In this work we attempt to analize the structure of the classes of deficient spline functions, that is, the ones generated by traslations on the integers of the truncated power functions. Since these classes are correlated with multiresolution structures, the main pourpose of this presentation is to design vector scaling functions, with minimal support. For this, we do not apply Fourier techniques, but elemental properties of the truncated power functions. The double-scale or refinement relationship is demonstrated again from the autosimilarity property of these functions.
We propose an approximation scheme on representation spaces which elements are piecewise polynomial functions, with deficient regularity on a pre-established grid of knots. We characterize these spaces, expose relevant properties and define appropriate bases. We design approximations methods based on orthogonal projections of a given signal, restricted to certain conditions, according with the regularity that is wished. We suggest applications for this procedure in the context of signal processing.
In this work we analyze the existence of single scaling functions embedded in a multiresolution analysis structure generated by a multiscaling function. Particularly, we consider the case of spline functions.
In this work we expose some interesting properties of multiresolution structures generated from multiscaling functions. Particularly, we explore relations between different families of spline multiscaling functions embedded in a common multiresolution analysis.
In this work we display and multiresolution analysis scheme restricted on the interval [0,N]. This scheme is developed for the case of Hermite spline functions but it can be implemented in more general cases. Embedded in this scheme we construct semiorthogonal multiwavelets. Also we expose several methods and algorithms for signal processing applications.
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