Andrzej K. Brodzik

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MOTIVATION One of the main tasks of DNA sequence analysis is identification of repetitive patterns. DNA symbol repetitions play a key role in a number of applications, including prediction of gene and exon locations, identification of diseases, reconstruction of human evolutionary history and DNA forensics. RESULTS A new approach towards identification of(More)
Alignment of DNA segments containing repetitive nucleotide base patterns is an important task in several genomics applications, including DNA sequencing, DNA fingerprinting, pathogen detection, and gene finding. One of the most efficient procedures used for this task is the cross correlation method. The main computations of the procedure are the discrete(More)
In this letter, closed-form expressions for the discrete Fourier transform (DFT) of a finite chirp are derived. It is shown that when the normalized chirp rate is coprime with the chirp length, then the DFT of a finite chirp is again a finite chirp with magnitude, chirp rate, and carrier frequency appropriately scaled. In particular, when the normalized(More)
In this work we consider the problem of global DNA sequence alignment. One of the best known and most efficient computational techniques used for this task is the cross-correlation method. We compare efficacy of evaluating periodic DNA sequence misalignment using the standard magnitude-and-phase cross- correlation technique with the lesser known phase-only(More)
Previously, a discretization of the linear FM chirp of length <i>N</i>=<i>KL</i> <sup>2</sup>, <i>L</i> and <i>KL</i> isin Z, was given and the conditions for its minimal Zak space support were derived. Chirps satisfying these conditions are known as finite chirps. In this work, subsets of finite chirps of length <i>N</i>=<i>L</i> <sup>2</sup>, <i>L</i> a(More)
General conditions are derived for an (N=KL<sup>2</sup>)-point discrete chirp with chirp rate a and carrier frequency b to have minimal support on the LtimesKL Zak transform lattice. Earlier, it has been shown that when the normalized chirp parameters amacr= aK, amacr= aK <sup>2</sup>, and 2bmacr = 2bK are integers, the last two of the same parity, then the(More)
Sparse representations of sequences facilitate signal processing tasks in many radar, sonar, communications, and information hiding applications. Previously, conditions for the construction of a compactly supported finite Zak transform of the linear FM chirp were investigated. It was shown that the discrete Fourier transform of a chirp is, essentially, a(More)