Binary tree-structured filter banks have been employed in the past to generate wavelet bases. While the relation between paraunitary filter banks and orthonormal bases is known to some extent, there are some extensions which are either not known, or not published so far. In particular it is known that a binary tree-structured filter bank with the same paraunitary polyphase matrix on all levels ...

Frisvad’s method for building a 3D orthonormal basis from a unit vector has accuracy problems in its published floating point form. These problems are investigated and a partial fix is suggested, by replacing the threshold 0.9999999 by the threshold -0.999805696, which decreases the maximum error in the orthonormality conditions from 0.623 to 0.0062.

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...

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.