% value of a
a=0.9;

% signal x(n)
for n=0:200
    x(n+1) = n*(a^n);
end
figure(1)
n=0:1:200;
stem(n,x)
xlabel('n');
ylabel('x(n)');

% question part (e)
n=[0 a];
d=[1 -2*a a*a];
[h1,w]=freqz(n,d,256);
h1mag=abs(h1);
figure(2)
plot(w,h1mag,'b','linewidth',2)
xlabel('Frequency');
ylabel('Magnitude Response');

% partial dtft for k =3
[h2,w]=freqz(x(1:4),1,256);
h2mag=abs(h2);
hold
plot(w,h2mag,'r','linewidth',2)

% partial dtft for k =10
[h3,w]=freqz(x(1:11),1,256);
h3mag=abs(h3);
plot(w,h3mag,'m','linewidth',2)

% partial dtft for k =20
[h4,w]=freqz(x(1:21),1,256);
h4mag=abs(h4);
plot(w,h4mag,'g','linewidth',2)

% partial dtft for k =40
[h5,w]=freqz(x(1:41),1,256);
h5mag=abs(h5);
plot(w,h5mag,'k','linewidth',2)

% supremum coefficients of the error
for k=1:200
   [hk,w]=freqz(x(1:k+1),1,256);
   ek=abs(h1-hk);
   coeff(k)=max(ek);
end
figure(3)
k=1:1:200;
stem(k,coeff)