Applications of the Fourier Transform In Chemical Instrumentation: A Computer Simulation With Mathcad

ABSTRACT: Chemical instrumentation based on FT is well known by experimental scientists and technicians; however, their mathematical principles are poorly understood. Unfortunately, the black-box design of many commercial instruments makes this double aim difficult to implement. Well designed computer simulations are one way of providing the background of this experience. Mathcad is one of the four most popular computational packages used in academic and industrial environments. Mathcad combines some of the best features from spreadsheets (like MS Excel) and symbolic math programs.. Mathcad contains functions for performing the discrete Fourier transform and its inverse. The function FFT returns the Fourier transform of a 2N element vector of real data representing measurements at regular intervals in the time domain. The function IFFT returns the inverse Fourier transform of a vector of real data representing values in the frequency domain. This paper describes two applications of the Fourier transform for data manipulation in chemical instrumentation by means of the Mathcad symbolic computational package, (version 2000 Professional for Windows on a PC-compatible). Both applications have similar aims, to improve the quality of spectroscopic or chromatographic signals It explores the advantages of the Fourier transform and digital filtering to smooth a noisy signal with a improvement of the signal-to-noise ratio of 45. The simulation of the convolution is carried out; the effect of the bandwidth of the filter function (slit of grating in spectrometry and dead volume in chromatography) and the effect of phase shift among the analytical signal and the filter signal are described. Deconvolution allows to recover the starting signal corresponding to a laser-excited fluorescence decay.