Linear Prediction by Samples from the Past

Reconstruction of signals inLp(ℝ)-space by generalized sampling series based on linear combinations ofB-splines†

“…Hence we obtain THEOREM 4.3 Let ϕ be a time-limited kernel and assume further that the vanishing moment condition (12) holds for some r ∈ N. Then for 1 ≤ p < ∞,…”

“…For the proof of (a), which is based on the Poisson summation formula, see, e.g., [6,13]; part (b) follows by mathematical induction with respect to s.…”

“…The approach to prediction theory in L p -space will, however, be treated in a separate paper; for earlier material in C(R)-space, see refs. [11][12][13]. The third, truly practical aim is to solve the present generalized sampling theory for signals which are not necessarily band-limited, in particular, time-limited, by employing specific rather simple kernels ϕ.…”

On Convergence Properties for a Class of Kantorovich Discrete Operators

“…Bardaro and I. Mantellini Finally, we apply these results to Kantorovich version of the generalized sampling operators introduced and widely studied by Butzer and his school (see, e.g., [9,10,20]), a modified version of Szász-Mirak'jan operator introduced in [4], and Baskakov operators.…”

Multivariate sampling Kantorovich operators: from the theory to the Digital Image Processing algorithm

“…[1,5,13]. The WKS sampling theorem provides an exact reconstruction formula for band limited, finite energy functions.…”