Genomic signal processing (GSP) refers to the use of digital signal processing (DSP) tools for analyzing genomic data such as DNA sequences. A possible application of GSP that has not been fully explored is the computation of the distance between a pair of sequences. In this work we present GAFD, a novel GSP alignment-free distance computation method. We introduce a DNA sequence-to-signal mapping function based on the employment of doublet values, which increases the number of possible amplitude values for the generated signal. Additionally, we explore the use of three DSP distance metrics as descriptors for categorizing DNA signal fragments. Our results indicate the feasibility of employing GAFD for computing sequence distances and the use of descriptors for characterizing DNA fragments.