A Direct Interpolation Method for Irregular Sampling

Abstract

In this paper, band-limited functions are reconstructed from their values taken at a sequence of irregularly spaced sample points. We use a modified Lagrange formula, which is attributed to Boas and Bernstein. The formula used in this paper differs from the classical Boas-Bernstein formula in the following way. Instead of using infinite canonical products with respect to the whole sequence of sample points, we use canonical products with respect to sequences of sample points which are irregularly spaced only on finite intervals. Estimates for the truncation error of this reconstruction method are given.

Universal truncation error upper bounds in irregular sampling restoration†

“…where the convergence is uniform on bounded subsets of R d under additional suitable conditions upon f and T. We will discuss the conditions for multidimensional case later (see [8,10,15,25,26] for onedimensional case). In this framework the sampling restoration procedure becomes of Lagrange-Yen type [6,15,25,29].…”

“…To investigate (14) we take the following auxiliary result. Namely, let κ ∈ R + \ {1} and let a : R + → R + be a positive monotone increasing function.…”

Direct weighted Lagrange-Yen type interpolation in L/sup 2/([-/spl pi/,/spl pi/]/sup 2/)

“…, where .f will be measured, could deviate from the uniform spacing into (xm, gn) = ( m + h,,n + g n ) , where lhml 5 M , ISn\ 5 X . Compare the similar 1D approaches in (Yen, 1956), (Flornes, 1998), (Flornes et al, 2000) as ~vell, together wit.11 (Pogiiny, 1999), for additional informations about sampling of handlimit.ed homogeneous rmdom fields.…”

Time shifted aliasing error upper bounds for truncated sampling cardinal series

“…such that is time shifted [5,11,[14][15][16]. In fact the expression for |A N (t, ω)| coincides with T J (f ; t) = |f (t) − Y J (f ; t)|, but it differs from | n∈Z\J f ( n ω )sinc(ωt − n)|, where J := {n: |n − ωt| N}.…”