New interpolation tools for digital signal processing

Abstract

In order to perform digital signal processing it is necessary to reduce the effect of the noise on the signals. Some digital filters developed previously for signal interpolation are tested on different signals with noise. We study their effect and characteristics. The question about the right interpolation of a data set is not new, but it needs versatility and high speed in order to be correctly performed on-line, directly, in real time. Most of the main properties of the B-spline functions give us the opportunity to implement new and original algorithms for standard interpolation. Any ordinary function could be described by using B-spline classic functions with a dedicated set of coefficients. In case of the reconstruction for an interpolative signal, it is mandatory to compute all those specific coefficients. In this paper in order to perform cubic spline type interpolation, we show a classic algorithm and part of his advantages and known issues. Also, new opportunities for proper establishing some algorithms that could fix some of these issues are revealed. We will detail a new way to properly determine the initial coefficients by using the polynomial simple form on short measuring intervals for the spline-function itself and its derivatives. Based on these conclusions, some observations for future use and improvement of the algorithm, there are shown.