for i=1:256
    x(i) = sin(2*pi*i*80) + sin(2*pi*i*46);
end

X = zeros(256,1);
for k=1:256
   for n=1:256
       X(k)=X(k) + x(n)*exp((-j*2*pi*(n-1)*(k-1))/256);
   end
end

built_in = fft(x);
error = abs(X) - abs(built_in)';

plot(abs(X)); hold on
plot(abs(built_in));
plot(error);
legend('My code', 'Matlab','error');