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...

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.

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...