2016/05/02 by Nikolai Dokuchaev, Dokuchaev, Nikolai · 1 citation
Computer Science · Engineering · Mathematics · #Blind Source Separation Techniques #Image and Signal Denoising Methods #Reservoir Engineering and Simulation Methods #cs.IT #math.IT #math.ST #msc:93E10 #msc:94A12 #msc:94A20 #stat.TH
paper · pdf · doi:10.48550/arxiv.1605.00414
arXiv admin note: text overlap with arXiv:1603.04174
arxiv created 2017/10/30 · arxiv updated 2017/10/31
The paper investigates possibility of recovery of sequences from their decimated subsequences. It is shown that this recoverability is associated with certain spectrum degeneracy of a new kind, and that a sequences of a general kind can be approximated by sequences featuring this degeneracy. This is applied to sparse sampling of continuous time band-limited functions. The paper shows that these functions allow an arbitrarily close approximation by functions that can be recovered from sparse equidistant samples with sampling distance larger than the distance defined by the critical Nyquist rate for the underlying function. This allows to bypass, in a certain sense, the restriction on the sampling rate defined by the Nyquist rate.