This paper examines the use of general orthonormal bases for system identification from frequency domain data. This idea has been studied in great depth for the particular case of the orthonormal trigonometric basis. Here we show that the accuracy of the estimate can be significantly improved by rejecting the trigonometric basis in favour of a more general orthogonal basis that is able to be ad...

In the present work a newer type of black box nonlinear model in Hammerstein structure is proposed. The model has Wavelet Network coupled with Orthonormal Basis Functions which is capable of modeling a class of non-linear systems with acceptable accuracy. Wavelet basis functions have the property of localization in both the time and frequency domains which enables wavelet networks to approximat...

This paper provides an overview of system identification using orthonormal basis function models, such as those based on Laguerre, Kautz, and generalised orthonormal basis functions. The paper is separated in two parts. In this first part, the mathematical foundations of these models as well as their advantages and limitations are discussed within the context of linear and robust system identif...

A key tool to analyze signals defined over a graph is the so called Graph Fourier Transform (GFT). Alternative definitions of GFT have been proposed, based on the eigendecomposition of either the graph Laplacian or adjacency matrix. In this paper, we introduce an alternative approach, valid for the general case of directed graphs, that builds the graph Fourier basis as the set of orthonormal ve...

This discussion sparse representations of signals in R. The sparsity of a signal is quantified by the number of nonzero components in its representation. Such representations of signals are useful in signal processing, lossy source coding, image processing, etc. We first speak of an uncertainty principle regarding the sparsity of any two different orthonormal basis representations of a signal S...

In a complex vector space of dimension N , by a full set of mutually unbiased bases (MUB’s) we mean a set of N+1 orthonormal bases such that the modulus square of the scalar product of any member of one basis with any member of any other basis is equal to 1/N . If we take e to denote the k vector in the α orthonormal basis, then having a full set of MUB’s amounts to having a collection e ; α = ...

We solve the Gauss law of SU(2) lattice gauge theory using the harmonic oscillator prepotential formulation. We construct a generating function of a manifestly gauge invariant and orthonormal basis in the physical Hilbert space of (d+1) dimensional SU(2) lattice gauge theory. The resulting orthonormal physical states are given in closed form. The generalization to SU(N) gauge group is discussed.

Today, companies need to make use of appropriate patterns such as supply chain management system to gain and preserve a position in competitive world-wide market. Supply chain is a large scaled network consists of suppliers, manufacturers, warehouses, retailers and final customers which are in coordination with each other in order to transform products from raw materials into finished goods wit...

We show asymptotic expansions of the eigenfunctions certain perturbations Jacobi operator in a bounded interval, deducing equiconvergence results between with respect to associated orthonormal basis and cosine basis. Several for pointwise convergence then follow.