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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 eigenvalues of the matrices that occur in certain nite-dimensional 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)
—There are two natural orderings in signals: temporal order and rank order. There is no compelling reason to explore only one of these orderings, either in the discrete-time or in the continuous time case. Nevertheless, the concept of rank order for continuous time signals remains virtually unstudied, which is in striking contrast to the discrete-time case:(More)
A compression-based similarity measure assesses the similarity between two objects using the number of bits needed to describe one of them when a description of the other is available. Theoretically, compression-based similarity depends on the concept of Kolmogorov complexity but implementations require suitable (normal) compression algorithms. We argue(More)
In this paper we introduce and analyze a new preconditioner for Toeplitz matrices that exhibits excellent spectral properties: the eigenvalues of the preconditioned matrix are highly clustered around the unity. As a result, it yields very rapid convergence when used to solve Toeplitz equations via the preconditioned conjugate gradient method. The new(More)
We propose a classification of several algorithms for solving the discrete-discrete band-limited interpolation and extrapolation problems. The classification is based on the dimension of certain underlying vector spaces, and distinguishes between time-domain and frequency-domain methods. This perspective allows a synthetic view of the problem, clarifies the(More)
| In this paper we analyze the performance of an iterative algorithm, similar to the discrete Papoulis-Gerchberg algorithm, and which can be used to recover missing samples in nite-length records of band-limited data. No assumptions are made regarding the distribution of the missing samples, in contrast with the often studied extrapolation problem, in which(More)
| In this paper we study the eigenvalues of a matrix S which arises in the recovery of lost samples from over-sampled 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(More)