% X(k)=1/N \sum_{n=0}^{N-1} x(n)*e^{-j*2*\pi*n*k/N}
% x(n)=\sum_{n=0}^{N-1} X(k)e^{j*2*\pi*n*k/N}

x = [8,8,8,8,8,8,8,8]
X = []
N = length(x)

for k = 0:(N - 1)
  Xk = 0;
  for n = 0:(N - 1)
    Xk = Xk + ( x(n + 1) .* exp(-1j * 2 * pi * n * k / N) );
  end
  X(end + 1) =  Xk;
end
X = 1/N * X

temp = 1/N * fft(x)

y = [];
for n = 0:(N - 1)
  xn = 0;
  for k = 0:(N - 1)
    xn = xn + ( X(k + 1) .* exp(1j * 2 * pi * n * k / N) );
  end
  y(end + 1) =  xn;
end
y