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Hermite functions and uncertainty principles for the Fourier and the windowed Fourier transforms.

Aline Bonami, Demange, Bruno, Jaming, Philippe (2003)

Revista Matemática Iberoamericana

We extend an uncertainty principle due to Beurling into a characterization of Hermite functions. More precisely, all functions f on Rd which may be written as P(x)exp(-(Ax,x)), with A a real symmetric definite positive matrix, are characterized by integrability conditions on the product f(x)f(y). We then obtain similar results for the windowed Fourier transform (also known, up to elementary changes of functions, as the radar ambiguity function or the Wigner transform). We complete the paper with...

Hierarchical models, marginal polytopes, and linear codes

Thomas Kahle, Walter Wenzel, Nihat Ay (2009)

Kybernetika

In this paper, we explore a connection between binary hierarchical models, their marginal polytopes, and codeword polytopes, the convex hulls of linear codes. The class of linear codes that are realizable by hierarchical models is determined. We classify all full dimensional polytopes with the property that their vertices form a linear code and give an algorithm that determines them.

Hierarchical residue number systems with small moduli and simple converters

Tadeusz Tomczak (2011)

International Journal of Applied Mathematics and Computer Science

In this paper, a new class of Hierarchical Residue Number Systems (HRNSs) is proposed, where the numbers are represented as a set of residues modulo factors of 2k ± 1 and modulo 2k . The converters between the proposed HRNS and the positional binary number system can be built as 2-level structures using efficient circuits designed for the RNS (2k-1, 2k, 2k+1). This approach allows using many small moduli in arithmetic channels without large conversion overhead. The advantages resulting from the...

How similarity matrices are?

Teresa Riera (1978)

Stochastica

In finite sets with n elements, every similarity relation (or fuzzy equivalence) can be represented by an n x n-matrix S = (sij), sij ∈ [0,1], such that sii = 1 (1 ≤ i ≤ n), sij = sji for any i,j and S o S = S, where o denotes the max-min product of matrices. These matrices represent also dendograms and sets of closed balls of a finite ultrametric space (vid. [1], [2], [3]).

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