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A tandem repeat (TR) is a DNA sequence where a pattern of nucleotides is repeated a number of times. TRs cover more than ten percent of the human genome. They have been proven to play an important role in human diseases, regulation, and evolution. TRs vary for different individuals, so they are commonly used in human gene mapping, linkage studies, and forensic DNA fingerprinting analysis. In this paper, an efficient algorithm is presented for detecting TRs, especially short tandem repeats (STRs), in a DNA sequence. The algorithm, based on the autoregressive (AR) model, is to analyze the spectrum of the DNA sequences. Our algorithm can find TRs effectively and quickly. Furthermore, it is robust to mutations, deletions, and insertions. In comparison with the fast Fourier transform (FFT), our results show that the AR model based algorithm can provide more detailed qualitative information than the FFT when we analyze the spectrum of the STRs. Here, the methods and ideas underlying the algorithm are presented and the effectiveness of the algorithm on TRs is demonstrated.