Improving Convergence for the Approximation of Non-Periodic Functions by Fourier Series

摘要

Approximation of functions by Fourier series plays an important role in many applied problems of digital signal processing. An effective method is presented for the construction of highly accurate mean-square approximations by Fourier series for nonperiodic functions. This technique employs the subtraction of specially selected functions that enhance the smoothness of the periodic extension of the approximated function. The main advantage of the method is that the function-setting interval is taken as a half-period rather than a whole period. This doubles the smoothness of the periodic extension. The efficiency of the method is illustrated by test functions of one and two variables.