2D DNA Representations Generated Using a New Coding and the Time-Frequency Analysis

The state of the art shows that Fourier transform based methods lack robustness in terms of the DNA characterization and detection. In fact, the Fourier analysis is limited by the shape and the fixed size of the analysis window; which can affect the representation resolution. In this paper, we review the power of the time-frequency analysis in characterizing the biological sequences. In particular, we study the performance of the wavelet analysis in distinguishing specific structures within the C. elegans genome. The method offers the possibility to visualize the genomic data within the form of explicit images in which DNA elements possess particular behavior. And thus, we can clearly identify homologous sequences through their common behavior. A comparison with the smoothed Fourier analysis and the Choi-Williams distribution is then established. Even the Smoothed Fourier technique is limited as it is a fixed resolution method; thereby the multi-resolution analysis is proposed to improve the DNA analysis. On the other hand, the Choi-Williams distribution increases the time-frequency resolution. Nevertheless, it exhibits the presence of cross-terms which can be considered as signal components. Most of all, one must digitize the DNA characters to be able to use the proposed tools. In line with this, we use the Frequency Chaos Game Signal (FCGS) as coding technique. The FCGS is built in such way that we can follow the frequency evolution of nucleotides' occurrence along the genome. Through this work, we demonstrate that color-scalogram is more effective than the spectrogram and the Choi-Williams representations; since it enables the characterization of different DNA types by specific texture. Besides the visual inspection of the representations, the Shannon entropy measure proves the effectiveness of the wavelet method.