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 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.

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.

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...

We consider the modeling of non-stationary discrete signals whose amplitude and frequency are assumed to be nonlinearly modulated over very short-time duration. We investigate the case where both instantaneous amplitude and frequency can be approximated by orthonormal polynomials. Previous works dealing with polynomial approximations refer to orthonormal bases built from a discretization of con...

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...