The System of Integer Shifts of The Gaussian Function and The Basis Splines

In this paper, we perform a comparative analysis of the interpolation properties of two systems of integer shifts that are important in digital signal processing: Gaussian functions and basic splines. It is established that the interpolation procedure with the help of basic splines becomes computationally unstable if their order exceeds the values. A similar effect is known for Gauss shifts, if the width parameter [7]. In this paper, we give this fact a theoretical justification by comparing basic splines of high orders with the Gaussian function. It is obtained that, starting from, these two functions differ little from each other. We have found simple analytic formulas that allow us to approximate basic splines by the Gaussian functio. Keywords: basis spline, Gauss function, interpolation, system of integer translates, moments.