ABSTRACT
This conclusion presents some closing remarks on the preceding chapters of the book. The shape spectrum of the fast Padé transform (FPT) is resolved better than in the fast Fourier transform (FFT) for the same signal length. Also, by using only half signal length, the FPT can achieve the same resolution as in the FFT which is computed with the full signal length. Crucially, the FPT is the most natural parametric method for solving the quantification problem. The Fourier integral of the Green operator is the evolution operator whose matrix element between any two Schrödinger states represents the auto-correlation function, or equivalently, the time signal. Hence, the data matrix or Hankel matrix from MRS and NMR is the quantum-mechanical evolution/relaxation matrix. No more information could be extracted from any studied system than what is provided by the corresponding quantum-mechanical wavefunction, or equivalently, the Green function.
