Odd extension for the Fourier approximation of nonperiodic functions

Approximation of functions by Fourier series plays an important role in applied digital signal processing. Proposed the method to odd continuation for nonperiodic function, which increases smoothness in comparison with existing methods. It is shown that the method leads to a substantial improvement of convergence of Fourier series for this function. The method extended to the function of two variables. For two-dimensional Fourier–approximation has been found the best way to truncating of the matrix of coefficients. The advantage of the new method is illustrated on test calculations.