Feasibility study for applying the lower-order derivative fast Padé transform to measured time signals

Magnetic resonance spectroscopy (MRS), as a powerful and versatile diagnostic modality in physics, chemistry, medicine and other basic and applied sciences, depends critically upon reliable signal processing. It provides time signals by encoding, but cannot quantify on its own. Mathematical methods do so. The signal processor of choice for MRS is the fast Padé transform (FPT). The spectrum in the FPT is the unique polynomial quotient for the given Maclaurin expansion. The parametric FPT (parameter estimator) performs quantification of time signals encoded with MRS by explicitly solving the spectral analysis problem. Thus far, the non-parametric FPT (shape estimator) could not quantify. However, the non-parametric derivative fast Padé transform (dFPT) can quantify despite performing shape estimation alone. The dFPT was successfully benchmarked on synthesized MRS time signals for derivative orders ranging from 1 to 50. It simultaneously improved resolution (by splitting apart tightly overlapped peaks) and enhanced signal-to-noise ratio (by suppressing the background baseline). The same advantageous features of improving both resolution and signal-to-noise ratio are presently found to be upheld with encoded MRS time signals. Moreover, it is demonstrated that the dFPT hugely outperforms the derivative fast Fourier transform even for derivatives of orders as low as four. The clinical implications are discussed.