Predictability of sequences and subsequences with spectrum degeneracy at periodically located points

2018/03/06 by Dokuchaev, Nikolai · 1 citation
#FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1803.02233

Abstract

The paper established sufficient conditions of predictability with degeneracy for the spectrum at M-periodically located isolated points on the unit circle. It is also shown that m-periodic subsequences of these sequences are also predictable if m is a divisor of M. The predictability can be achieved for finite horizon with linear predictors defined by convolutions with certain kernels. As an example of applications, it is shown that there exists a class of sequences that is everywhere dense in the class of all square-summable sequences and such that its members can be recovered from their periodic subsequences. This recoverability is associated with certain spectrum degeneracy of a new kind.

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• On recovery of sequences from subsequences: the case of non-periodic spectrum gaps

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