The present disclosure provides techniques for a power factor correction system having an arbitrary input waveform. The present disclosure provides two example methods of digital power factor correction that allow for a high power factor on an arbitrary input waveform. The two example methods are applicable to both constant-current inputs and constant-voltage inputs. One example method samples the arbitrary input waveform to produce a reference table used to synchronize the input voltage with the input current in a constant current system, and to synchronize the input current to the input voltage in a constant voltage system. A second example method uses instantaneous input values as a reference in performing power factor correction.