Teori Konvolusi Diskrit( ) = ( ) . ( )( ) =( ) =

Misalkan : = + = 0… + − 2Maka :

( ) =( ) =

Dimana :

=Soal

Diketahui :

a = 1, 2, 3, 1, 2

N = 5

B = 1, 3, 5, 7

M = 4

Ditanya :

Cp ?

Jawab :

Perhitungan Analitik( ) = 1 + 2 + 3 + + 2( ) = 1 + 3 + 5 + 7( ) = ( ). ( )( ) = (1 + 2 + 3 + + 2 )(1 + 3 + 5 + 7 )( ) = 1 + 3 + 5 + 7 + 2 + 6 + 10 + 14 + 3 + 9 + 15 + 21 ++ 3 + 5 + 7 + 2 + 6 + 10 + 14( ) = 1 + (3 + 2) + (5 + 6 + 3) + (7 + 10 + 9 + 1) + (14 + 15 + 3 + 2)+ (21 + 5 + 6) + (7 + 10) + 14( ) = 1 + 5 + 14 + 27 + 34 + 32 + 17 + 14Jadi :

== = = 1= = + = 5= = + + = 14= = + + + = 27= = + + + + = 34= = + + + + + = 32= = + + + + + + = 17

= = + + + + + + + = 14 Pemrograman dengan Matlab

1. Metode Iterasi

1. clear all;2. a=input('Masukkan matriks a: ');3. b=input('Masukkan matriks b: ');4. M=length(a);5. N=length(b);6. A=[a,zeros(1,N)];7. B=[b,zeros(1,M)];8. for i=1:N+M-19. C(i)=0;10. for j=1:M11. if(i-j+1>0)12. C(i)=C(i)+A(j)*B(i-j+1);13. else14. end;15. end;16. end;17. disp('C[p] = ');18. disp(C);19. stem(C);20. ylabel('C[p]');21. xlabel('p');22. title('Konvolusi dari Dua Sinyal');

Gambar 1. Tampilan Matlab Editor Konvolusi Diskrit

Gambar 2. Tampilan Matlab Command Window Konvolusi Diskrit

Gambar 3. Plot Konvolusi Diskrit Dua Sinyal

2. Cara Cepat

1. clear all;2. a=input('Masukkan matriks a: ');3. b=input('Masukkan matriks b: ');4. C=conv(a,b);5. disp('Cp =');6. disp(C);

Gambar 4. Tampilan Matlab Editor Cara Cepat Konvolusi Diskrit

Gambar 5. Tampilan Command Window Cara Cepat Konvolusi Diskrit