A note on error estimation for spline interpolation method with sampling bases

Abstract

The spline interpolation using the sampling bases has a feature of real‐time computation which is not observed in other methods since the result of interpolation is derived directly from the sampled value sequence. Then it is necessary that the sampling function should be truncated in a finite interval. This paper aims to clarify the relation in this method between the error in the result of interpolation due to the truncation and the length of the truncation interval. The result is summarizes in a correspondence table for the truncation interval length and the error. In the proposed interpolation method, the truncation interval length to ensure the given tolerable range of error can be determined using the correspondence table.

Precise interpolation for band‐limited digital signals based on sampling theorem incorporated with window functions

“…Further, a concept of the generating function [10] is introduced and an optimum interpolation function is systematically derived for various cases. In another approach, the interpolation function derived from the spline bases is used and the truncation error is reported [22,23]. The difference of the present paper from the above two examples is that the interpolation function is separated to the window function part and the impulse response part of an ideal LPF and the optimization of the window function part is emphasized in the present paper.…”

A practical least squares approximation based on biorthonormal expansions in the signal space of piecewise polynomials

“…The upper bound for amplitude of the sampling function in m S was derived in [10]. By referring the proposition in [10], one of the upper bounds of the sampling function is sunmierized in the following lemma..…”

“…By referring the proposition in [10], one of the upper bounds of the sampling function is sunmierized in the following lemma..…”

“…By Lemmas 1 and 2 in [10], and the Lemma 4, the above constants are evaluated. Table 1 shows the constants, 'U, mu.…”

“…Equation (9) means that -,V'o( t) is a even function and then has aa symmetric property with respect tot = 0. Let {W''_ _,, be sampling points, the sampling basis in mS is defined by the functions l(alV"k} k z satisfying (10) and then its biorthonorrr)al basis in "'S is derived as the functions "' sa.t;isf ing…”