1. An apparatus for digitally filtering a video signal, comprising: an analog-to-digital converter for converting the video signal into a plurality of sampled values; and a correction circuit, coupled to the analog-to-digital converter, for determining whether distribution of at least one portion of the sampled values belongs to one of a plurality of specific types according to the sampled values, compensating the at least one portion of the sampled values according to a correction operation corresponding to the one of the specific types to generate a digital output signal corresponding to the video signal.