A synchronization system includes a signal generating module that generates a signal comprising modulated waveforms and a timing window generator that generates a timing window. A proportional integral controller (a) divides the timing window into a first half window and a second half window, (b) demodulates the digital signal in the first half window and the second half window, (c) compares an amplitude of demodulated signal in the first half window to an amplitude of demodulated signal in the second half window, (d) calculates a new location for the timing window, and (e) repeats (b), (c), and (d) until the amplitude in the first half window equals the amplitude in the second half window.