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Optimal Spline Generators for Derivative Sampling

S. Aziznejad, A. Naderi, M. Unser

Proceedings of the Thirteenth International Conference on Sampling Theory and Applications (SampTA'19), Bordeaux, French Republic, July 8-12, 2019, pp. 1-4.



The goal of derivative sampling is to reconstruct a signal from the samples of the function and of its first-order derivative. In this paper, we consider this problem over a shift-invariant reconstruction subspace generated by two compact-support functions. We assume that the reconstruction subspace reproduces polynomials up to a certain degree. We then derive a lower bound on the sum of supports of its generators. Finally, we illustrate the tightness of our bound with some examples.


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