A comparative study of cross-correlation methods for alignment of DNA sequences containing repetitive patterns

In this work we consider the problem of global DNA sequence alignment. One of the best known and most efficient computational techniques used for this task is the cross-correlation method. We compare efficacy of evaluating periodic DNA sequence misalignment using the standard magnitude-and-phase cross- correlation technique with the lesser known phase-only cross-correlation method. We prove that for a periodic DNA sequence whose length is a prime number the standard approach leads to significant sidelobes in the cross-correlation, the magnitude of which increases with the length of the sequence, while the phase-only approach allows attaining a perfect cross-correlation with zero sidelobes. Numerical experiments on synthesized data are included and robustness of the phase-only method to random DNA insertions and imperfect DNA fragment matches is discussed.