Convolution Idempotents with a given Zero-set
arXiv:2001.00739 · doi:10.1109/TSP.2020.3016137
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.