Odd extension for fourier approximation of nonperiodic functions
Р. В. Голованов, N. N. Kalitkin, K. I. Lutskiy · Mathematical Models and Computer Simulations · 2013
Approximation of functions by Fourier series plays an important role in applied digital signal processing. The method of odd extension of a nonperiodic function, which increases smoothness compared to existing methods, is proposed. The method is shown to result in a considerable acceleration of convergence of the Fourier series for this function. The method is generalized to the function of two variables. For the two-dimensional Fourier approximation, the optimal technique of truncating the coefficient matrix is found. The advantage of the method is illustrated by test calculations.