Trigonometric transforms for finding repeats in DNA sequences

The detection of many forms of periodicities in DNA sequences has been an active area of research in recent years. Most of the signal processing based methods have primarily focussed on using the short-time discrete Fourier transform (ST-DFT) as the key tool in identifying such repeat sequences. In this paper, we propose to use different fast discrete transforms such as the discrete cosine transform (DCT), the discrete sine transform (DST), and the discrete Hartley transform (DHT), to locate these patterns. In specific, we derive a new unified multirate DSP model that i) allows the derivation of new closed form DNA spectrum expressions for the above trigonometric transforms, ii) includes the DFT model as a special case, and iii) suggests an efficient way to improve the detection of repeats by digital filtering.