The Phase Information of the DFT As known, we can get a 'phase spectrum' from the DFT of a input signal. Assume, we do a DFT on a given equal interval sampled 50Hz AC signal, the signal is a complete whole cycle, but the start sample point may at any point. And I get the amplitude and phase from the DFT, but what's the reference point of the phase?
If you assume that for a given DFT length $N$ your signal is given by

$$x[n]=A\cos(2\pi n/N+\phi),\quad n=0,1,\ldots,N-1$$

i.e. its period equals $N$, then the first DFT coefficient (starting to count from $0$) is given by

$$X[1]=A\frac{N}{2}e^{j\phi}$$