I have read about Fourier transformation that real signals are "mirrored" in the real and negative halves of the Fourier transform because of the nature of the Fourier transform. For example, if we have the real signal $x$ whose length is $N$, its $X = FFT(x)$ should be conjugate symmetric. That means the $X^*[m] = X[N-m]$.
That is ok, and I have read it clearly HERE
My question: assuming you have a real signal $x = [-1, 1, -1, 1];$ its $X = FFT(x) = [0, 0, -4 , 0]$ So, in that case, we cannot say that $X^*[m] = X[N-m]$. Why ?
Is what I said above is right ? in which cases is right?