Convolution Idempotents With a Given Zero-Set
Convolution Idempotents With a Given Zero-Set
We investigate the structure of N-length discrete signals h satisfying h <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">*</sub> 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 = p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</sup> is a …