In this paper we present a general and very simple construction for generating complete orthonormal bases for system identiication. This construction provides a unifying formulation of orthonormal bases since the common FIR and recently popular Laguerre and Kautz model structures are restrictive special cases of our construction. A distinguishing feature of our construction is that it can gener...

and Applied Analysis 3 Definition 2.6. We say {Λj ∈ B H,Hj }j 1 is g-orthonormal basis for H with respect to {Hj}, if it is g-biorthonormal with itself and for any f ∈ H one has

We construct an orthonormal basis for the family of bi-variate α-modulation spaces. The construction is based on local trigonometric bases, and the basis elements are closely related to so-called brushlets. As an application, we show that m-term nonlinear approximationwith the system in an α-modulation space can be completely characterized.

Let Ω ⊆ R be an open set of measure 1. An open set D ⊆ R is called a tight orthogonal packing region for Ω if D − D does not intersect the zeros of the Fourier Transform of the indicator function of Ω. Suppose that Λ is a discrete subset of R. The main contribution of this paper is a new way of proving the folowing result (proved by Lagarias, Reeds and Wang and, in the case of Ω being the cube,...

A family of eigenfields of a specific Stokes eigenproblem is described which constitute an orthonormal basis of a Sobolev-Hilbert space of incompressible flow fields obeying no-slip boundary conditions. This basis is used to describe a representation theorem for such fields, including spectral formulae for the kinetic energy and the enstrophy. Some other properties of the vorticity and the heli...

The paper deals with structural properties of a class of strictly causal systems. It is shown that a special physically correct internal structure of a given system representation caled dissipation normal form can be derived as a natural consequence of strict causality, dissipativity, minimality and asymptotic stability requirements. A generalization of classic Tellegen’s theorem together with ...

In this work we propose a kernel-based blind source separation (BSS) algorithm that can perform nonlinear BSS for general invertible nonlinearities. For our kTDSEP algorithm we have to go through four steps: (i) adapting to the intrinsic dimension of the data mapped to feature space F , (ii) finding an orthonormal basis of this submanifold, (iii) mapping the data into the subspace of F spanned ...

Recently an upsurge in research relating to Laguerre filters for use in system optimization [1], system identification [2] and reduced-order modeling [3] has been noticed. The main reason for the good performance of Laguerre filters is that they form a uniformly bounded orthonormal basis in Hardy space [1]. Another reason, and this represents the novelty of the work carried out in this paper, i...

Adapted waveform analysis uses a library of orthonormal bases and an efficiency functional to match a basis to a given signal or family of signals. It permits efficient compression of a variety of signals such as sound and images. The predefined libraries of modulated waveforms include orthogonal wavelet-packets, and localized trigonometric functions, have reasonably well controlled time-freque...

For 0 < ρ < 1, let μρ be the Bernoulli convolution associated with ρ. Jorgensen and Pedersen [P. Jorgensen, S. Pedersen, Dense analytic subspaces in fractal L2-spaces, J. Anal. Math. 75 (1998) 185–228] proved that if ρ = 1/q where q is an even integer, then L(μρ) has an exponential orthonormal basis. We show that for any 0 < ρ < 1, L(μρ) contains an infinite orthonormal set of exponential funct...