Generalised sampling theorem for band-limited functions

Relevant Sampling of Band-limited Functions

We study the random sampling of band-limited functions of several variables. If a band-limited function with bandwidth has its essential support on a cube of volume R, then O(Rd logR) random samples suffice to approximate the function up to a given error with high probability.

Irregular sampling of band-limited functions on the sphere

Article history: Received 27 September 2013 Received in revised form 5 May 2014 Accepted 13 May 2014 Available online xxxx Communicated by W.R. Madych MSC: 65T99 42C10 33C55 65D15

Band-limited Functions: / / -convergence

Improved-resolution digital holography using the generalized sampling theorem for locally band-limited fields.

We describe the recording conditions that, together with the appropriate numerical reconstruction process, permit high-lateral-resolution reconstruction of in-line digital holograms. By high resolution, we mean a resolution that is beyond the Nyquist frequency, which is achieved by common methods. The proposed method is based on a previously reported generalized sampling theory that presents th...

Sampling for approximating $R$-limited functions

Abstract. R-limited functions are multivariate generalization of band-limited functions whose Fourier transforms are supported within a compact region R ⊂ Rn. In this work, we generalize sampling and interpolation theorems for band-limited functions to R-limited functions. More precisely, we investigated the following question: “For a function compactly supported within a region similar to R, d...