Average sampling theorem

The Sampling Theorem and the Bandpass Theorem

Sampling theorem for polynomial interpolation

The classic polynomial interpolation approach is used to derive a sampling theorem for the class of signals that are the response of systems described by differential equations with constant coefficients. In particular, the polynomial that interpolates the signal between the sampling points for increasing order will give increasing accuracy for stable one-sided sequences, if the sampling rate i...

3: the Shannon Sampling Theorem

In this final set of notes, we would like to end where we began. In the first set of notes, we mentioned that mathematics could be used to show how CDs and MP3s can reproduce our music well, even though the file sizes of MP3s are relatively small. In this set of notes, we attempt to describe how this is possible. Surprisingly, the exponential function will play a key role. We assume familiarity...

Boas' Formula and Sampling Theorem

In 1937, Boas gave a smart proof for an extension of the Bernstein theorem for trigonometric series. It is the purpose of the present note (i) to point out that a formula which Boas used in the proof is related with the Shannon sampling theorem; (ii) to present a generalized Parseval formula, which is suggested by the Boas’ formula; and (iii) to show that this provides a very smart derivation o...

Average sampling restoration of harmonizable processes

The harmonizable Piranashvili–type stochastic processes are approximated by finite time shifted average sampling sums. Explicit truncation error upper bounds are established. Various corollaries and special cases are discussed. Submitted: May 7, 2014 Address correspondence to Tibor Pogány, Faculty of Maritime Studies, University of Rijeka, Studentska 2, HR-51000 Rijeka, Croatia; E-mail: poganj@...