ABSTRACT
This chapter presents the total shape spectra, by giving the explicit numerical values of the reconstructed spectral parameters. In this respect, the most stringent criterion is the exact retrieval of the known complex frequencies and amplitudes. The chapter examines examine a synthesized noise-free free induction decay (FID) in order to reconstruct the input spectral parameters. A favorable result from the presently-designed testing on a typical synthesized FID will provide an impetus to apply the fast Pade transform (FPT) to distinguish genuine and spurious resonances in encoded time signals from magnetic resonance spectroscopy. The intensities at larger times quickly become immersed into the zero-valued background for this noiseless FID. Such a situation favors those signal processors, like the FPT, that are capable of reconstructing all the signal components by using the first, relatively short part of the FID with sizable intensities. The expansion coefficients in the Maclaurin development are the time signal points, that are equivalent to the quantum-mechanical auto-correlation functions.
