55 lines
937 B
Matlab
55 lines
937 B
Matlab
% value of a
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a=0.9;
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% signal x(n)
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for n=0:200
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x(n+1) = n*(a^n);
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end
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figure(1)
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n=0:1:200;
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stem(n,x)
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xlabel('n');
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ylabel('x(n)');
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% question part (e)
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n=[0 a];
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d=[1 -2*a a*a];
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[h1,w]=freqz(n,d,256);
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h1mag=abs(h1);
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figure(2)
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plot(w,h1mag,'b','linewidth',2)
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xlabel('Frequency');
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ylabel('Magnitude Response');
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% partial dtft for k =3
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[h2,w]=freqz(x(1:4),1,256);
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h2mag=abs(h2);
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hold
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plot(w,h2mag,'r','linewidth',2)
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% partial dtft for k =10
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[h3,w]=freqz(x(1:11),1,256);
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h3mag=abs(h3);
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plot(w,h3mag,'m','linewidth',2)
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% partial dtft for k =20
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[h4,w]=freqz(x(1:21),1,256);
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h4mag=abs(h4);
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plot(w,h4mag,'g','linewidth',2)
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% partial dtft for k =40
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[h5,w]=freqz(x(1:41),1,256);
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h5mag=abs(h5);
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plot(w,h5mag,'k','linewidth',2)
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% supremum coefficients of the error
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for k=1:200
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[hk,w]=freqz(x(1:k+1),1,256);
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ek=abs(h1-hk);
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coeff(k)=max(ek);
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end
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figure(3)
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k=1:1:200;
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stem(k,coeff)
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