In a digital system with more than one clock source, lack of synchronization between the clock sources may cause overflow or underflow in sample buffers, also called sample slipping. Sample slipping may lead to undesirable artifacts in the processed signal due to discontinuities introduced by the addition or removal of extra samples. To smooth out discontinuities caused by sample slipping, samples are filtered to when a buffer overflow condition occurs, and the samples are interpolated to produce additional samples when a buffer underflow condition occurs. The interpolated samples may also be filtered. The filtering and interpolation operations can be readily implemented without adding significant burden to the computational complexity of a real-time digital system.