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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.09371 |
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| _version_ | 1866909076157366272 |
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| author | Said, Karim A. Liu, Lingjia A., A. Beex |
| author_facet | Said, Karim A. Liu, Lingjia A., A. Beex |
| contents | It is well known that index (discrete-time)-limited sampled sequences leak outside the support set when a band-limiting operation is applied. Similarly, a fractional shift causes an index-limited sequence to be infinite in extent due to the inherent band-limiting. Index-limited versions of discrete prolate spheroidal sequences (DPSS) are known to experience minimum leakage after band-limiting. In this work, we consider the effect of a half-sample shift and provide upper bounds on the resulting leakage energy for arbitrary sequences. Furthermore, we find an orthonormal basis derived from DPSS with members ordered according to energy concentration after half sample shifts; the primary (first) member being the global optimum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09371 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maximally Concentrated Sequences after Half-sample Shifts Said, Karim A. Liu, Lingjia A., A. Beex Signal Processing It is well known that index (discrete-time)-limited sampled sequences leak outside the support set when a band-limiting operation is applied. Similarly, a fractional shift causes an index-limited sequence to be infinite in extent due to the inherent band-limiting. Index-limited versions of discrete prolate spheroidal sequences (DPSS) are known to experience minimum leakage after band-limiting. In this work, we consider the effect of a half-sample shift and provide upper bounds on the resulting leakage energy for arbitrary sequences. Furthermore, we find an orthonormal basis derived from DPSS with members ordered according to energy concentration after half sample shifts; the primary (first) member being the global optimum. |
| title | Maximally Concentrated Sequences after Half-sample Shifts |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2401.09371 |