Stability in unlimited sampling
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915891026853888 |
|---|---|
| author | Romero, José Luis Shafkulovska, Irina |
| author_facet | Romero, José Luis Shafkulovska, Irina |
| contents | Folded sampling replaces clipping in analog-to-digital converters by reducing samples modulo a threshold, thereby avoiding saturation artifacts. We study the reconstruction of bandlimited functions from folded samples and show that, for equispaced sampling patterns, the recovery problem is inherently unstable. We then prove that imposing any a priori energy bound restores stability, and that this regularization effect extends to non-uniform sampling geometries. Our analysis recasts folded-sampling stability as an infinite-dimensional lattice shortest-vector problem, which we resolve via harmonic-analytic tools (the spectral profile of Fourier concentration matrices) and, alternatively, via bounds for integer Tschebyschev polynomials. Our work brings context to recent results on injectivity and encoding guarantees for folded sampling and further supports the empirical success of folded sampling under natural energy constraints. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24425 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stability in unlimited sampling Romero, José Luis Shafkulovska, Irina Functional Analysis Information Theory 94A20, 94A15, 94A24, 42C15, 42A05 Folded sampling replaces clipping in analog-to-digital converters by reducing samples modulo a threshold, thereby avoiding saturation artifacts. We study the reconstruction of bandlimited functions from folded samples and show that, for equispaced sampling patterns, the recovery problem is inherently unstable. We then prove that imposing any a priori energy bound restores stability, and that this regularization effect extends to non-uniform sampling geometries. Our analysis recasts folded-sampling stability as an infinite-dimensional lattice shortest-vector problem, which we resolve via harmonic-analytic tools (the spectral profile of Fourier concentration matrices) and, alternatively, via bounds for integer Tschebyschev polynomials. Our work brings context to recent results on injectivity and encoding guarantees for folded sampling and further supports the empirical success of folded sampling under natural energy constraints. |
| title | Stability in unlimited sampling |
| topic | Functional Analysis Information Theory 94A20, 94A15, 94A24, 42C15, 42A05 |
| url | https://arxiv.org/abs/2603.24425 |