A global model structure is developed for parametrization and identification of a general class of Linear Parameter-Varying (LPV) systems. By using a fixed orthonormal basis function (OBF) structure, a linearly parametrized model structure follows for which the coefficients are dependent on a scheduling signal. An optimal set of OBFs for this model structure is selected on the basis of local li...

We address the problem of restoring, while preserving possible discontinuities, fields of noisy orthonormal vector sets, taking the orthonormal constraints explicitly into account. We develop a variational solution for the general case where each image feature may correspond to multiple n-D orthogonal vectors of unit norms. We first formulate the problem in a new variational framework, where di...

We give many examples of bivariate nonseparable compactly supported orthonormal wavelets whose scaling functions are supported over [0,3]x[0,3]. The Holder continuity properties of these wavelets are studied.

In this paper, we provide a family of compactly supported orthonormal complex wavelets with dilation 4 such that the generating wavelet functions are symmetric/antisymmetric and have linearly increasing orders of vanishing moments and smoothness.

In this work we consider smooth orthonormal factorizations of smooth matrixvalued functions of constant rank. In particular, we look at Schur, singular value, and related decompositions. Furthermore, we consider the case in which the functions are periodic and study periodicity of the factors. We allow for eigenvalues and singular values to coalesce.

We construct orthonormal bases compatible with bi-variate homogeneous $$\alpha $$ -modulation spaces and the associated of Triebel–Lizorkin type. The construction is based on generating a separable -covering using carefully selected tensor products univariate brushlet functions regard to this covering. show that systems form an unconditional for -spaces

where [(z) is continuous, it is clear that given an e>0 and a complete orthonormal sequence {<£„}, there exists an N = N(D, K, £, {„}) such that m^N an...

The proportional-bandwidth and constant-bandwidth timefrequency signal decompositions of the wavelet, Gabor, and Wilson Manuscript received August 21, 1992; revised May 26, 1993. The Guest Editor coordinating the review of this paper and approving it for publication was Dr. Patrick Flandrin. This work was supported in part by the Sound Group of the computer-based Education Research Laboratory, ...

We give general mathematical results concerning oscillating singularities and we study examples of functions composed only of oscillating singularities. These functions are deened by explicit coeecients on an orthonormal wavelet basis. We compute their HH older regularity and oscillation at every point and we deduce their spectrum of oscillating singularities.