Study of different genetic properties in a DNA or RNA sequences requires converting base sequence into numerical sequence through genomic signal processing (GSP) techniques. It is noteworthy to mention that genomic signal is digital in a very real sense, as it can be represented in the form of sequences of finite number of entities. In particular, DNA and proteins can be represented by character strings. In this paper, multi-rate filter has been used and different numerical mapping schemes of a DNA sequence has been taken as input of the filter. At the same time, designing of a different mapping scheme filter have been done when we are decimating the input signal.