A complex digital phase locked loop for use in a digital demodulator includes a phase detector for producing a phase error indicative of a difference in phase between a complex digital input signal and a complex digital feedback signal. The phase error is input to a controller, which multiplies the phase error by a gain factor selected to stabilize and optimize the phase locked loop and produces an output signal for use in extracting a frequency deviation present in the complex digital input signal. The output signal is also input to a numerically controlled oscillator that tracks the phase of the complex digital input signal based on the output signal and produces the complex digital feedback signal.