Nonequispaced fast Fourier transforms for bandlimited functions
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910912396394496 |
|---|---|
| author | Kircheis, Melanie Potts, Daniel |
| author_facet | Kircheis, Melanie Potts, Daniel |
| contents | In this paper we consider the problem of approximating function evaluations $f(\boldsymbol x_j)$ at given nonequispaced points $\boldsymbol x_j$, $j=1,\dots N$, of a bandlimited function from given values $\hat{f}(\boldsymbol k)$, $\boldsymbol k\in \mathcal I_{\boldsymbol M}$, of its Fourier transform. Note that if a trigonometric polynomial is given, it is already known that this problem can be solved by means of the nonequispaced fast Fourier transform (NFFT). In other words, we introduce a new NFFT-like procedure for bandlimited functions, which is based on regularized Shannon sampling formulas. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_07155 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonequispaced fast Fourier transforms for bandlimited functions Kircheis, Melanie Potts, Daniel Numerical Analysis 65Txx, 65T50, 94A20 In this paper we consider the problem of approximating function evaluations $f(\boldsymbol x_j)$ at given nonequispaced points $\boldsymbol x_j$, $j=1,\dots N$, of a bandlimited function from given values $\hat{f}(\boldsymbol k)$, $\boldsymbol k\in \mathcal I_{\boldsymbol M}$, of its Fourier transform. Note that if a trigonometric polynomial is given, it is already known that this problem can be solved by means of the nonequispaced fast Fourier transform (NFFT). In other words, we introduce a new NFFT-like procedure for bandlimited functions, which is based on regularized Shannon sampling formulas. |
| title | Nonequispaced fast Fourier transforms for bandlimited functions |
| topic | Numerical Analysis 65Txx, 65T50, 94A20 |
| url | https://arxiv.org/abs/2502.07155 |