Fourier transformation as inverse problem — An improved algorithm

• DOI: 10.1556/ageod.47.2012.2.7
• Publication Date: 2012-04-28T02:37:22Z
• Authors: M. Dobróka; H. Szegedi; P. Vass; E. Turai
• Keywords: Basis function; Eigenfunction

This paper presents a new algorithm for the inversion-based 1D Fourier transformation. The continuous spectra are assumed as series expansion with scaled Hermite functions square-integrable set of basis functions. coefficients determined by solving an over-determined inverse problem. In order to define quick and easy-to-use formula in calculating Jacobi matrix problem special feature used. It is well-known, that basic eigenfunctions generalized extending its validity Using eigenvalues, given this generalization, very simple can be derived resulting more accurate transform algorithm. procedure numerically tested using synthetic data.