Functions and Analysis


Positivity of the Fourier Transform of the Shortest Maximal Order Convolution Mask for Cardinal B-splines

Authors: Markus Sprecher

Positivity of the Fourier transform of a convolution mask can be used to define an inverse convolution and show that the spatial dependency decays exponentially. In this document, we consider, for an arbitrary order, the shortest possible convolution mask which transforms samples of a function to Cardinal B-spline coefficients and show that it is unique and has indeed a positive Fourier transform. We also describe how the convolution mask can be computed including some code.

Comments: 6 Pages.

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Submission history

[v1] 2018-12-18 12:16:21

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