Approximation of discontinuous signals by sampling Kantorovich series
By Danilo Costarelli, Anna Maria Minotti, Gianluca Vinti. 2015
87 citations recorded by the source corpus.
In this paper, the behavior of the sampling Kantorovich operators has been studied, when discontinuous signals are considered in the above sampling series. Moreover, the rate of approximation for the family of the above operators is estimated, when uniformly continuous and bounded signals are considered. Further, also the problem of the linear prediction by sampling values from the past is analyzed. At the end, the role of duration-limited kernels in the previous approximation processes has been treated, and several examples have been provided.
Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/8ebd9fdb08cc52ad81fe91653c1d1197cb89a998
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Citations in the corpus
- Approximation Results in Orlicz Spaces for Sequences of Kantorovich Max-Product Neural Network Operators (2018, background): “…satisfying the above assumptions are, the logistic function σ ℓ ( x ) := (1 + e − x ) − 1 (see e.g., [27, 28, 25]), the sigmoidal function generated by the hyperbolic tangent σ h ( x ) := (tanh x +1) / 2 , x ∈ R , (see [37]) and the ramp function ([19]): and many others, see e.g., [25, 24, 26].”
- An Inverse Result of Approximation by Sampling Kantorovich Series (2018, background): “Moreover, for the reconstruction of signals in terms of splines using finite number of samples from the past, see [12, 18].”
- A characterization of the convergence in variation for the generalized sampling series (2017, unknown): “, [21, 22, 19]), and the corresponding averaged-kernel (see Figure 2, right) takes now the form”