Abstract. We consider a Galerkin method for an elliptic pseudodifferential operator of order zero on a two-dimensional manifold. We use piecewise linear discontinuous trial functions on a triangular mesh and describe an orthonormal wavelet basis. Using this basis we can compress the stiffness matrix from N to O(N logN) nonzero entries and still obtain (up to logN terms) the same convergence rat...

Laguerre filters constitute an orthonormal basis for the Hilbert space, for this they are used in system identification and reduced-order modelling. In this paper a new property of Laguerre filters is introduced: it is shown that the system having as transfer function the sum of the first n + 1 functions has all the singular values equals each other. On the basis of this property a generalizati...

This paper considers the design of wavelet tight frames based on iterated oversampled filter banks. The greater design freedom available makes possible the construction of wavelets with a high degree of smoothness, in comparison with orthonormal wavelet bases. In particular, this paper takes up the design of systems that are analogous to Daubechies orthonormal wavelets—that is, the design of mi...

A solution is presented for the problem of realizing a minimal state-space model of an LTI discrete-time system from a partial expansion in terms of generalized orthonormal basis functions, also known as Hambo basis functions. For the solution of the minimal partial realization problem fruitful use is made of the Hambo operator transform theory that underlies the basis function expansion. The r...

We explain the coarse geometric origin of fact that certain spectral subspaces topological insulator Hamiltonians are delocalized, in sense they cannot admit an orthonormal basis localized wavefunctions, with respect to any uniformly discrete set localization centers. This is a robust result requiring neither spatial homogeneity nor symmetries and applies Landau levels disordered quantum Hall s...

We use the concept of multiresolution analysis and orthonormal basis of wavelet functions to construct an estimator for an unknown density in a given Sobolev’s space. We show consistency with the rate of convergence equal to the optimal minimax rate of convergence. We also discuss some of the features of this new method of estimation on a numerical example.

This paper introduces an orthonormal version of the sliding-window Projection Approximation Subspace Tracker (PAST). The new algorithm guarantees the orthonormality of the signal subspace basis at each iteration. Moreover, it has the same complexity as the original PAST algorithm, and like the more computationally demanding natural power (NP) method, it satisfies a global convergence property, ...

The main features of a novel approach for audio signal encoding are described. The approach combines non-linear transform coding and structured approximation techniques, together with hybrid modeling of the signal class under consideration. Essentially, several different components of the signal are estimated and transform coded using an appropriately chosen orthonormal basis. Different models ...