Approximation error of the Whittaker cardinal series in terms of an averaged modulus of smoothness covering discontinuous signals

摘要: The Whittaker–Shannon–Kotel'nikov sampling theorem enables one to reconstruct signals f bandlimited [−πW,πW] from its sampled values f(k/W), k∈Z, in terms of (SWf)(t)≡∑k=−∞∞f(kW)sinc(Wt−k)=f(t)(t∈R). If is continuous but not bandlimited, normally considers limW→∞(SWf)(t) the supremum-norm, together with aliasing error estimates, expressed of modulus continuity or derivatives. Since practice are however often discontinuous, this paper concerned convergence SWf Lp(R)-norm for 1