Numerical Projection Method For Inverse Fourier Transform And Its Application

Numerical projection method of the Fourier transform inversion from data given on a finite interval is proposed. It is based on an expansion of the solution into a series of eigenfunctions of the Fourier transform. The number of terms of the expansion depends on the length of the data interval. Convergence of the solution of the method is proved. The projection method for the case of the sine Fourier transform and the set of the odd Hermite functions being its eigenfunctions are examined and applied to numerical Fourier filtering.