ABSTRACT
A large number of parametric estimators can be used for tackling spectral analysis of time signals. Long-time practice across interdisciplinary fields firmly established that the most adequate strategy for this purpose is the powerful methodology of rational approximations. The quantum-mechanical formalism of the Green functions implemented via the fast Pade transform can be used to spectrally analyze the time signals that are either generated theoretically as auto-correlation functions or measured experimentally as free induction decay curves. Regarding the general issue of prior information, minimal knowledge needed in advance could be the assumption that the time signal possesses a structure. One of the justifications for the statement is the proven equivalence of generic time signals with quantum-mechanical auto-correlation functions. Due to this fact, every data analysis based upon time signals is automatically within the realm of quantum mechanics. The quantification problem in magnetic resonance spectroscopy is the same as the harmonic inversion from quantum theory of resonances and spectroscopy.
