A Novel Signal Processing Measure to Identify Exact and Inexact Tandem Repeat Patterns in DNA Sequences

The identification and analysis of repetitive patterns are active areas of biological and computational research. Tandem repeats in telomeres play a role in cancer and hypervariable trinucleotide tandem repeats are linked to over a dozen major neurodegenerative genetic disorders. In this paper, we present an algorithm to identify the exact and inexact repeat patterns in DNA sequences based on orthogonal exactly periodic subspace decomposition technique. Using the new measure our algorithm resolves the problems like whether the repeat pattern is of period P or its multiple (i.e., 2P, 3P, etc.), and several other problems that were present in previous signal-processing-based algorithms. We present an efficient algorithm of O(NLw logLw), where N is the length of DNA sequence and Lw is the window length, for identifying repeats. The algorithm operates in two stages. In the first stage, each nucleotide is analyzed separately for periodicity, and in the second stage, the periodic information of each nucleotide is combined together to identify the tandem repeats. Datasets having exact and inexact repeats were taken up for the experimental purpose. The experimental result shows the effectiveness of the approach

From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals

Conventional sub-Nyquist sampling methods for analog signals exploit prior information about the spectral support. In this paper, we consider the challenging problem of blind sub-Nyquist sampling of multiband signals, whose unknown frequency support occupies only a small portion of a wide spectrum. Our primary design goals are efficient hardware implementation and low computational load on the supporting digital processing. We propose a system, named the modulated wideband converter, which first multiplies the analog signal by a bank of periodic waveforms. The product is then lowpass filtered and sampled uniformly at a low rate, which is orders of magnitude smaller than Nyquist. Perfect recovery from the proposed samples is achieved under certain necessary and sufficient conditions. We also develop a digital architecture, which allows either reconstruction of the analog input, or processing of any band of interest at a low rate, that is, without interpolating to the high Nyquist rate. Numerical simulations demonstrate many engineering aspects: robustness to noise and mismodeling, potential hardware simplifications, realtime performance for signals with time-varying support and stability to quantization effects. We compare our system with two previous approaches: periodic nonuniform sampling, which is bandwidth limited by existing hardware devices, and the random demodulator, which is restricted to discrete multitone signals and has a high computational load. In the broader context of Nyquist sampling, our scheme has the potential to break through the bandwidth barrier of state-of-the-art analog conversion technologies such as interleaved converters.Comment: 17 pages, 12 figures, to appear in IEEE Journal of Selected Topics in Signal Processing, the special issue on Compressed Sensin