Convolution Idempotents with a given Zero-set
| Autor: | Brad Osgood, Aditya Siripuram |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
FOS: Computer and information sciences
Bandlimiting Pure mathematics Conjecture Zero set Information Theory (cs.IT) Computer Science - Information Theory Structure (category theory) 020206 networking & telecommunications 02 engineering and technology Convolution Base (group theory) Signal Processing 0202 electrical engineering electronic engineering information engineering Electrical and Electronic Engineering Prime power Mathematics Interpolation |
| Popis: | 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 $N=p^M$ is a prime power, we characterize all such $h$ with a prescribed zero set in terms of base- $p$ expansions of nonzero indices in $\mathcal{F}^{-1}h$ . |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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