分野別セミナー

Recovering a continuous function from discrete samples and assessing the information lost are the fundamental problems in sampling theory and signal processing. Whittaker-Kotel'nikov-Shannon (WKS) theorems allow the coding of a continuous band-limited signal by a sequence of its discrete samples without the loss of information. On the other hand sampling results are important not only because of signal processing applications. WKS theorems are equivalent to various fundamental results in mathematics.
I will discuss some classical results and new truncation error upper bounds in the WKS sampling theorem for bandlimited stochastic processes. Lp([0; T]) and uniform approximations of sub-Gaussian random processes will be presented. Some specifications of the general results for which the assumptions can be easily verified will be given. Direct analytical and probability methods were employed to obtain the results.


The presentation is based on the joint paper with Prof. Yu.Kozachenko:
Whittaker–Kotel'nikov–Shannon approximation of φ-sub-Gaussian random processes, will appear in the Journal of Mathematical Analysis and Applications.