A New Robust Fourier Transform Algorithm Using Inversion Tools

This paper presents a new method for the calculation of the Fourier transformation. The idea of the new algorithm is based on the series expansion of the complex spectrum by scaled Hermite functions. The special feature of the basic Hermite functions that they are the eigen-functions of the Fourier transformation. This property also valid for the scaled Hermite functions. Using this property of the scaled Hermite functions a simple formula can be given for the calculation of the Jacobi’s matrix, without integration. Therefore the 1D Fourier transform can be calculated quickly and easily. The new procedure is numerically tested by using synthetic data in order to demonstrate the accuracy and noise rejection capability of the new (inversion-based) Fourier transform algorithm.