I am new to Digital Signal Processing field and trying to understand what is phase unwrapping and why it is needed. So far i have read that it's done to avoid phase jumps and to avoid multiple of 2pi is added to the difference between the two phases, but what i don't understand why phase jump happens. I guess this is the missing link in my understanding.
Thanks
Consider a simple oscillatory system in the xy plane (a point moving in a circle, with constant speed and amplitude). You have the time series of x and y of that point. You can apply the estimator phi = arctg(y/x) (since "amplitude and speed are constants").
Now, supose your system starts at phi=0, so phi(t=0) = 0 rads. Just before the it completes the first cicle, phi(t) approx 2Pi rads (one turn, as we expected). Just after that moment, in the begining of the 2nd cicle, phi(t) approx 0 again (oops, we want it to be 2pi! But note that x and y should have returned to the same values x(0) and y(0)... so we should expect that actg should be again 0). And in the end of that 2nd cicle, one has phi(t) = 2pi rads again (and we want it to be 4pi! Buts x and y shall now have the same values as in the final of the 1st cicle, and arctg naturally will be near 2pi and not 4pi).
So, for each cicle, the function arctg doesn't know that a complete turn was made. So, YOU need manually add 2Pi for each turn.
I suggest the following references:
Boashash, B. (1992). Estimating and interpreting the instantaneous frequency of a signal. II. Algorithms and applications. Proceedings of the IEEE, 80(4), 540–568. doi:10.1109/5.135378
Boccaletti, S., Kurths, J., Osipov, G., Valladares, D. L., & Zhou, C. S. (2002). The synchronization of chaotic systems. Physics Reports, 366, 1–101. doi:10.1016/S0370-1573(02)00137-0
