nlong=1024;
xlong=zeros(1,nlong);
hlong=xlong;
n1=6; n2=8;
x=ones(1,n1);
alfa=0.5;
h=alfa.^(0:n2-1);
for i=1:n1, xlong(i)=x(i); end
for i=1:n2, hlong(i)=h(i); end
y=conv(x,h);
Xlong=fft(xlong);
Hlong=fft(hlong);
x1=[x zeros(1,max(0,n2-n1))];
h1=[h zeros(1,max(0,n1-n2))];
X1=fft(x1);
H1=fft(h1);
Y1=X1.*H1;
Y=fft(y);
Ylong=Xlong.*Hlong;
figure(1);
gh1=subplot(1,3,1);
xflong=(-pi:2*pi/length(Xlong):pi-2*pi/length(Xlong))+pi;
set(gh1,'Xlim',[0,6.28]);
hold on
plot(xflong,abs(Xlong),'k');
title('X(\Omega)');
xlabel('\Omega');
gh2=subplot(1,3,2);
hflong=(-pi:2*pi/length(Hlong):pi-2*pi/length(Hlong))+pi;
set(gh2,'Xlim',[0,6.28]);
hold on
plot(hflong,abs(Hlong),'k');
title('H(\Omega)');
xlabel('\Omega');
gh3=subplot(1,3,3);
yflong=(-pi:2*pi/length(Ylong):pi-2*pi/length(Ylong))+pi;
set(gh3,'Xlim',[0,6.28]);
hold on
plot(yflong,abs(Ylong),'k');
title('Y(\Omega), (*) N=8, (+) N=13, (o) N=16');
xlabel('\Omega');
subplot(1,3,1);
x1f=(-pi:2*pi/length(X1):pi-2*pi/length(X1))+pi;
stem(x1f,abs(X1),'r*');
subplot(1,3,2);
h1f=(-pi:2*pi/length(H1):pi-2*pi/length(H1))+pi;
stem(h1f,abs(H1),'r:*');
subplot(1,3,3);
y1f=(-pi:2*pi/length(Y1):pi-2*pi/length(Y1))+pi;
stem(y1f,abs(Y1),'r:*');
yf=(-pi:2*pi/length(Y):pi-2*pi/length(Y))+pi;
stem(yf,abs(Y),'b:+');
figure(2);
ghf2=stem(0:length(y)-1,y,'k:');
hold on
xlabel('n');
ylabel('y[n]');
y1=ifft(Y1);
stem(0:length(y1)-1,abs(y1),'r:*');
n3 = pow2(nextpow2(n1+n2-1));  % Transform length
x3=[x zeros(1,n3-n1)];
h3=[h zeros(1,n3-n2)];
X3=fft(x3);
H3=fft(h3);
Y3=X3.*H3;
y3=ifft(Y3);
figure(1);
subplot(1,3,1);
x3f=(-pi:2*pi/length(X3):pi-2*pi/length(X3))+pi;
stem(x3f,abs(X3),'k:o');
subplot(1,3,2);
h3f=(-pi:2*pi/length(H3):pi-2*pi/length(H3))+pi;
stem(h3f,abs(H3),'k:o');
subplot(1,3,3);
y3f=(-pi:2*pi/length(Y3):pi-2*pi/length(Y3))+pi;
stem(y3f,abs(Y3),'k:o');
figure(2);
stem(0:length(y3)-1,y3,'b:+');
set(gca,'Ylim',[0,ceil(max(max(y),max(max(y1),max(abs(y3)))))]);
title('(+) convoluzione, (*) DFT N=8, (o) DFT N=16');