This article considers optimal foldover plans for nonregular designs. By using the indicator function, we deŽ ne words with fractional lengths. The extended word-length pattern is then used to select among nonregular foldover designs. Some general properties of foldover designs are obtained using the indicator function. We prove that the full-foldover plan that reverses the signs of all factors...

When an orthogonal array is projected on a small number of factors, as is done in screening experiments, the question of interest is the structure of the projected design, by which we mean its decomposition in terms of smaller arrays of the same strength. In this paper we investigate the decomposition of arrays of strength t having t + 1 factors. The decomposition problem is well-understood for...

This paper considers the classical sampling theorem in multiresolution spaces with scaling functions as interpolants. As discussed by Xia and Zhang, for an orthogonal scaling function to support such a sampling theorem, the scaling function must be cardinal (interpolating). They also showed that the only orthogonal scaling function that is both cardinal and of compact support is the Haar functi...

An orthogonal decomposition method and implementation algorithm for speech signal processing are proposed in this paper. In the reproducing kernel function of Hilbert space ] , [ 1 2 b a W , a set of normalized orthogonal function system n j x 1 * )} ( {φ is generated, and speech signals can be orthogonally decomposed in ] , [ 1 2 b a W according to the basis n j x 1 * )} ( {φ , the orthogonal ...

We present an in-depth examination of the effectiveness of radial basis function kernel (beyond Gaussian) estimators based on orthogonal random feature maps. We show that orthogonal estimators outperform state-of-the-art mechanisms that use iid sampling under weak conditions for tails of the associated Fourier distributions. We prove that for the case of many dimensions, the superiority of the ...

We present an in-depth examination of the effectiveness of radial basis function kernel (beyond Gaussian) estimators based on orthogonal random feature maps. We show that orthogonal estimators outperform state-of-the-art mechanisms that use iid sampling under weak conditions for tails of the associated Fourier distributions. We prove that for the case of many dimensions, the superiority of the ...