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OT3OS1

OT3OS1. 19.10.2010. Z transformacija 1. Veza z transformacije X ( z ) i Furijeove transformacije X ( e j  ). Z transformacija 2. Z transformacija 3. MATLAB. Funkcija roots nule =roots(b); polovi=roots(a); Funkcija zplane figure,zplane(nule,polovi) figure,zplane(b,a).

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OT3OS1

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  1. OT3OS1 19.10.2010.

  2. Z transformacija1 Veza z transformacije X(z) i Furijeove transformacije X(ej)

  3. Z transformacija2

  4. Z transformacija3

  5. MATLAB • Funkcija roots nule=roots(b); polovi=roots(a); • Funkcija zplane figure,zplane(nule,polovi) figure,zplane(b,a) nule i polovi – vektori kolone b i a – vektori vrste

  6. Zadatak 1 Nacrtati impulsni i frekvencijki odziv za moving average filtar dužine 4.

  7. Zadatak 1 – rešenje

  8. Zadatak 1 – grafici

  9. Primer 1

  10. Primer 1 - MATLAB !!! impz “vraća” kolonu!!!

  11. Primer 1 - MATLAB

  12. Zadatak 1 Dat je impulsni odziv sistema: Odrediti diferencnu jednačinu sistema.

  13. Zadatak 1 - rešenje Linearnost Kašnjenje

  14. Zadatak 1 - MATLAB

  15. Zadatak 1 - MATLAB close all, clear; b=[0 0 0 0.064]; a=[1 -0.4]; figure,zplane(b,a); [H,w]=freqz(b,a); figure,plot(w/pi,abs(H)); zx=-1.2:0.001:1.2; zy=-1.2:0.002:1.2; [zxm,zym]=meshgrid(zx,zy); z=zxm+1i*zym; Hz=0.064*z.^(-3)./(1-0.4*z.^(-1)); figure,mesh(zxm,zym,20*log10(abs(Hz))),xlabel('x'),ylabel('y'), xlim([-1.2 1.2]),ylim([-1.2 1.2]); figure,mesh(zxm,zym,20*log10(abs(Hz))),xlabel('x'),ylabel('y'), xlim([-1.2 1.2]),ylim([-1.2 1.2]),view([0 90]);

  16. Zadatak 1 - MATLAB

  17. Zadatak 1 - MATLAB

  18. Zadatak 1 - MATLAB

  19. Zadatak 1 - MATLAB

  20. Zadatak 2 Dat je sistem opisan diferencnom jednačinom: Odrediti impulsni odziv sistema.

  21. Zadatak 2 - rešenje

  22. Zadatak 2 - MATLAB N=50; n=[0:N-1]; x=zeros(N,1); x(1)=1; hML(1)=x(1); for brojac=2:N hML(brojac)=x(brojac)-0.5*x(brojac-1)+0.8*hML(brojac-1); end; h=0.375*0.8.^n; h(1)=h(1)+0.625; stem(n,[hML;h]'),xlabel('n'),ylabel('h(n)'), legend('h_{ML}','h');

  23. Zadatak 2 - MATLAB close all, clear; b=[1 -0.5]; a=[1 -0.8]; figure,zplane(b,a); [H,w]=freqz(b,a); figure,plot(w/pi,abs(H)); zx=-1.2:0.001:1.2; zy=-1.2:0.002:1.2; [zxm,zym]=meshgrid(zx,zy); z=zxm+1i*zym; Hz=(1-0.5*z.^(-1))./(1-0.8*z.^(-1)); figure,mesh(zxm,zym,20*log10(abs(Hz))),xlabel('x'),ylabel('y'), xlim([-1.2 1.2]),ylim([-1.2 1.2]); figure,mesh(zxm,zym,20*log10(abs(Hz))),xlabel('x'),ylabel('y'), xlim([-1.2 1.2]),ylim([-1.2 1.2]),view([0 90]);

  24. Zadatak 2 - MATLAB

  25. Zadatak 2 - MATLAB

  26. Zadatak 2 - MATLAB

  27. Zadatak 2 - MATLAB

  28. Zadatak 2 - MATLAB

  29. Zadatak 2 - MATLAB

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