In this presentation, the ill-posed problem of computation of the Fourier transform /hat{f} for a noisy bandlimited signal is discussed. Here, /hat{f} is computed by a regularized Fourier series which is obtained by a regularization of the Fourier transformed sampling formula of Shannon. If the regularization parameter tends to zero, the uniform and L2-convergence of this method is proved. Numerical examples show the performance of this approach. And the results are extended to the two-dimensional case. 

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