An apparatus provides a digital representation of a time difference between a periodic reference signal having a reference signal period and a periodic input signal having an input signal period. The apparatus includes a free-running finite state machine (FSM) that traverses a multiplicity of states in a predetermined order, the state having corresponding state vectors, each of which is held for a state dwell time. A timing circuit receives the reference signal, the input signal and the FSM state vectors, and determines a state transition count equal to a number of FSM state transitions that occur during a counting interval, which corresponds to the time difference between the reference and input signals. A digital low-pass filter receives the state transition counts and provides an output value including weighted sums of the state transition counts, proportional to the time difference between the reference and input signal. A period of the FSM is independent of the reference signal period.