ABSTRACT
The fast Pade transforms (FPT) converges upon reaching constancy or stabilization of the whole set of the retrieved frequencies and amplitudes of all the physical resonances. Furthermore, such stabilization is a true signature of the reconstruction of the exact number of resonances. During reconstruction of the exact input data, the convergence stage itself is reached with an exponential convergence rate. This accomplishment establishes the FPT as a spectral analyzer which is capable of yielding an exponentially accurate approximation for time signals from magnetic resonance spectroscopy and other related fields. Both the stability of all the spectral parameters for every genuine resonance and the constancy of the estimate of the true number of resonances can be established by the concept of Froissart doublets or pole-zero cancellation. By its nature, noise represents spurious information which corrupts the genuine part of the signal. However, pole-zero cancellations could be used to discriminate between noise and the physical information in the investigated time signal.
