Repetitive sequences of DNA are meaningful and of great importance to human functions. Previous researchers have proposed various methods to discover repetitive sequences in DNA sequence. However, the unknown lengths for repetitive sequences are usually predicted randomly or determined by rules of thumb rather than using a systematical criterion. We propose a new algorithm based on the cumulative Fourier spectral contents of DNA sequence to identify the candidate lengths of repetitive sequences or repeats in DNA sequences. After the candidate lengths of repeats are known, one can identify the repeats and their copy numbers using an exact method. Both of the simulated and real datasets are used to illustrate the performance of the proposed algorithm. The results are also compared to two well-known methods such as Spectral Repeat Finder (SRF) and Gibbs sampler. Furthermore, we demonstrate the use of CSRF in some well-known repeats-finding methods such as SRF, Gibbs sampler, MEME.
