%% ASKHSH 2
%% Erwthma a)

n=[1:20];
x=rand(length(n));
 N=length(x);
 figure(1)
 stem(n,x,'filled')
  title('{x[n]');
  xlabel('n');
 ylabel('x[n]');

for k=0:N-1
for n=0:N-1
X1(n+1)=x(n+1).*exp(-j*2*pi*n*k/N);
end
X(k+1)=sum(X1);
end
X;
n=1:20;%%Xronos pou orizetai to shma
figure(2);
subplot(2,1,1)
stem(n,X,'filled')
 title('Metasximatismos fourier kata kataskeuh.');
 xlabel('n');
 ylabel('F(x[n])');

 Z=fft(x);  % Elenxoume an ta apotelesmata mas sumpiptoun me thn etoimh sinarthsh matlab

 subplot(2,1,2)
 stem(n,Z,'filled')
 title('Metasximatismos fourier me tin etimh sinartish fft');
  xlabel('n');
 ylabel('F(x[n])');




 %% erwthma b)
 for n=0:N-1
     for k=0:N-1
         Xn1(k+1)=Z(k+1)*exp(j*2*pi*n*k/N);
     end
         Xn(n+1)=sum(Xn1);
 end

 Xn=Xn/N;