Convolution Idempotents with a given Zero-set
Information Theory
2023-07-19 v1 math.IT
Abstract
We investigate the structure of N-length discrete signals h satisfying h*h=h that vanish on a given set of indices. We motivate this problem from examples in sampling, Fuglede's conjecture, and orthogonal interpolation of bandlimited signals. When N is a prime power, we characterize all such h with a prescribed zero set in terms of digit expansions of nonzero indices in the inverse DFT of h.
Cite
@article{arxiv.2001.00739,
title = {Convolution Idempotents with a given Zero-set},
author = {Aditya Siripuram and Brad Osgood},
journal= {arXiv preprint arXiv:2001.00739},
year = {2023}
}