• FOURIER APPROACH TO FUNCTION APPROXIMATION

Abstract

Function approximation is fundamental to many real world problems and Fourier method may be considered as one of the powerful technique for numerical approximation of functions .The inverse FT (IFT) is used to reconstruct the data from the coefficients known FT transforms of observed data. However, it is always difficult to predict the accuracy of any such approximation. We have used exponential, periodic and piece wise functions and the simulations assumes the functions as the output of a Gaussian function with infinite frequencies. The Fourier approximation has been strictly evaluated in statistical terms for its accuracy. The RMSE is found to be least (0.1601) for periodic function as compared to exponential (6.007) and piece wise function (2.70) and on evaluation of the approximation from 100 points to 200 points as expected the RMSE values show a marginal decrease However, acceptance of the results of exponential function approximation may depend on the stiffness and the desired accuracy. The results indicate that Fourier approach may viewed as a suitable method for approximating functions exponential, periodic and piece-wise.