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Unformatted text preview: angle(p(3))*k+phi3)... +2*r5*(abs(p(5)).ˆk).*cos(angle(p(5))*k+phi5)+r7*abs(p(7)).ˆk % this form for the impulse response is obtained by examining first the % poles (first six poles are complex conjugate and the seventh one is real) % figure (5) plot(k,h,’*’); grid; xlabel(’Discrete time’); ylabel(’Impulse response’) print -deps figure5_5.eps % (c) Step response (F(z)=z/(z-1)) numstep=conv(num,[1 0]); denstep=conv(den,[1 -1]); numstep_z=conv(num_z,[1 0]); [Rs,ps,ress]=residue(numstep,denstep); ps ps1=abs(ps(1)) ps4=abs(ps(4)) ps6=abs(ps(6)) angleps1=angle(ps(1)) angleps4=angle(ps(4)) angleps6=angle(ps(6)) Rs rs1=abs(Rs(1)) r3=abs(Rs(3)) rs4=abs(Rs(4)) rs6=abs(Rs(6)) rs8=abs(Rs(8)) phis1=angle(Rs(1)) phis4=angle(Rs(4)) phis6=angle(Rs(6)) ystep=2*rs1*(abs(ps(1)).ˆk).*cos(angle(ps(1))*k+phis1)+rs3*abs(ps(3)).ˆk... +2*rs4*(abs(ps(4)).ˆk).*cos(angle(ps(4))*k+phis4)... +2*rs6*(abs(ps(6)).ˆk).*cos(angle(ps(6))*k+phis6)+rs8*abs(ps(8)).ˆk % this form for the impulse response is obtained by examining the poles % (a pair of complex conjugate poles, followed by a real pole, two pairs of % complex conjugate poles and a real pole) % figure (6) plot(k,ystep,’*’); grid; xlabel(’Discrete time’); ylabel(’Step response’) print -deps figure5_6.eps % % PART 3 % % from (5.45) and (5.67) we have numIy=[1 -2 3 -1]; denIy=[1 0 0 0]; % using formula (5.55) we obtain numzi=-[1 -2 3 -1]; denzi=den; k=0:1:10; yzi=dimpulse(numzi,denzi,k); % figure (7) plot(k,yzi,’*’); grid; xlabel(’Discrete time’); ylabel(’Zero-input response’) print -deps figure5_7.eps 29 CHAPTER 5 MATLAB Results >...
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