Abstract As well-known, generalized sampling operators and sampling Kantorovich operators are able to approximate continuous signals and even Lᵖ L p -signals in the latter case. Anyway, in the situation of a signal affected by noise, these operators are not very efficient to approximate the original signal (i. e. , filtered by the noise) when the parameter goes to infinity. In order to solve this problem, we introduce a new type of operators, which we call the mean sampling Kantorovich operators. We study its approximation properties and made a comparison with the classical sampling Kantorovich operator in dealing with noisy signals.
Corso et al. (Tue,) studied this question.