Strikingly stable convergence of the Fast Padé Transform (FPT) for high-resolution parametric and non-parametric signal processing of Lorentzian and non-Lorentzian spectra

We investigate the prospect for designing a high-resolution parametric method for signal processing of both Lorentzian and non-Lorentzian spectra offering an accurate and robust performance with efficiency and stability comparable to the fast Fourier transform. It is demonstrated that the standard fast Padé transform is well suited for successfully accomplishing this multifaceted task as opposed to various fitting algorithms that all yield non-unique solutions to quantification problems. This is substantiated by computations on time signals encoded in the brain of healthy volunteers and patients using Magnetic Resonance Spectroscopy.