Detecting Periodicities in Eukaryotic Genomes by Ramanujan Fourier Transform

Ramanujan Fourier transform (RFT) nowadays is becoming a popular signal processing method. RFT is used to detect periodicities in exons and introns of eukaryotic genomes in this article. Genomic sequences of nine species were analyzed. The highest peak in the spectrum amplitude corresponding to each exon or intron is regarded as the significant signal. Accordingly, the periodicity corresponding to the significant signal can be also regarded as a valuable periodicity. Exons and introns have different periodic phenomena. The computational results reveal that the 2-, 3-, 4-, and 6-base periodicities of exons and introns are four kinds of important periodicities based on RFT. It is the first time that the 2-base periodicity of introns is discovered through signal processing method. The frequencies of the 2-base periodicity and the 3-base periodicity occurrence are polar opposite between the exons and the introns. With regard to the cyclicality of the Ramanujan sums, which is the base function of the transformation, RFT is suggested for studying the periodic features of dinucleotides, trinucleotides, and q nucleotides.