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This letter introduces a new representation of discrete signals based on the mathematical notions of functionals and continuous dual spaces. A new and more general sampling theorem is also suggested. Next, the problems of interpolating and resampling discr ...
We provide a new comparison between hexagonal and orthogonal lattices, based on approximation theory. For each of the lattices, we select the “natural” spline basis function as generator for a shift-invariant function space; i.e., the tensor-product B-spli ...
We study the spatialization of the sound field in a room, in particular the evolution of room impulse responses as function of their spatial positions. The presented technique allows us to completely characterize the sound field in any arbitrary location i ...
This paper presents a chronological overview of the developments in interpolation theory, from the earliest times to the present date. It brings out the connections between the results obtained in different ages, thereby putting the techniques currently us ...
The E-star algorithm is a path planning method capable of dynamic replanning and user-configurable path cost interpolation. It calculates a navigation function as a sampling of an underlying smooth goal distance that takes into account a continuous notion ...
We present a simple but generalized interpolation method for digital images that uses multiwavelet-like basis functions. Most of interpolation methods uses only one symmetric basis function; for example, standard and shifted piecewise-linear interpolations ...
Method of interpolating digital samples (fN, fn) using interpolation functions ( psi , psi (x-x0)) that are shifted by an arbitrary shift value (x0) relative to said samples (fN, fn). It will be shown that there is a non-zero and non-trivial optimal value ...
This paper presents an interpolation method based on shifted versions of two piecewise linear generators, which provides approximation order 2 like usual piecewise-linear interpolation; i.e., this method is able to represent the constant and the ramp exact ...
We consider using spline interpolation to improve the standard filtered back-projection (FBP) tomographic reconstruction algorithm. In particular, we propose to link the design of the filtering operator with the interpolation model that is applied to the s ...
This article describes a method of constructing parametric models out of captured motion and skeleton data. Casting the problem as scattered data interpolation, our work is based on a multi-step approximation for the interpolation function with motion data ...
