Improving Fourier Partial Sum Approximation for Discontinuous Functions Using a Weight Function

Beong In Yun
2017 Abstract and Applied Analysis  
We introduce a generalized sigmoidal transformation wm(r;x) on a given interval [a,b] with a threshold at x=r∈(a,b). Using wm(r;x), we develop a weighted averaging method in order to improve Fourier partial sum approximation for a function having a jump-discontinuity. The method is based on the decomposition of the target function into the left-hand and the right-hand part extensions. The resultant approximate function is composed of the Fourier partial sums of each part extension. The
more » ... nsion. The pointwise convergence of the presented method and its availability for resolving Gibbs phenomenon are proved. The efficiency of the method is shown by some numerical examples.
doi:10.1155/2017/1364914 fatcat:ahk5rmsnlbbnhgfzcqg63qx7aq