Abstract There has re ently been interest in the use of orthonormal bases for the purposes of SISO system identi ation. Con urrently, but separately, there has also been vigorous work on estimation of MIMO systems by omputationally heap and reliable s hemes. These latter ideas have olle tively be ome known as `4SID' methods. This paper is a ontribution overlapping these two s hools of thought b...

This contribution deals with the problem of structure determination for generalized orthonormal basis models used in system identiication. The model structure is parameterized by a pre-speciied set of poles. Given this structure and experimental data a model can be estimated using linear regression techniques. Since the variance of the estimated model increases with the number of estimated para...

A Wilson orthonormal basis was constructed in 1991 by I. Daubechies, S. Jaffard and J.L. Journé from Gabor tight frame elements, when the redundancy of the Gabor system is 2. In 1994 P. Auscher gave a characterization of the atoms for which the Wilson system is an orthonormal basis. Afterwards, K. Gröchenig posed a question whether the construction of an orthonormal Wilson basis is possible for...

Suppose that {ek} is an orthonormal basis for a separable, infinite-dimensional Hilbert space H. Let D be a diagonal operator with respect to the orthonormal basis {ek}. That is, D = ∑∞ k=1 λkek⊗ek, where {λk} is a bounded sequence of complex numbers. Let T = D + u1 ⊗ v1 + · · ·+ un ⊗ vn. Improving a result [2] of Foias et al., we show that if the vectors u1, . . . , un and v1, . . . , vn satis...

This short note presents four examples of compactly supported symmetric refinable componentwise polynomial functions: (i) a componentwise constant interpolatory continuous refinable function and its derived symmetric tight wavelet frame; (ii) a componentwise constant continuous orthonormal and interpolatory refinable function and its associated symmetric orthonormal wavelet basis; (iii) a diffe...

\If it is true, it can be proved." | Enrico Fermi ABSTRACT. The Balian{Low theorem (BLT) is a key result in time-frequency analysis, originally stated by Balian and, independently, by Low, as: If a Gabor system fe 2imbt g(t ? na)g m;n2Z with ab = 1 forms an orthonormal basis for L 2 (R), then Z 1 ?1 jtg(t)j 2 dt Z 1 ?1 j ^ g()j 2 dd = +1: The BLT was later extended from orthonormal bases to exa...

In this paper, a novel method is proposed to extract a stable feature set representative of image content. Each image is represented by a linear combination of fractal orthonormal basis vectors. The mapping coefficients of an image projected onto each orthonormal basis constitute a feature vector. The distance remains consistent, i.e., isometric embedded, between any image pairs before and afte...

A systematic construction method of orthonormal basis on self-similar sets is given by the use of representations of the Cuntz algebras. We introduce two kinds of orthonormal basis of self-similar sets including explicit description for the Cantor set, the Sierpiński gasket and the Sierpiński carpet.