Whittaker-Kotelnikov-Shannon sampling theorem and aliasing error. (English) Zbl 0845.94003

Fang, Gensun

J. Approximation Theory 85, No. 2, 115-131 (1996).

The authors generalize the Whittaker-Kotelnikov-Shannon sampling theorem from functions in \(B_{\sigma,2}\) to those of \(B_{\sigma, p}\), \(1< p< \infty\), in norm \(L_p (\mathbb R)\) (where \(B_{\sigma,p}\) is the set of all functions from \(L_p (\mathbb R)\) which can be continued to entire functions of exponential type \(\leq \sigma\)). Under additional conditions they describe the asymptotic behaviour of the aliasing error and determine an error bound if \(f\in L^r_p (\mathbb R)\), \(r\in\mathbb N\).

Reviewer: Ralph-Hardo Schulz (Berlin)

MSC:

94A20	Sampling theory in information and communication theory
94A12	Signal theory (characterization, reconstruction, filtering, etc.)
41A25	Rate of convergence, degree of approximation
41A58	Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)

Keywords:

Whittaker-Kotelnikov-Shannon sampling theorem; asymptotic behaviour; aliasing error; error bound