17 November 2000 Comparing DNA sequences using wavelets
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Wavelet transforms are commonly used in signal processing to identify local signals in both the time and frequency domain. The application described in this paper uses this concept to show that wavelets of similar DNA sequences converge whereas wavelets of dissimilar DNA sequences diverge. To demonstrate this conclusion, several DNA sequences from different organisms were retrieved form John Hopkins University's Genome Database. Statistical tests were applied to these sequences to measure the degree of similarity. Subsequently, a series of wavelet transforms were applied to the DNA sequences. As a result, the wavelet transforms were found to converge on sequences containing identical proteins and were found to diverge on sequences containing dissimilar ones. A description of the algorithm and statistical tests are provided in addition to analytical results. Application of this wavelet analysis technique has shown to be more efficient than the standard homology search algorithms currently being used. The algorithm has O(Nlog(N)) time complexity whereas standard search algorithms have O(N2) Time complexity. Hence, wavelet transforms can be used to quickly locate or match common protein coding in DNA sequences form large medical databases.
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Abdelmoula Elharti, Donna M. Kocak, "Comparing DNA sequences using wavelets", Proc. SPIE 4122, Mathematics and Applications of Data/Image Coding, Compression, and Encryption III, (17 November 2000); doi: 10.1117/12.409243; https://doi.org/10.1117/12.409243

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