We consider a problem that arises in the field of frequency domain system identification. If a discrete-time system has an input-output relation Y (z) = G(z)U(z), with transfer function G, then the problem is to find a rational approximation Ĝn for G. The data given are measurements of input and output spectra in the frequency points zk: {U(zk), Y (zk)}k=1 together with some weight. The approxi...

A well-performing set of radial basis functions (RBFs) can emerge from genetic competition among individual RBFs. Genetic selection of the individual RBFs is based on credit sharing which localizes competition within orthogonal niches. These orthogonal niches are derived using singular value decomposition and are used to apportion credit for the overall performance of the RBF network among indi...

In this report we analyse the image reconstruction accuracy when using different orthogonal basis functions as the kernel for a reversible image transform. In particular we examine the Discrete Cosine Transform(DCT), Discrete Tchebichef Transform(DTT), Haar Transform, and Walsh-Hadamard Transforms(WHT). We have found that the DCT provides the greatest energy compactness properties for continuou...

There is a natural orthogonal basis of the 6-qubit decoherence-free (DF) space robust against collective noise. Interestingly, most of the basis states can be obtained from one another just permuting qubits. This property: (a) is useful for encoding qubits in DF subspaces, (b) allows the implementation of the Bennett-Brassard 1984 (BB84) protocol in DF subspaces just permuting qubits, which com...

By Cayley’s theorem, any finite group G of order n can be regarded as a subgroup of the symmetric group $n. Let χ be any irreducible complex character of G and let V n χ (G) denote the symmetry classes of tensors associated with G and χ. In this paper assuming the Cayley representation of G, we obtain a formula for the dimension of V n χ (G) and discuss its non-vanishing in general. A necessary...

Sets of orthogonal basis functions over circular areas – pupils in optical applications – are known in the literature for the full circle (Zernike or Jacobi polynomials) and the annulus. Here, an orthogonal set is proposed if the area is two non-overlapping circles of equal size. The geometric master parameter is the ratio of the pupil radii over the distance between both circles. Increasingly ...

UNEQUAL-LENGTH BASIS FUNCTIONS Trac D. Tran Truong Q. Nguyen University of Wisconsin, ECE Department 1415 Engineering Dr., Madison WI 53706 [email protected], [email protected] ABSTRACT In this paper, the theory, design, and implementation of the Generalized Lapped Orthogonal Transform (GenLOT) with unequal-length basis functions are investigated. Necessary constraints on the building ...

The Gram-Schmidt Process (GSP) is used to convert a non-orthogonal basis (a set of linearly independent vectors) into an orthonormal basis (a set of orthogonal, unit-length vectors). The process consists of taking each vector and then subtracting the elements in common with the previous vectors. This paper introduces an Enhanced version of the Gram-Schmidt Process (EGSP) with inverse, which is ...