1)3(y
50408
1W)5(G)4(G
8
1)5(y
50408
1)5(G)4(G
8
1)1(y
220368
1W)3(G)2(G
8
1)6(y
720368
1)3(G)2(G
8
1)2(y
720368
1W)1(G)0(G
8
1)4(y
220368
1)1(G)0(G
8
1)0(y
327G05G326G404G203G201G362G360G
28
08
08
08