Computation of fourier transforms for noisy bandlimited signals

摘要

In this paper, the ill-posed problem of computation of the Fourier transform f? for a noisy bandlimited signal f is discussed. Here, 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 L~2- convergence of this method is proved. Numerical examples show the performance of this approach.