Deconvolution, differentiation and Fourier transformation algorithms for noise-containing data based on splines and global approximation

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 (64 K RAM) and suffer 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 behaviour and the pleasant mathematical character of splines makes it possible to perform these mathematical operations on large data input in a limited computing time on a small computer system. Comparison is made with widely used routines.