In this paper a general transform theory is presented that underlies expansions of stable discrete-time transfer functions in terms of rational orthonormal bases. The types of bases considered are generated by cascade connections of stable all-pass functions. If the all-pass sections in such a network are all equal, this gives rise to the Hambo basis construction. In this paper a more general c...

The Local Cosine Decomposition of Coifman and Wickerhauser 1] is modiied by incorporating two degrees of freedom that increase the adaptability of the best basis. These are relative shifts between resolution levels and adaptive polarity foldings. The resultant expansion is shift-invariant, and yields adaptive time-frequency distributions which are characterized by high resolution, high concentr...

Let R d be an open set of measure 1. An open set D R d is called a tight orthogonal packing region for if D ? D does not intersect the zeros of the Fourier Transform of the indicator function of and D has measure 1. Suppose that is a discrete subset of R d. 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 bei...

We study the roundoff error propagation in an algorithm which computes the orthonormal basis of a Krylov subspace with Householder orthonormal matrices . Moreover, we analyze special implementations of the classical GMRES algorithm, and of the Full Orthogonalization Method . These techniques approximate the solution of a large sparse linear system of equations on a sequence of Krylov subspaces ...

We invert the Fredholm equation representing the light scattered by a single spherical particle or a distribution of spherical particles to obtain the particle size distribution function and refractive index. We obtain the solution by expanding the distribution function as a linear combination of a set of orthonormal basis functions. The set of orthonormal basis functions is composed of Schmidt...

out-of-core singular-value-decomposition algorithm. The algorithm is designed for tall narrow matrices that are too large to fit in main memory and are stored on disks. We have implemented the algorithm and combined it with a larger eigensolver code to obtain the electronic states of a semiconductor nanocrystal. The computationalchemistry application requires finding an orthonormal basis for a ...

This paper studies continuous-time system model sets that are spanned by "xed pole orthonormal bases. The nature of these bases is such as to generalise the well-known Laguerre and two-parameter Kautz bases. The contribution of the paper is to establish that the obtained model sets are complete in all of the Hardy spaces H p (P), 1(p(R, and the right half plane algebra A(P) provided that a mild...

Many nonlinear systems can be described by a Wiener-Schetzen model. In this model, the linear dynamics are formulated in terms of orthonormal basis functions (OBFs). The nonlinearity is modeled by a multivariate polynomial. In general, an infinite number of OBFs is needed for an exact representation of the system. This paper considers the approximation of a Wiener system with finite-order infin...

In this paper, model sets for continuous–time linear time invariant systems that are spanned by fixed pole orthonormal bases are investigated. These bases generalise the well known Laguerre and two–parameter Kautz cases. It is shown that the obtained model sets are norm dense in the Hardy space H1(Π) under the same condition as previously derived by the authors for the norm denseness in the (Π ...