Reduction of noise amplification in processing noise containing data using global approximation based on spline functions

Abstract

One of the main problems in the analysis of measured spectra is how to reduce the influence of noise in data processing. We show a deconvolution, a differentiation, and a Fourier transform algorithm that can be run on a small computer (64K random access memory) which suffers less from noise than commonly used routines. This objective is achieved by implementing spline based functions in mathematical operations to obtain global approximation properties in our routines. The convenient behavior and the pleasant mathematical character of splines makes it possible to perform these mathematical operations on large data input in a reasonable computing time on a small computer system. Some examples of the performance of a differentiation, deconvolution, and Fourier transform routine are shown.