Band-limited functions and the sampling theorem

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...

Average sampling of band-limited stochastic processes

We consider the problem of reconstructing a wide sense stationary band-limited process from its local averages taken either at the Nyquist rate or above. As a result, we obtain a sufficient condition under which average sampling expansions hold in mean square and for almost all sample functions. Truncation and aliasing errors of the expansion are also discussed.