Paulo Jorge S. G. Ferreira

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We overview and discuss several methods for the Fourier analysis of symbolic data, such as DNA sequences, emphasizing their mutual connections. We consider the indicator sequence approach, the vector and the symbolic autocorrelation methods, and methods such as the spectral envelope, that for each frequency optimize the symbolic-no-numeric mapping to(More)
The problem of finding the shortest absent words in DNA data has been recently addressed, and algorithms for its solution have been described. It has been noted that longer absent words might also be of interest, but the existing algorithms only provide generic absent words by trivially extending the shortest ones. We show how absent words relate to the(More)
In this paper we study the eigenvalues of a matrix S which arises in the recovery of lost samples from oversampled band-limited signals. Emphasis is placed on the variation of the eigenvalues as a function of the distribution of the missing samples and as a function of the oversampling parameter. We present a number of results which help to understand the(More)
It is well known that a band-limited oversampled signal is completely determined even if an arbitrary finite number of samples is lost. We show that an alternative simple proof of this fact carries over to generalized sampling expansions. More precisely, we show that any finite number of missing samples can be recovered from the remaining ones, in the case(More)
This paper explores the relationship between Toeplitz and circulant matrices. Upper and lower bounds for all eigenvalues of hermitian Toeplitz matrices are given, capitalizing on the possibility of embedding a Toeplitz matrix in a circulant, and of expressing any nn Toeplitz matrix as a sum of two matrices with known eigenvalues. The bounds can be(More)
The eigenvalues of the matrices that occur in certain finitedimensional interpolation problems are directly related to their well posedness and strongly depend on the distribution of the interpolation knots, that is, on the sampling set. We study this dependency as a function of the sampling set itself and give accurate bounds for the eigenvalues of the(More)