Fourier methods for biosequence analysis

Novel methods are discussed for using fast Fourier transforms for DNA or protein sequence comparison. These methods are also intended as a contribution to the more general computer science problem of text search. These methods extend the capabilities of previous FFT methods and show that these methods are capable of considerable refinement. In particular, novel methods are given which (1) enable the detection of clusters of matching letters, (2) facilitate the insertion of gaps to enhance sequence similarity, and (3) accommodate to varying densities of letters in the input sequences. These methods use Fourier analysis in two distinct ways. (1) Fast Fourier transforms are used to facilitate rapid computation. (2) Fourier expansions are used to form an 'image' of the sequence comparison.