The role of the symbolic-to-numerical mapping in the detection of DNA periodicities

The detection of many forms of periodicities in DNA sequences has been an active area of research in recent years. Most of the signal processing based methods have used the simple Voss mapping to map the symbolic DNA sequence into binary indicator ones before computing some form of the so-called DNA spectrum to locate these repeats. A key research issue that remains however open is whether the success of these techniques is Voss specific. In this paper, we first propose a new and generic matrix based framework that comprises most of the widely used mappings in the literature as special cases. By using this approach, we can then show that the standard DNA spectrum is in fact in variable under most of these mappings. Finally, we demonstrate that a number of potential new mappings naturally follow from the suggested framework.