Tandem repeats in genomic sequences are characterized by two or more contiguous copies of a pattern of nucleotides. The role of these repeats as molecular markers is well established in various genetic disorders, human evolution studies, DNA forensics and intron retention. In this work a computational method has been developed for the extraction of both exact and approximate tandem repeats. The proposed algorithm uses Ramanujan Fourier Transform (RFT) to identify periodicities in the DNA sequences. Since RFT estimates the period directly, rather than inferring it from the signal's spectrum, it provides a more sensitive and rapid detection of tandem repeats as compared to other available popular computational methods.