An asynchronous sample rate tracker with rapid acquisition and good steady state performance is provided. In one embodiment, dual tracking loops are used to control reading from a FIFO sample buffer and generation of a ratio of source and local sampling rates. One tracking loop is used for rapid acquisition when the buffer is either empty or full with another tracking loop being used for steady-state operation. The steady-state tracking loop incorporates a low-pass filter to remove the effects of momentary variations in source sampling rates.