I am looking for a way to get information on the direction a wave is traveling. What I have got is a real function $\Phi(x,t)$ and it's time derivative $\dot{\Phi}(x,t)$ that obeys the wave equation $\Phi_{tt} - \Phi_{xx} = 0$.
I can decompose this wave into reft and right going parts $\Phi(x,t) = f(x - c t) + g(x+ct)$.
Now is there a possibility to get from a FFT only the frequencies of left going waves $g(x + ct)$ if I know $\Phi(x,t)$ and it's time derivative $\dot{\Phi}(x,t)$?