Relevant sampling of 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

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.

Band Limited Functions on Quantum Graphs

The notion of band limited functions is introduced on a quantum graph. The main results of the paper are a uniqueness theorem and a reconstruction algorithm of such functions from discrete sets of values. It turns out that some of our band limited functions can have compact supports and their frequencies can be localized on the “time” side. It opens an opportunity to consider signals of a varia...