I am trying to obtain phase versus time information from a discrete time sampled signal. As an example: suppose I have a signal F = sin(w*t + phi) where the value of w is constant, but the value of phi is a function of time. So, if I aquire the signal at some sampling rate, I can perform FFT(F) resulting in amplitude and phase information. Since the value of phi is a function of time, the resulting FFT amplitude spectrum will indicate a spread in frequency values located somewhere around w, with a range of phase values also around w.
My question is this: How can I extract the phase versus frequency values such that I can determine the values of phi (in signal F) as a function of time? I don't believe that performing an IFFT(phase) will result in phi(t).