The high smooth continuations for Fourier approximations of non-periodic functions

Approximation of functions by Fourier series plays an important role in many applied problems of digital signal processing. It is shown how it is expedient to construct the mean-square approximation of high accuracy Fourier series for nonperiodic functions. The method uses subtraction of specially selected features that enhance the smoothness of the periodic continuation of the approximated function. The main advantage of the method is that segment of the job function is taken as half of the period, and not for the whole period. This allows to do twice as better smoothness of periodic continuation. The effectiveness of the method is illustrated on the test functions of one or two variables.