A Smooth Interpolation Method for Nonuniform Samples Based on Sampling Functions Composed of Piecewise Polynomials

Abstract

Interpolation of nonuniform samples is required for various cases of signal processing. In such a case, we often use sampling functions to interpolate signals. We show one example of sampling functions to interpolate signals from nonuniform samples, inheriting the properties of the C-type Fluency sampling functions introduced by Toraichi et al. The proposed sampling function is locally supported and composed with piecewise polynomial functions of degree 2 as the C-type Fluency sampling function. In this paper, we extend the C-type Fluency sampling function and derive the nonuniform sampling function which has a favorable property such that it can interpolate flat signal from samples that are constant. By using this sampling function, we get smooth and small undulate signal from samples of arbitrary.