The computation of fourier transform via Gauss-regularized fourier series

In this paper, we construct a new regularized Fourier series, that is the Gauss-regularized Fourier series. Moreover, we find this regularized Fourier series can be used to compute the Fourier transforms of bandlimited signals. When the regularization parameter tends to zero, we prove that this regularized Fourier series is uniform and L2-convergence. Numerical results demonstrate the superiority of the new method over some previous methods.