We investigate the fundamental limitations of dispersion mitigation filters. By analyzing the dispersion compensating process from basic principles, we demonstrate how a digital filter can mitigate arbitrarily weak dispersion without oversampling. We calculate the maximum distance the signal can pass with and without dispersion compensation, beyond which no data decoding is possible. Furthermore, we show the exact mathematical relation between this maximum distance and the length of the compensating filter - with and without a Forward Error Correction (FEC).