Predictability of sequences and subsequences with spectrum degeneracy at periodically located points
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arXiv
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| Format: | Preprint |
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2018
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| _version_ | 1866929364572045312 |
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| author | Dokuchaev, Nikolai |
| author_facet | Dokuchaev, Nikolai |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1803_02233 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Predictability of sequences and subsequences with spectrum degeneracy at periodically located points Dokuchaev, Nikolai Information Theory Spectral Theory 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. |
| title | Predictability of sequences and subsequences with spectrum degeneracy at periodically located points |
| topic | Information Theory Spectral Theory |
| url | https://arxiv.org/abs/1803.02233 |