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

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 \(f\in L^r_p (\mathbb R)\), \(r\in\mathbb N\).


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)
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