% value of a
wc=0.4*pi;

% signal x(n)
for n=-50:50
if (n == 0)
    x(n+51) = wc/pi;
else
    x(n+51) = sin(wc*n)/(pi*n);
end
end
figure(1)
n=-50:1:50;
stem(n,x)
xlabel('n')
ylabel('x(n)')

% Ideal lpf
n=0;
for w=0:0.05*pi:pi;
    n=n+1;
    wfreq(n)=w;
    if  (w <= wc)
        hlpf(n)=1;
    else
        hlpf(n)=0;
    end
end
figure(2)
plot(wfreq,hlpf,'b','linewidth',2)
xlabel('Frequency')
ylabel('DTFT of Ideal Lowpass Filter')

% partial dtft for k =10
k=10;
[h2]=freqz(x(51-k:51+k),1,wfreq);
h2mag=abs(h2);
hold
plot(wfreq,h2mag,'r','linewidth',2)

% partial dtft for k =20
k=20;
[h3]=freqz(x(51-k:51+k),1,wfreq);
h3mag=abs(h3);
plot(wfreq,h3mag,'m','linewidth',2)

% partial dtft for k =30
k=30;
[h4]=freqz(x(51-k:51+k),1,wfreq);
h4mag=abs(h4);
plot(wfreq,h4mag,'k','linewidth',2)