A solution is presented for the problem of realizing a discrete-time LTI state-space model of minimal McMillan degree such that its :rst N expansion coe;cients in terms of generalized orthonormal basis match a given sequence. The basis considered, also known as the Hambo basis, can be viewed as a generalization of the more familiar Laguerre and two-parameter Kautz constructions, allowing genera...

A global model structure is developed for parametrization and identification of a general class of Linear Parameter-Varying (LPV) systems. By using a fixed orthonormal basis function (OBF) structure, a linearly parametrized model structure follows for which the coefficients are dependent on a scheduling signal. An optimal set of OBFs for this model structure is selected on the basis of local li...

This paper reports on numerical experiments on the ‘independent component analysis’ (ICA) of some nonGaussian stochastic processes. It is found that the orthonormal basis discovered by ICA are strikingly close to wavelet basis.

A local ring is an associative with unique maximal ideal. We associate each Artinian singleton basis four invariants (positive integers) p,n,s,t. The purpose of this article to describe the structure such rings and classify them (up isomorphism) same invariants. Every can be constructed over its coefficient subring by a certain polynomial called associated polynomial. These polynomials play sig...

It is shown that the discrete Calderón condition characterizes completeness of orthonormal wavelet systems, for arbitrary real dilations. That is, if a > 1, b > 0, and the system Ψ = {aψ(ax − bk) : j, k ∈ Z} is orthonormal in L(R), then Ψ is a basis for L(R) if and only if ∑ j∈Z |ψ̂(aξ)| = b for almost every ξ ∈ R. A new proof of the Second Oversampling Theorem is found, by similar methods.

This paper investigates the mathematical background of multiresolution analysis in the specific context where the signal is represented by irregularly sampled data at known locations. The study is related to the construction of nested piecewise polynomial multiresolution spaces represented by their corresponding orthonormal bases. Using simple spline basis orthonormalization procedures involves...

A linear operator on a Hilbert space may be approximated with nite matrices by choosing an orthonormal basis of the Hilbert space. For an operator that is not compact such approximations cannot converge in the norm topology on the space of operators. Multiplication operators on spaces of L2 functions are never compact; for them we consider how well the eigenvalues of the matrices approximate th...

In this paper, we develop a new method for weighted least squares 2D linear-phase FIR filter design. It poses the problem of filter design as the problem of projecting the desired frequency response onto the subspace spanned by an appropriate orthonormal basis. We show how to compute the orthonormal basis efficiently in the cases of quadrantallysymmetric filter design and centro-symmetric filte...

The mathematical and numerical least squares solution of a general linear system of equations is discussed. Perturbation and differentiability theorems for pseudoinverses are given. Computational procedures for calculating least squares solutions using orthonormal transformations, multiplying matrices by a matrix of orthonormal basis vectors for the null-space of a given matrix, sequential proc...

where each θj is supported only on Ω ⊂ {1, 2, . . . , N}, with |Ω| = K. The matrix Ψ is orthonormal, with dimension N × N (we consider only signals sparse in an orthonormal basis). We denote by Φj the measurement matrix for signal j, where Φj is of dimension M ×N , where M < N . We let yj = Φjxj = ΦjΨθj be the observations of signal j. We assume that the measurement matrix Φj is random with i.i...