Two recursive algorithms for the Fourier series

Abstract

Numerical computation of Fourier series is an important problem of the numerical application theory. In this paper, we present two recursive algorithms for evaluation of the Fourier series,

$$f(x) = a_0 /2 + \sum\limits_{i = 1}^n {(a_i } cos ix + b_i sin ix),$$

, wherea _i andb _i are known complex constants andx is an evaluation point. Compared to some traditional algorithms, the new algorithms take only half of the arithmetic operations.