Twierdzenie o próbkowaniu z perspektywy przestrzeni Hilberta

Abstract

Sampling theorem is a fundamental theorem used for digital signal processing of analogue signals. Its classic derivation relies on Fourier series and Fourier transform, used as independent mathematical tools. By using Hilbert space, it is possible to present all these tools as special cases of representation of vector in the orthonormal basis. Such representation can be easily understood using an analogy with the projection of vector onto the Cartesian plane. His approach allows relatively easy understanding of sampling and reconstruction of signal, thanks to using a vector space, the idea known from linear algebra course. The aim of this paper is to present this approach in a tutorial style.