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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.03667 |
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| _version_ | 1866912316985966592 |
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| author | Dokuchaev, Nikolai |
| author_facet | Dokuchaev, Nikolai |
| contents | The paper establishes an analog Whittaker-Shannon-Kotelnikov sampling theorem for unbounded non-decaying band-limited signals. An explicit interpolation formula is obtained for signals sublinear growth with rate of growth less than 1/2. At any time, the rate of decay for the $k$th coefficients of this formula is $\sim 1/k^2$. In addition, the paper obtains a method for calculating the coefficients of the interpolation formula applicable to signals with arbitrarily high rate of polynomial growth. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_03667 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sampling Theorem and explicit interpolation formula for non-decaying unbounded signals Dokuchaev, Nikolai Functional Analysis Spectral Theory The paper establishes an analog Whittaker-Shannon-Kotelnikov sampling theorem for unbounded non-decaying band-limited signals. An explicit interpolation formula is obtained for signals sublinear growth with rate of growth less than 1/2. At any time, the rate of decay for the $k$th coefficients of this formula is $\sim 1/k^2$. In addition, the paper obtains a method for calculating the coefficients of the interpolation formula applicable to signals with arbitrarily high rate of polynomial growth. |
| title | Sampling Theorem and explicit interpolation formula for non-decaying unbounded signals |
| topic | Functional Analysis Spectral Theory |
| url | https://arxiv.org/abs/2410.03667 |